Reduction of Residual Electrostatic Forces in Casimir Force Measurements by In Situ Ar Ion Bombardment
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Studies of the Casimir force have undergone rapid progress, due to its importance in fundamental physics as well as nanotechnology. The archetypal Casimir force originates from modifications of the quantum zero point photon spectrum due to the presence of two perfectly conducting ideal metal plates, whose separation sets the allowed modes. Alternatively, the Casimir force can be described as the retarded interaction of charge and current fluctuations induced by photons. In going from ideal metal plates to normal metal plates, early theoretical approaches neglected the imaginary terms in the permittivity. However the use of the complete properties of real material boundaries which include finite dissipation for zero point photons scattering from free electrons have now been realized to lead to both puzzling theoretical and experimental inconsistencies. The precision of the experiments have steadily improved challenging our understanding of zero point photon scattering from real materials. Primarily, experiments for distances below 1 micron have consistently shown that inclusion of material losses are not in agreement. Experiments largely above 1micron report agreement with theory including material losses. A key difference in the room temperature Casimir force at the different length scales is the role of thermal photons which play an increasing role at larger separations. This disagreement raises a fundamental question on the nature of zero point photon scattering from real materials as compared to that of thermal photons.
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Various factors such as the use of approximations and the role of roughness have been ruled out as the cause of the disagreement. Residual electrostatic forces due to patch potentials have been suggested as another possibility to explain the discrepancy. Precision experiments of the Casimir force have required that the residual potential between the two surfaces V_0 be independent of separation to confirm the negligible role of large surface adsorbates. Surface adsorbates are commonly removed in situ by use of ions directed at the surface. In this review period we proposed and demonstrated the use of an Ar+ ion gun to in situ clean the interacting Au surfaces and reduce the residual electrostatic force. Surfaces with a large residual potential are chosen for demonstration purposes.
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Results: We use a custom built atomic force microscope based setup to measure the Casimir force between an Au coated sphere and plate. The Au sphere is attached to a Si microcantilever. The resonance frequency shift of this cantilever is measured using an optical interferometer and corresponds to the gradient of the sphere plate force. The measurements were performed at high vacuum (3x10^-8 torr). The adsorbates on the surface were removed using the Ar+ ion gun. In the ion gun, energetic Ar+ ions are created using electron impact. The source has an ionization chamber that contains two filaments where the electron impact is produced. In order to reduce the effect of impurities from the filament heating, the filament is off-axis from the ionization chamber. There is no direct line of sight from the hot filament to the target. The filament current was held at approximately 2 amps. A focusing lens is utilized in order to increase the concentration of ions. The electrons are then extracted and accelerated. The chamber was backfilled with argon gas to a pressure of 5x10^−5 torr. The beam voltage was set for 500 V and the beam was run for a total of one hour. The removal of the adsorbates will reduce the large islands of work function difference. The mechanism of the ion gun cleaning is purely kinetic. Low beam voltage was chosen in ...","publicAccessMandate":"0","publicationResearch":["Physical Review B~2014~89~A.A. Banishev, J. Wagner, T. Emig, R. Zandi, U. Mohideen~10.1103/PhysRevB.89.235436~235436~,? Experimental and theoretical investigation of the angular dependence of the Casimir force between sinusoidally corrugated surfaces~","International Journal of Modern Physics A~2012~27~Banishev AA, Chang C-C, Castillo-Garza R, Klimchitskaya GL, Mostepanenko VM, and Mohideen U.~1260001.~Observation of reduction in Casimir force without change in dielectric permittivity.~2015-12-30 16:00:53.663","International Journal of Modern Physics A~2012~27~Banishev AA, Chang C-C, Castillo-Garza R, Klimchitskaya GL, Mostepanenko VM, and Mohideen U. 2012,27:1260001~10.1142/S0217751X12600019~1260001~Observation of reduction in Casimir force without change in dielectric permittivity~","Physical Review B~2012~85~Banishev AA, Chang C-C, Klimchitskaya GL, Mostepanenko VM, and Mohideen U.~10.1103/PhysRevB.85.195422~195422~Measurement of the gradient of the Casimir force between a nonmagnetic gold sphere and a magnetic nickel plate.~","Physical Review B~2012~85~Banishev AA, Chang C-C, Klimchitskaya GL, Mostepanenko VM, and Mohideen U.~195422.~Measurement of the gradient of the Casimir force between a nonmagnetic gold sphere and a magnetic nickel plate.~2015-12-30 16:00:53.66","International Journal of Modern Physics A~2011~26~Banishev A. A.; Chang Chia-Cheng; Mohideen U~3900~Critical steps in data analysis for precision Casimir force measurements with seminconducting films~N~","Physical Review B~2014~89~Banishev A.A, J. Wagner, T. Emig, R. Zandi, U. Mohideen,~235436~Experimental and theoretical investigation of the angular dependence of the Casimir force between sinusoidally corrugated surfaces,~2015-12-30 16:00:53.703","Physical Review B~2012~85~Banishev A., Chang C.-C, Klimchitskaya G.L., Mostepanenko V.M., Mohideen U.~045436~Modifying the Casimir force between Indium Tin Oxide Films and Au Sphere~N~","Applied Physics Letters~2012~100~Banishev A., Chang C.-C, Zandi R., Mohideen U.~033112~Modulation and Cancellation of the Casimir force by using Radiation Pressure~N~","Physical review letters~2013~110~Banishev A, Klimchitskaya G, Mostepanenko V, Mohideen U.~10.1103/PhysRevLett.110.137401~137401~Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate~","Physical Review Letters~2013~110~Banishev A, Klimchitskaya G, Mostepanenko V, Mohideen U.~137401.~Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate.~2015-12-30 16:00:53.683","Physical Review Letters~2013~110~Banishev A, Wagner J, Emig T, Zandi R, Mohideen U.~10.1103/PhysRevLett.110.250403~250403~Demonstration of Angle-Dependent Casimir Force between Corrugations~","Physical Review Letters~2013~110~Banishev A, Wagner J, Emig T, Zandi R, Mohideen U.~250403.~Demonstration of Angle-Dependent Casimir Force between Corrugations.~2015-12-30 16:00:53.7","Physical Review B~2011~Bezerra, V.B., Klimchitskaya, G.L., Mohideen, U., Mostepanenko, V.M., and Romero, C.~075417~Impact of surface imperfections on the Casimir force for lenses of centimeter-size curvature radii~N~","Review of Scientific Instruments~2013~84~Castillo-Garza R, Mohideen U.~10.1063/1.4790195~025110~Variable-temperature device for precision Casimir-force-gradient measurement~","Review of Scientific Instruments~2013~84~Castillo-Garza R, Mohideen U.~025110~Variable-temperature device for precision Casimir-force-gradient measurement.~2015-12-30 16:00:53.686","Physical Review B~2013~88~Castillo-Garza R, Xu J, Klimchitskaya G, Mostepanenko V, Mohideen U.~10.1103/PhysRevB.88.075402~075402~Casimir interaction at liquid nitrogen temperature: Comparison between experiment and theory~","Physical Review B~2013~88~Castillo-Garza R, Xu J, Klimchitskaya G, Mostepanenko V, Mohideen U.~075402.~Casimir interaction at liquid nitrogen temperature: Comparison between experiment and theory.~2015-12-30 16:00:53.693","Physical Review B~2012~85~Chang C-C, Banishev AA, Castillo-Garza R, Klimchitskaya GL, Mostepanenko VM, and Mohideen U.~165443.~Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using an atomic force microscope in a frequency-shift technique.~2015-12-30 16:00:53.68","Physical Review Letters~2011~107~Chang C. -C.; Banishev A. A.; Klimchitskaya G. L.; V.M. Mostepanenko, U. Mohideen~090403~Reduction of the Casimir Force from Indium Tin Oxide Film by UV Treatment~N~","Physical Review B~2010~81~Chiu HC, Klimchitskaya GL, Marachevsky VN, Mostepanenko VM, Mohideen U.~115417.~Lateral Casimir force between sinusoidally corrugated surfaces: Asymmetric profiles, deviations from the proximity force approximation, and comparison with exact theory.~2015-12-30 16:00:53.623","International Journal of Modern Physics A~2010~25~Chiu HC, Mohideen U.~22~Experimental features of the recent lateral Casimir force measurement.~2015-12-30 16:00:53.656","INTERNATIONAL JOURNAL OF MODERN PHYSICS A~2010~25~Chiu, HC, Mohideen, U~2240~EXPERIMENTAL FEATURES OF THE RECENT LATERAL CASIMIR FORCE MEASUREMENT~N~","International Journal of Modern Physics A~2011~26~Decca R. S.; Fischbach E.; Klimchitskaya G. L.; Mohideen U., Mostempanenko V.M.~3930~Capacitance measurements and electrostatic calibrations in experiments measuring the Casimir force~N~","Physical Review D~2013~87~Klimchitskaya GL, Mohideen U, Mostepanenko VM.~10.1103/PhysRevD.87.125031~125031~Constraints on corrections to Newtonian gravity from two recent measurements of the Casimir interaction between metallic surfaces~","Physical Review D~2013~87~Klimchitskaya GL, Mohideen U, Mostepanenko VM.~125031.~Constraints on corrections to Newtonian gravity from two recent measurements of the Casimir interaction between metallic surfaces.~2015-12-30 16:00:53.696","Physical Review D~2012~86~Klimchitskaya GL, Mohideen U, Mostepanenko VM.~10.1103/PhysRevD.86.065025~065025~Constraints on non-Newtonian gravity and light elementary particles from measurements of the Casimir force by means of a dynamic atomic force microscope~","Physical Review D~2012~86~Klimchitskaya GL, Mohideen U, Mostepanenko VM.~065025.~Constraints on non-Newtonian gravity and light elementary particles from measurements of the Casimir force by means of a dynamic atomic force microscope.~2015-12-30 16:00:53.673","INTERNATIONAL JOURNAL OF MODERN PHYSICS B~2011~25~Klimchitskaya, GL, Mohideen, U, Motstepanenko, VM.~171~Control of the Casimir force using semiconductor test bodies~N~","Physical Review Letters~2011~107~Lin Hsiang-Ku; Zandi Roya; Mohideen Umar; and Leonid Pryadko~228104~Fluctuation-Induced Forces Between Inclusions in a Fluid Membrane Under Tension~N~","Physical Review B~2012~86~Noruzifar E, Emig T, Mohideen U, Zandi R.~10.1103/PhysRevB.86.115449~115449~Collective charge fluctuations and Casimir interactions for quasi-one-dimensional metals~","Physical Review B~2012~86~Noruzifar E, Emig T, Mohideen U, Zandi R.~115449.~Collective charge fluctuations and Casimir interactions for quasi-one-dimensional metals.~2015-12-30 16:00:53.67","Physical Review B~2010~Zandi, R. Emig, T. Mohideen, U.~195423~Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models~N~"],"startDate":"08/01/2010","title":"Probing the Coherent Scattering of Zero-point Photons in the Casimir Force using Diffraction Gratings","transType":"Continuing Grant","ueiNumber":"MR5QC5FCAVH5"},{"abstractText":"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). This award provides support to Washington University in St. Louis in their effort to build an extremely sensitive and versatile torsion balance. The instrument will probe possible deviations from the inverse square law of Newtonian gravity at sub-millimeter distances, and study Casimir forces, which are macroscopic manifestations of quantum fluctuations of the electromagnetic vacuum. The torsion balance that will be built is comprised of a gold-coated aluminum disk, suspended by its edge with a fine torsion fiber, inside a high vacuum chamber. The suspended disk is viewed by an auto collimating optical lever of sub-nanoradian resolution. A large circular sheet of gold acts as a source of the force fields under study. This plate will be mounted in close proximity to the disk, with its face nearly parallel to it. It will be moved to and fro, and also in a yaw-like oscillation through a small angle, while the response of the suspended disk is being continuously recorded by the optical lever. The frequency, amplitude and phase of the angular oscillations of the suspended disk carry information about any deviations from Newtonian gravity and the Casimir force at sub-millimeter length scales.\r\n\r\nThese experiments will probe the finite temperature corrections to the Casimir force and any deviations from the inverse square law of gravity, such as those predicted by new theories of particle physics, including those that postulate extra spatial dimensions. These new theories attempt to unify gravitation with electromagnetic, nuclear and the weak forces, and suggest the existence of hitherto undiscovered particles that can act as dark matter dominating the formation and the dynamics of galaxies. The Casimir force is a macroscopic manifestation of the quantum vacuum that could be related to the dark energy responsible for the accelerated expansion of the universe. Thus, any confirmed deviations from the inverse square law will have a large impact on knowledge of fundamental physics, astrophysics and cosmology. The experimental effort and the instrumentation are highly interdisciplinary, involving vacuum technology, optics, mechanical engineering, signal analysis, and of course, physics. This project provides an excellent training ground for post-doctoral scholars, graduate and undergraduate students. In addition, undergraduate students from technical colleges will be included in this project as a part of the outreach effort at Washington University.\r\n","activeAwd":"false","agency":"NSF","arraAmount":"502191","awardAgencyCode":"4900","awardee":"WASHINGTON UNIVERSITY, THE","awardeeAddress":"1 BROOKINGS DR","awardeeCity":"SAINT LOUIS","awardeeCountryCode":"US","awardeeDistrict":"01","awardeeDistrictCode":"MO01","awardeeName":"Washington University","awardeePhone":"3147474134","awardeeStateCode":"MO","awardeeZipCode":"631304862","cfdaNumber":"47.049","date":"08/31/2009","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"502191","expDate":"08/31/2013","fundAgencyCode":"4900","fundProgramName":"Gravity Exp. & Data Analysis","fundsObligated":["FY 2009 = $502,191.00"],"fundsObligatedAmt":"502191","histAwd":"false","id":"0855646","initAmendmentDate":"08/31/2009","jrnl":[{"artPageNum":"052516","artTitl":"General approach to Casimir force problems based on local reflection amplitudes and Huygensâ?? principle","auth":"C. 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D. Markle and R. Cowsik~10.1103/PhysRevA.85.052516~052516~General approach to Casimir force problems based on local reflection amplitudes and Huygensâ?? principle~N~","Phys. Rev. A~2012~85~C. D. Markle and R. Cowsik~052516~General approach to Casimir force problems based on local reflection amplitudes and Huygens?s principle~"],"startDate":"09/01/2009","title":"Experimental Investigation of Forces in the Submillimeter Range","transType":"Standard Grant","ueiNumber":"L6NFUM28LQM5"},{"abstractText":"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). This project will involve theoretical studies of several topics relating to quantum fluctuations and gravitation. Particular attention will be paid to issues relating to the correlation and anti-correlation of fluctuations of the quantum stress tensor that describes, among other things, the local energy density in a quantum field. The topics to be investigated include the effects of quantum stress tensor fluctuation in cosmology, especially in inflationary models. Previous work by the PI and his collaborators has indicated that these effects may be able to slowly accumulate, and thereby have a potentially significant role in the evolution of the universe. This possibility will be further studied. A closely related topic is the search for the probability distribution for stress tensor fluctuations, which is of interest in inflationary models, including ones which explore the possibility of a \"multiverse\" much larger than the observable universe. Other aspects of this project will seek to propose new laboratory experiments looking for negative energy density and related \"sub-vacuum\" phenomena, where some quantity fluctuates below its usual value in empty space. The project will examine selected aspects of the Casimir force, especially its fluctuations, and of fluctuations in condensed matter systems. These topics are of interest both for their own sake, and as analog models to better understand quantum effects in gravity theory. \r\n\r\nThis project is expected to have a broader impact through possible benefits to other fields of science, to education, and to technology. The insights and techniques of this work may be useful outside of the specific subfields of physics being investigated. The project will further education through the training of graduate students and by the involvement of faculty at primarily teaching institutions. It should also produce examples which can be used to explain some of the concepts of quantum theory and relativity to students on a variety of educational levels. The work on Casimir forces may eventually be useful in nanotechnology. A better knowledge of Casimir forces is likely to become important for the construction of small scale devices. Similarly, the study of quantum correlations in this project may have applications to quantum information and quantum computing.","activeAwd":"false","agency":"NSF","arraAmount":"240000","awardAgencyCode":"4900","awardee":"TRUSTEES OF TUFTS COLLEGE","awardeeAddress":"80 GEORGE ST","awardeeCity":"MEDFORD","awardeeCountryCode":"US","awardeeDistrict":"05","awardeeDistrictCode":"MA05","awardeeName":"Tufts University","awardeePhone":"6176273696","awardeeStateCode":"MA","awardeeZipCode":"021555519","cfdaNumber":"47.049","date":"08/08/2009","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"240000","expDate":"07/31/2012","fundAgencyCode":"4900","fundProgramName":"Gravity Theory","fundsObligated":["FY 2009 = $240,000.00"],"fundsObligatedAmt":"240000","histAwd":"false","id":"0855360","initAmendmentDate":"08/08/2009","jrnl":[{"artPageNum":"125038","artTitl":"Probability distributions for quantum stress tensors in four dimensions","auth":"Christopher J. Fewster, L. H. Ford, Thomas A. 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A","jrnlVol":"84","jrnlYr":"2011"}],"latestAmendmentDate":"08/08/2009","managingPec":"124400","orgCodeDir":"03000000","orgCodeDiv":"03010000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Physics","orgUrl":"http://www.nsf.gov/div/index.jsp?div=phy","parentUeiNumber":"WL9FLBRVPJJ7","pdPIName":"Lawrence H Ford","perfAddress":"80 GEORGE ST","perfCity":"MEDFORD","perfCountryCode":"US","perfDistrict":"05","perfDistrictCode":"MA05","perfLocation":"Tufts University","perfStateCode":"MA","perfZipCode":"021555519","pi":["Lawrence H Ford ford@cosmos.phy.tufts.edu"],"piEmail":"ford@cosmos.phy.tufts.edu","piFirstName":"Lawrence","piId":"000110613","piLastName":"Ford","piMiddeInitial":"H","poEmail":"pmarrone@nsf.gov","poName":"Pedro Marronetti","poPhone":"7032927372","primaryProgram":["01R00910DB RRA RECOVERY ACT"],"progEleCode":"124400","program":"UNASSIGNED, RECOVERY ACT ACTION, PHYSICS OF THE UNIVERSE, OTHER RESEARCH OR EDUCATION","progRefCode":"0000, 6890, 7483, OTHR","publicAccessMandate":"0","publicationResearch":["Phys. Rev. D~2012~85~Christopher J. Fewster, L. H. Ford, Thomas A. Roman~10.1103/PhysRevD.85.125038~125038~Probability distributions for quantum stress tensors in four dimensions~N~","Phys. Rev. D~2010~81~Christopher J. Fewster, L. H. Ford, Thomas A. Roman~121901(R)~Probability distributions of smeared quantum stress tensors~N~","Phys. Rev. D~2011~84~Chun-Hsien Wu, Jen-Tsung Hsiang, L. H. Ford, Kin-Wang Ng~10.1103/PhysRevD.84.103515~103515~Gravity Waves from Quantum Stress Tensor Fluctuations in Inflation~N~","PHYSICAL REVIEW D~2010~82~Ford, LH; Miao, SP; Ng, KW; Woodard, RP; Wu, CH~10.1103/PhysRevD.82.04350~http://wok-ws.isiknowledge.com/WoS?recid=190850711#000280612100001~Quantum stress tensor fluctuations of a conformal field and inflationary cosmology~Y~","Phys. Rev. D~2009~80~Hongwei Yu, N.F. Svaiter, L.H. Ford~124019~Quantum Lightcone Fluctuations in Compactified Spacetimes~N~","Phys. Lett. A~2011~375~Jen-Tsung Hsiang, Chun-Hsien Wu, L. H. Ford~2296~Negative Power Spectra in Quantum Field Theory~N~","Phys. Lett. A~2011~375~Jen-Tsung Hsiang, Chun-Hsien Wu, L. H. Ford~2296~Negative Power Spectra in Quantum Field Theory~N~","J. Phys. Conf. Series~2011~330~Jen-Tsung Hsiang, Chun-Hsien Wu, L.H. Ford, Kin-Wang Ng~012006~Quantum Stress Tensor Fluctuation Effects in Inflationary Cosmology~N~","Phys. Rev. D~2011~83~Jen-Tsung Hsiang, L. H. Ford, Da-Shin Lee, Hoi-Lai Yu~084027~Quantum Modifications to Gravity Waves in de Sitter Spacetime~N~","Phys. Rev. D~2011~83~Jen-Tsung Hsiang, L. H. Ford, Da-Shin Lee, Hoi-Lai Yu~084027~Quantum Modifications to Gravity Waves in de Sitter Spacetime~N~","Int. J. Mod. Phys. A~2010~25~L.H. Ford~2355~Negative Energy Densities in Quantum Field Theory~N~","Phys. Rev. D~2009~80~L.H. Ford, N.F. Svaiter~065034~A Fluid Analog Model for Boundary Effects in Field Theory~N~","Phys. Rev. D~2009~80~L.H. Ford, N.F. Svaiter~065034~A Fluid Analog Model for Boundary Effects in Field Theory~N~","Annals of Physics~2011~326~L. H. Ford, Thomas A. Roman~2294~Effects of Vacuum Fluctuation Suppression on Atomic Decay Rates~N~","Phys. Rev. A~2011~84~Victor Parkinson, L.H. Ford~062102~A Model for Non-Cancellation of Quantum Electric Field Fluctuations~N~"],"startDate":"08/15/2009","title":"Research on Gravitation and Quantum Fluctuation Phenomena","transType":"Standard Grant","ueiNumber":"WL9FLBRVPJJ7"},{"abstractText":"\"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).\"\r\n\r\nField theories provide our best known description of the fundamental interactions of Nature. In many situations, one can make significant progress by considering the theory. Perturbatively, starting from a collection of waves propagating independently.\r\nThis research project will address two situations in which this perturbative approach fails in a fundamental way. The first situation arises when one considers the possibility of waves forming coherent lumps that do not disperse. While static objects of this kind have been well studied, much less is known about solutions that undergo regular oscillations, called oscillons or breathers. Such objects are especially of interest in the early universe, when the large energies needed to form them are available. This project will investigate the existence of oscillons in particle physics models, the rate at which they would have formed in the early universe, and the potential role they could play in generating the out-of-equilibrium conditions necessary for baryogenesis, the process by which ordinary matter formed in the early universe.\r\nThe second situation arises when one considers quantum mechanical effects that cannot be approximated by weak coupling. This project will focus on Casimir forces induced by quantum electromagnetic fluctuations in conductors or strong dielectrics, and their analogs in related theories. In such situations the Casimir force depends on coherent properties of the geometry and orientation of the objects, and differs qualitatively from the result one would obtain perturbatively. Recently developed techniques have made it possible to calculate Casimir forces for a broad set of new geometries and materials. These techniques will be used to study shape, orientation, and material dependence of Casimir forces and to formulate and attempt to prove universal theorems governing their behavior. Similar techniques will also be used to study Casimir energies of electroweak string solutions in the Standard Model of particle physics. The broader impacts are as follows: The techniques and results of this research are potentially applicable to a wide range of other branches of physics, applied physics, and nonlinear dynamics, as are the computational tools to be developed during the course of this work. The source code for these tools will be made publicly available for use by other researchers. This research program will also significantly impact the teaching of physics at Middlebury College, both through the undergraduates directly involved and through enhancements to the curriculum that will grow out of this work. Students participating in any of these aspects will have the opportunity to develop new skills in computational physics and nonlinear dynamics, and to use these skills to better understand fundamental concepts in physics.","activeAwd":"false","agency":"NSF","arraAmount":"120000","awardAgencyCode":"4900","awardee":"PRESIDENT AND FELLOWS OF MIDDLEBURY COLLEGE","awardeeAddress":"9 OLD CHAPEL RD","awardeeCity":"MIDDLEBURY","awardeeCountryCode":"US","awardeeDistrict":"00","awardeeDistrictCode":"VT00","awardeeName":"Middlebury College","awardeePhone":"8024435000","awardeeStateCode":"VT","awardeeZipCode":"05753","cfdaNumber":"47.049","date":"06/14/2009","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"120000","expDate":"06/30/2013","fundAgencyCode":"4900","fundProgramName":"Elem. 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Fluctuations, whether of quantum, thermal, or non-equilibrium origin, are an inherent part of physical matter. Constraining these fluctuations by boundaries, geometry or topology, leads to a myriad of interactions, patterns and phases. This proposal aims at quantifying such phenomena in several contexts.\r\nSpecific questions that will be addressed by the research include:\r\n(i) The forces between neutral objects are due to constrained electromagnetic fluctuations. How do these forces depend on the shapes and orientations of these objects? Can one hold an object in stable equilibrium using only such forces?\r\n(ii) How does the confinement of critical thermal fluctuations of the order parameter lead to the thinning of helium films at the onset of superfluidity?\r\n(iii) What is the role of rigidity in the melting of double-stranded polymers such as DNA? How do fluctuations soften the elasticity of polymers and sheets? \r\n(iv) What governs the distribution of escape times, from a confining interval, in a process that is slower than diffusion? Is there a common description for such processes? \r\n(iv) How can we classify and catalog entangled proteins?\r\n\r\nFluctuating systems are characterized by probability distribution functions. Statistical physics provides the relative weights of different configurations in equilibrium, and the time evolution of weights away from equilibrium. The methods of statistical field theory are appropriate for handling quantum fluctuations of the electromagnetic field. The Casimir force between different materials and its dependence of geometry can be obtained by constraining the fluctuations on the bodies. Transfer matrix and renormalization group methods will be used to address questions involving semi-flexible polymers. Anomalous dynamics will be studied by a combination of scaling theory, and Monte Carlo and Molecular Dynamics simulations.\r\n\r\nEducation is an important component of this award. This research project is interdisciplinary; methods from statistical physics will be applied to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web will have impact on broader scientific community. The PI will also be an organizer of a workshop at the Kavli Institute for Theoretical Physics on the subject of fluctuation?induced forces.\r\n\r\n\r\nNONTECHNICAL SUMMARY:\r\n\r\nThis award supports theoretical research and education on the materials and physical consequences of fundamental principles of statistical physics. The research encompasses a wide range of physical systems and phenomena that are connected through the unifying question of how confinement modifies behavior and properties. The effects of confinement are an inherent part of physical systems and the effects of boundaries and geometry lead to a myriad of interactions, patterns and phases. This research quantifies such phenomena in several contexts. Varied research questions are addressed.\r\n\r\n(i) Theoretical predictions concerning the forces between neutral objects, due to mere proximity, known as Casimir forces, are decades old, but have only recently been measured and even more recently been the subject of experiments to investigate their application in devices. This research moves from what is known for simple planar geometries to investigating how these forces depend on the shapes and orientations of the objects. Unanswered fundamental questions are taken up, such as can one hold an object in stable arrangement using only such forces?\r\n(ii) This thrust focuses on how the confinement of helium films alters their behavior from simple fluids to exhibit a variety of unusual fluid properties. Films of the element helium are essentially two dimensional liquids that exist at very low temperatures and exhibit behavior governed by quantum mechanics.\r\n(iii) A related topic is the role of confinement induced in molecules by crowding and interacting with other members of bulk collection. This aspect of the research studies the softening and elasticity of polymers and flexible sheets. In this case, confinement arises through the entanglement of long molecules.\r\n\r\nEducation is an important component of this award. This research project is interdisciplinary; methods from statistical physics will be applied to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web will have impact on broader scientific community. The PI will also be an organizer of a workshop for the broader theoretical physics community at the Kavli Institute for Theoretical Physics.\r\n\r\n\r\n","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"MASSACHUSETTS INSTITUTE OF TECHNOLOGY","awardeeAddress":"77 MASSACHUSETTS AVE","awardeeCity":"CAMBRIDGE","awardeeCountryCode":"US","awardeeDistrict":"07","awardeeDistrictCode":"MA07","awardeeName":"Massachusetts Institute of Technology","awardeePhone":"6172531000","awardeeStateCode":"MA","awardeeZipCode":"021394301","cfdaNumber":"47.049","date":"09/11/2008","dirAbbr":"MPS","divAbbr":"DMR","estimatedTotalAmt":"390000","expDate":"08/31/2012","fundAgencyCode":"4900","fundProgramName":"CONDENSED MATTER & MAT THEORY","fundsObligated":["FY 2008 = $130,000.00","FY 2009 = $130,000.00","FY 2010 = $130,000.00"],"fundsObligatedAmt":"390000","histAwd":"false","id":"0803315","initAmendmentDate":"09/11/2008","jrnl":[{"artTitl":"First-passage distributions in a collective model of anomalous diffusion with tunable exponent","auth":"Amitai, A; Kantor, Y; Kardar, M","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevE.81.01110","jrnlTitl":"PHYSICAL REVIEW E","jrnlVol":"81","jrnlYr":"2010","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=186360124#000274003300013"},{"artTitl":"Only signaling modules that discriminate sharply between stimulatory and nonstimulatory inputs require basal signaling for fast cellular responses","auth":"Artomov, M; Kardar, M; Chakraborty, AK","authIndCode":"Y","dgtlObjId":"10.1063/1.348281","jrnlTitl":"JOURNAL OF CHEMICAL PHYSICS","jrnlVol":"133","jrnlYr":"2010","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=192114885#000282475400039"},{"artPageNum":"18958","artTitl":"Purely stochastic binary decisions in cell signaling models without underlying deterministic bistabilities","auth":"Artyomov, MN; Das, J; Kardar, M; Chakraborty, AK","authIndCode":"Y","dgtlObjId":"10.1073/pnas.070611010","endPageNum":"18963","jrnlTitl":"PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA","jrnlVol":"104","jrnlYr":"2007","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=159607850#000251498700018"},{"artTitl":"Casimir forces beyond the proximity approximation","auth":"Bimonte, G; Emig, T; Jaffe, RL; Kardar, M","authIndCode":"Y","dgtlObjId":"10.1209/0295-5075/97/5000","jrnlTitl":"EPL","jrnlVol":"97","jrnlYr":"2012","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=205193979#000301952600001"},{"artTitl":"Material dependence of Casimir forces: Gradient expansion beyond proximity","auth":"Bimonte, G; Emig, T; Kardar, M","authIndCode":"Y","dgtlObjId":"10.1063/1.368690","jrnlTitl":"APPLIED PHYSICS LETTERS","jrnlVol":"100","jrnlYr":"2012","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=204882643#000300436800097"},{"artTitl":"Dilution and resonance-enhanced repulsion in nonequilibrium fluctuation forces","auth":"Bimonte, G; Emig, T; Kruger, M; Kardar, M","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevA.84.04250","jrnlTitl":"PHYSICAL REVIEW A","jrnlVol":"84","jrnlYr":"2011","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=201188716#000295626300006"},{"artTitl":"A Stevedore's Protein Knot","auth":"Bolinger, D; Sulkowska, JI; Hsu, HP; Mirny, LA; Kardar, M; Onuchic, JN; Virnau, P","authIndCode":"Y","dgtlObjId":"10.1371/journal.pcbi.100073","jrnlTitl":"PLOS COMPUTATIONAL BIOLOGY","jrnlVol":"6","jrnlYr":"2010","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=189177988#000278125300008"},{"artTitl":"Configurations of polymers attached to probes","auth":"Bubis, R; Kantor, Y; Kardar, M","authIndCode":"Y","dgtlObjId":"10.1209/0295-5075/88/4800","jrnlTitl":"EPL","jrnlVol":"88","jrnlYr":"2009","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=185410905#000272835000026"},{"artPageNum":"238104","artTitl":"Formation and Stability of Synaptic Receptor Domains","auth":"C.A. 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\n
Fluctuations are ubiquitous in nature, from thermal motion of molecules in a fluid at rest, to non-equilibrium fluctuations of air in a tempest. Even the vacuum is teeming with quantum fluctuations of the electromagnetic field. Constraining these fluctuations by boundaries of different shapes or topology, leads to a myriad of interactions, patterns and phases. This NSF project explored a number of such phenomena, including:
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* Ordinary (uncharged) matter is held together by forces due to quantum fluctuations of charge and current. These fluctuation-induced forces at short distances are sensitive to shape, and we developed a formalism that can compute such shape dependence. In particular, we obtained forces between objects with sharp edges and tips.
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* Very similar methodology can be employed to compute forces exerted by molecules due to thermal (rather than quantum mechanical) fluctuations. We have shown that the force exerted by a fluctuating polymer on the tip of an atomic force microscope has a very simple form, dependent only on temperature and separation.
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* A prime example of non-equilibrium is provided by objects at different temperatures. This is of course a classical problem studied in elementary physics classes. However, again at close proximity, the heat transferred between the two objects can be very different- possibly thousand times larger- than obtained from classical computations due to the fluctuating fields. The formalism we developed for calculation of forces can also be adapted to compute heat transfer in these non-classical settings.
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* Yet another instance of non-equilibrium is a non-stationary object, such as a rotating sphere or cylinder. Classically, an isolated rotating body will maintain its rotation forever due to conservation of angular momentum. We show that an electrically neutral conductor actually slows down due to interactions with the fluctuating electromagnetic fields in the surrounding vacuum. This is tantamount to friction, with the energy lost radiated away.
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* Non-equilibrium processes are also at the basis of biological phenomena. It is known that the diffusion and reactions of fluctuating molecules on a membrane can lead to a dynamic form of aggregation into regular patterns. Interpreting recent experiments, we have suggested that such aggregates may form precursors to structures observed at a neural synapse.
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The methodology employed in tackling the diversity of problems indicated above is that of Statistical Physics. The tools of Statistical Physics provide the means of understanding how intricate and complex phenomena can emerge from interactions amongst large numbers of relatively simple ingredients. A broader impact of research supported by NSF is education and broader dissemination of the this methodology. Indeed, the research is closely linked to courses taught by the PI, which through textbooks and distribution by the web have reached a large number of students. Many of these students are engaged in interdisciplinary fields of research spanning biophysics to geophysics.
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\n\t\t\t\t \tLast Modified: 09/05/2012
\n\t\t\t\t\tModified by: Mehran Kardar
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Rev. Lett.~2011~106~M. Kruger, T. Emig, and M. Kardar~210404~Nonequilibrium Electromagnetic Fluctuations: Heat Transfer and Interactions~N~","EuroPhys. Lett.~2011~95~M. Kruger, T. Emig, G. Bimonte, and M. Kardar~21002~Non-equilibrium Casimir forces: Spheres and sphere-plate~N~","Computational and Mathematical Methods in Medicine~2011~2011~Quantitative Model for Efficient Temporal Targeting of Tumor Cells and Neovasculature~790721~M. Kohandel, C. A. Haselwandter, M. Kardar, S. Sengupta, and S. Sivaloganathan~N~","PHYSICAL REVIEW D~2009~80~Rahi, SJ; Emig, T; Graham, N; Jaffe, RL; Kardar, M~10.1103/PhysRevD.80.08502~http://wok-ws.isiknowledge.com/WoS?recid=184464214#000271353700116~Scattering theory approach to electrodynamic Casimir forces~Y~","PHYSICAL REVIEW A~2008~78~Rahi, SJ; Emig, T; Jaffe, RL; Kardar, M~10.1103/PhysRevA.78.01210~http://wok-ws.isiknowledge.com/WoS?recid=172877529#000258180300034~Casimir forces between cylinders and plates~Y~","PHYSICAL REVIEW E~2008~78~Rahi, SJ; Hertzberg, MP; Kardar, M~10.1103/PhysRevE.78.05191~http://wok-ws.isiknowledge.com/WoS?recid=175075008#000261213600075~Melting of persistent double-stranded polymers~Y~","PHYSICAL REVIEW LETTERS~2010~105~Rahi, SJ; Kardar, M; Emig, T~10.1103/PhysRevLett.105.07040~http://wok-ws.isiknowledge.com/WoS?recid=191022460#000280850600001~Constraints on Stable Equilibria with Fluctuation-Induced (Casimir) Forces~Y~","PHYSICAL REVIEW A~2008~77~Rahi, SJ; Rodriguez, AW; Emig, T; Jaffe, RL; Johnson, SG; Kardar, M~10.1103/PhysRevA.77.03010~http://wok-ws.isiknowledge.com/WoS?recid=161853228#000254541100001~Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders~Y~","PHYSICAL REVIEW E~2009~79~Safford, K; Kantor, Y; Kardar, M; Kudrolli, A~10.11~http://wok-ws.isiknowledge.com/WoS?recid=182035271#000267698700046~Structure and dynamics of vibrated granular chains: Comparison to equilibrium polymers~Y~"],"startDate":"09/15/2008","title":"Constrained Fluctuations","transType":"Continuing Grant","ueiNumber":"E2NYLCDML6V1"},{"abstractText":"This is a combined experimental and theoretical project to investigate the role of geometry, thermal photons and their interplay in the electromagnetic Casimir force. H.B.G. Casimir, calculated an extraordinary property that two parallel uncharged metallic plates placed in empty space would be attracted to each other. This force and the corresponding effect, now known as the Casimir effect, results from the alteration by the plates (boundaries) of the zero point electromagnetic energy that pervades all of space as predicted by quantum field theory. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as a function of the size, geometry and topology of the boundary. This study will build on the rapid theoretical advances in the area of simple geometry dependencies in the last two years. Investigations into the geometry dependence of the lateral Casimir force for surfaces with periodic corrugation on nanometer length scales, which will incorporate cooperative diffraction like effects for the zero-point photons will be carried out. Additionally, the role of thermal photons in the Casimir effect will be explored. The role of thermal photons is not completely understood due to problems effectively incorporating the dielectric losses of the material and interesting predictions of non-trivial geometry dependence have also been advanced for thermal photons. Finally a preliminary investigation of the role of negative index of refraction materials in the Casimir force will be launched. The results of this complete study will also allow the setting of stringent limits on modern unification theories which predict the presence of new forces or compactified extra dimensions. \r\nEven though the Casimir effect originates from quantum fluctuations, it results in large forces on macroscopic objects separated by distances less than a micron. The role of Casimir forces in the fabrication, function and yield of micromechanical devices has recently become well recognized. This investigation will lead to improved nano-electromechanical devices such as nano actuators, micro mirrors for optical communication and nano tweezers. The research program also involves the training of a graduate student and a minority undergraduate student in laboratory research and nanotechnology. \r\n","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"THE REGENTS OF THE UNIVERSITY OF CALIFORNIA","awardeeAddress":"900 UNIVERSITY AVE","awardeeCity":"RIVERSIDE","awardeeCountryCode":"US","awardeeDistrict":"39","awardeeDistrictCode":"CA39","awardeeName":"University of California-Riverside","awardeePhone":"9518275535","awardeeStateCode":"CA","awardeeZipCode":"925219800","cfdaNumber":"47.049","date":"06/04/2007","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"382210","expDate":"07/31/2010","fundAgencyCode":"4900","fundProgramName":"OPTICAL PHYSICS","fundsObligated":["FY 2007 = $142,210.00","FY 2008 = $120,000.00","FY 2009 = $120,000.00"],"fundsObligatedAmt":"382210","histAwd":"false","id":"0653657","initAmendmentDate":"06/04/2007","jrnl":[{"artPageNum":"036102","artTitl":"Comment on \"Precision measurement of the Casimir-Lifshitz force in a fluid\"","auth":"B. 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Geyer, G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko~036102~Comment on \"Precision measurement of the Casimir-Lifshitz force in a fluid\"~N~","PHYSICAL REVIEW A~2007~75~Castillo-Garza, R; Chang, CC; Jimenez, D; Klimchitskaya, GL; Mostepanenko, VM; Mohideen, U~10.1103/PhysRevA.75.06211~http://wok-ws.isiknowledge.com/WoS?recid=158690904#000247624300031~Experimental approaches to the difference in the Casimir force due to modifications in the optical properties of the boundary surface~Y~","PHYSICAL REVIEW B~2007~76~Chen, F; Klimchitskaya, GL; Mostepanenko, VM; Mohideen, U~10.1103/PhysRevB.76.03533~http://wok-ws.isiknowledge.com/WoS?recid=157495457#000248500800113~Control of the Casimir force by the modification of dielectric properties with light~Y~","OPTICS EXPRESS~2007~15~Chen, F; Klimchitskaya, GL; Mostepanenko, VM; Mohideen, U~4823~4829~http://wok-ws.isiknowledge.com/WoS?recid=155852965#000245782500042~Demonstration of optically modulated dispersion forces~Y~","Reviews of Modern Physics~2009~81~G.L. Klimchitskaya, U. Mohideen and V.M. Mostepanenko~1827~The Casimir force between real materials: experiment and theory~N~","Journal of Physics A~2008~41~G.L. Klimchitskaya, U. Mohideen, and V.M. Mostepanenko~9~Thermal Casimir-Polder force between an atom and a dielectric plate: thermodynamics and experiment~N~","Journal of Physics A~2008~41~H-C. Chiu, C.C. Chang , R. Castillo-Garza, F. Chen, U. Mohideen~164022~Experimental procedures for precision measurements of the Casimir force with an atomic force microscope~N~","Physical Review B (Rapid Communication)~2009~80~H.C. Chiu, G.L. Klimchitskaya, V.N. Marachevsky, V.M. Mostepanenko, and U. Mohideen~121402~Demonstration of the assymmetric lateral Casimir force between corrugated surfaces in the nonadditive regime~N~","Physical Review B~2010~81~HC. Chiu, G.L. Klimchitskaya, V.N. Marachevsky, V.M. Mostepanenko, U. Mohideen~115417~Lateral Casimir force between sinusoidally corrugated surfaces: Asymmetric profiles, deviations from the proximity force approximation, and comparison with exact theory~N~","JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL~2007~40~Klimchitskaya, GL; Mohideen, U; Mostepanenko, VM~10.1088/1751-8113/40/17/F0~F339~F346~http://wok-ws.isiknowledge.com/WoS?recid=156001631#000246085400004~Kramers-Kronig relations for plasma-like permittivities and the Casimir force~Y~","JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL~2007~40~Klimchitskaya, GL; Mohideen, U; Mostepanenko, VM~10.1088/1751-8113/40/34/F0~F841~F847~http://wok-ws.isiknowledge.com/WoS?recid=157408067#000248786600003~Pulsating Casimir force~Y~","Journal of Physics: Conference Series~2009~161~R.C. Castillo-Garza, C.C. Chang, Y. Dong, and U. Mohideen~012005~Customized silicon cantilevers for Casimir force experiments using focused ion beam milling~N~","Internation Journal of Modern Physics A~2009~24~V.M. Mostepanenko, R.S. Decca, E. Fischbach, B. Geyer, G.L. Klimchitskaya, D.E. Krause, D. Lopez and U. Mohideen~1721~Why screening effects do not influence the Casimir force~N~"],"startDate":"08/01/2007","title":"Investigation of the role of geometry, thermal photons and their interplay in the electromagnetic Casimir force","transType":"Continuing Grant","ueiNumber":"MR5QC5FCAVH5"},{"abstractText":"This project will involve theoretical research on several topics related to quantum theory and gravitation. There will be special emphasis on phenomena related to quantum fluctuations including the operational meaning of spacetime geometry fluctuations, the probability distribution of quantum\r\nstress tensor fluctuations, the role of stress tensor fluctuations in inflation, and selected aspects of the Casimir force. This project seeks to integrate studies of the quantum nature of the gravitational field with studies of fluctuating electromagnetic forces. It is hoped that this type of investigation will lead to a deeper understanding of both types of phenomena. \r\nThis project is expected to have a broader impact through possible benefits to other fields of science, to education, and to technology. It will entail international collaborations, and hence help to forge links with researchers in other countries. The insights and techniques of this work may be useful outside of the specific subfields of physics being investigated. The project will further education through the training of graduate students and by the involvement of faculty at primarily teaching institutions. It should also produce examples which can be used to explain some of the concepts of quantum theory and relativity to students on a variety of educational levels. The work on Casimir forces may eventually be useful in nanotechnology where a better knowledge of Casimir forces is likely to become important for the construction of small scale devices.\r\n\r\n","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"TRUSTEES OF TUFTS COLLEGE","awardeeAddress":"80 GEORGE ST","awardeeCity":"MEDFORD","awardeeCountryCode":"US","awardeeDistrict":"05","awardeeDistrictCode":"MA05","awardeeName":"Tufts University","awardeePhone":"6176273696","awardeeStateCode":"MA","awardeeZipCode":"021555519","cfdaNumber":"47.049","date":"03/28/2006","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"0","expDate":"12/31/2009","fundAgencyCode":"4900","fundProgramName":"Gravity Theory","fundsObligated":["FY 2006 = $48,000.00","FY 2007 = $48,000.00","FY 2008 = $48,000.00"],"fundsObligatedAmt":"144000","histAwd":"false","id":"0555754","initAmendmentDate":"03/28/2006","jrnl":[{"artPageNum":"062501","artTitl":"Brownian Motion in Robertson-Walker Space-Times from Electromagnetic Vacuum Fluctuations","auth":"C. H. G. Bessa, V. Bezerra and L.H. Ford","authIndCode":"N","jrnlTitl":"J. Math. Phys.","jrnlVol":"50","jrnlYr":"2009"},{"artPageNum":"103502","artTitl":"Possible Constraints on the Duration of Inflationary Expansion from Quantum Stress Tensor Fluctuations","auth":"Chun-Hsien Wu, Kin-Wang Ng and L.H. Ford","authIndCode":"N","jrnlTitl":"Phys. Rev. D","jrnlVol":"75","jrnlYr":"2007"},{"artPageNum":"065034","artTitl":"A Fluid Analog Model for Boundary Effects in Field Theory","auth":"Ford L H and Svaiter, N.F.","authIndCode":"N","jrnlTitl":"Phys. Rev. D","jrnlVol":"80","jrnlYr":"2009"},{"artPageNum":"065034","artTitl":"A Fluid Analog Model for Boundary Effects in Field Theory","auth":"Ford L H and Svaiter, N.F.","authIndCode":"N","jrnlTitl":"Phys. Rev. D","jrnlVol":"80","jrnlYr":"2009"},{"artPageNum":"030602","artTitl":"Quantum Density Fluctuations in Classical Liquids","auth":"Ford L H and Svaiter, N.F.","authIndCode":"N","jrnlTitl":"Phys. Rev. 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Letts.~2009~102~Ford L H and Svaiter, N.F.~030602~Quantum Density Fluctuations in Classical Liquids~N~","J. Phys. Conference Series~2009~161~Ford L H and Svaiter, N.F.~012034~The Phononic Casimir Effect: An Analog Model~N~","J. Phys. Conference Series~2009~161~Ford L H and Svaiter, N.F.~012034~The Phononic Casimir Effect: An Analog Model~N~","Int. J. Mod. Phys. A~2009~24~Hsiang, J-T and Ford, L.H.~1705~Decoherence and Recoherence in Model Quantum Systems~N~","Int. J. Mod. Phys. A~2009~24~Hsiang, J-T and Ford, L.H.~1705~Decoherence and Recoherence in Model Quantum Systems~N~","Phys. Rev. D~2008~78~Hsiang, J-T and Ford, L.H.~065012~Decoherence by Squeezed States in Electron Interferometry~N~","Int. J. Theor. Phys.~2007~46~L.H. Ford~2218~Frequency Spectra and Probability Distributions for Quantum Fluctuations~N~","AIP Conf. Proc.~2008~977~L. H. Ford and C-H Wu~145~Quantum Stress Tensor Fluctuations and their Physical Effects~N~","AIP Conf. Proc.~2008~977~L. H. Ford and C-H Wu~145~Quantum Stress Tensor Fluctuations and their Physical Effects~N~","Phys. Rev. D~2007~77~L.H. Ford and T.A. Roman~045018~Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum~N~","Phys. Rev. D~2007~77~L.H. Ford and T.A. Roman~045018~Negative Energy in Superposition and Entangled States~N~","Phys. Rev. D~2008~78~R. T. Thompson and L. H. Ford~024014~Enhanced Black Hole Horizon Fluctuations~N~","Class. Quant. Grav.~2008~25~R. T. Thompson and L. H. Ford~154006~Enhanced Geometry Fluctuations in Minkowski and Black Hole Spacetimes~N~","Phys. Rev. D~2006~74~R. T. Thompson and L.H. Ford~024012~Spectral Line Broadening and Angular Blurring due to Spacetime Geometry Fluctuations~N~","Phys. Rev. D~2006~74~R. T. Thompson and L.H. Ford~024012~Spectral Line Broadening and Angular Blurring due to Spacetime Geometry Fluctuations~N~","Phys. Rev. D~2009~80~Yu, H., Svaiter, N.F, and Ford, L.H.~124019~Quantum Lightcone Fluctuations in Compactified Spacetimes~N~"],"startDate":"07/01/2006","title":"Research on General Relativity and Quantum Fluctuations","transType":"Continuing Grant","ueiNumber":"WL9FLBRVPJJ7"},{"abstractText":"The proposed research concerns the development and application of semiclassical methods to describe macroscopic quantum effects of current interest and significance. A primary goal is to achieve a transparent description that allows one to better understand and reliably estimate such effects with reduced computational effort. Particular topics to be investigated include\r\ni) the development of a reliable and simple method to estimate the sign and\r\nmagnitude of a Casimir force, ii) the effect of vacuum fluctuations on realistic conductors and iii) the accuracy of the semi-classical approximation to Casimir energies. No ultraviolet infinities arise in this approximation, but all contributions to the spectral density that are not due to classical periodic rays have been subtracted. The relation to zeta-function regularization of Casimir energies will be further explored using Selberg's trace formula. Comparisons with more numerical approaches to determine Casimir forces will be investigated.\r\n","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"RUTGERS, THE STATE UNIVERSITY","awardeeAddress":"3 RUTGERS PLZ","awardeeCity":"NEW BRUNSWICK","awardeeCountryCode":"US","awardeeDistrict":"12","awardeeDistrictCode":"NJ12","awardeeName":"Rutgers University New Brunswick","awardeePhone":"8489320150","awardeeStateCode":"NJ","awardeeZipCode":"089018559","cfdaNumber":"47.049","date":"05/25/2006","dirAbbr":"MPS","divAbbr":"PHY","estimatedTotalAmt":"0","expDate":"04/30/2009","fundAgencyCode":"4900","fundProgramName":"AMO Theory/Atomic, Molecular &","fundsObligated":["FY 2006 = $45,000.00","FY 2007 = $45,000.00"],"fundsObligatedAmt":"90000","histAwd":"false","id":"0555580","initAmendmentDate":"05/25/2006","jrnl":[{"artPageNum":"214","artTitl":"Confinement by Design?","auth":"Martin Schaden","authIndCode":"N","jrnlTitl":"Brazilian Journal of Physics","jrnlVol":"37","jrnlYr":"2007"},{"artTitl":"Dependence of the Direction of the Casimir Force on the Shape of the Boundary","auth":"Schaden, M","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevLett.102.06040","jrnlTitl":"PHYSICAL REVIEW LETTERS","jrnlVol":"102","jrnlYr":"2009","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=176798242#000263389500003"},{"artTitl":"Sign and other aspects of semiclassical Casimir energies","auth":"Schaden, M","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevA.73.04210","jrnlTitl":"PHYSICAL REVIEW A","jrnlVol":"73","jrnlYr":"2006","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=150065680#000237147700031"},{"artPageNum":"052105","artTitl":"Numerical and semiclassical analysis of some generalized Casimir pistons","auth":"Schaden,M.","authIndCode":"N","dgtlObjId":"10.1103/PhysRevA.79.052105","jrnlTitl":"Physical Review A","jrnlVol":"79","jrnlYr":"2009"},{"artPageNum":"012021","artTitl":"Numerical Calculation of the Force on some Generalized Casimir Pistons","auth":"Schaden,M.","authIndCode":"N","dgtlObjId":"10.1088/1742-6596/161/1/012021","jrnlTitl":"Journal of Physics: Conference Series","jrnlVol":"161","jrnlYr":"2009"},{"artTitl":"Effects of diffusion and surface interactions on the line shape of electron paramagnetic resonances in the presence of a magnetic field gradient","auth":"Schaden, M; Zhao, KF; Wu, Z","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevA.76.06250","jrnlTitl":"PHYSICAL REVIEW A","jrnlVol":"76","jrnlYr":"2007","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=159967707#000251985900048"},{"artTitl":"Effects of diffusion and surface interactions on the line shape of electron paramagnetic resonances in the presence of a magnetic field gradient (vol 76, artn 062502, 2007)","auth":"Schaden, M; Zhao, KF; Wu, Z","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevA.77.04990","jrnlTitl":"PHYSICAL REVIEW A","jrnlVol":"77","jrnlYr":"2008","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=162407861#000255457100211"},{"artTitl":"Method for measuring surface-interaction parameters of spin-polarized Rb atoms on coated Pyrex glass surfaces using edge enhancement","auth":"Zhao, KF; Schaden, M; Wu, Z","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevA.78.03490","jrnlTitl":"PHYSICAL REVIEW A","jrnlVol":"78","jrnlYr":"2008","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=173568967#000259689400211"},{"artTitl":"Nonperturbative broadening of paramagnetic resonance lines by transverse magnetic field gradients","auth":"Zhao, KF; Schaden, M; Wu, Z","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevA.78.01341","jrnlTitl":"PHYSICAL REVIEW A","jrnlVol":"78","jrnlYr":"2008","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=172877644#000258180300155"}],"latestAmendmentDate":"04/08/2008","managingPec":"128400","orgCodeDir":"03000000","orgCodeDiv":"03010000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Physics","orgUrl":"http://www.nsf.gov/div/index.jsp?div=phy","parentUeiNumber":"","pdPIName":"Martin Schaden","perfAddress":"123 WASHINGTON ST","perfCity":"NEWARK","perfCountryCode":"US","perfDistrict":"10","perfDistrictCode":"NJ10","perfLocation":"Rutgers University Newark","perfStateCode":"NJ","perfZipCode":"071023026","pi":["Martin Schaden mschaden@andromeda.rutgers.edu"],"piEmail":"mschaden@andromeda.rutgers.edu","piFirstName":"Martin","piId":"269758394","piLastName":"Schaden","poEmail":"","poName":"Richard Houghton Pratt","poPhone":"","primaryProgram":["app-0106","app-0107"],"progEleCode":"128400","program":"UNASSIGNED, OTHER RESEARCH OR EDUCATION","progRefCode":"0000, OTHR","publicAccessMandate":"0","publicationResearch":["Brazilian Journal of Physics~2007~37~Martin Schaden~214~Confinement by Design?~N~","PHYSICAL REVIEW LETTERS~2009~102~Schaden, M~10.1103/PhysRevLett.102.06040~http://wok-ws.isiknowledge.com/WoS?recid=176798242#000263389500003~Dependence of the Direction of the Casimir Force on the Shape of the Boundary~Y~","PHYSICAL REVIEW A~2006~73~Schaden, M~10.1103/PhysRevA.73.04210~http://wok-ws.isiknowledge.com/WoS?recid=150065680#000237147700031~Sign and other aspects of semiclassical Casimir energies~Y~","Physical Review A~2009~79~Schaden,M.~10.1103/PhysRevA.79.052105~052105~Numerical and semiclassical analysis of some generalized Casimir pistons~N~","Journal of Physics: Conference Series~2009~161~Schaden,M.~10.1088/1742-6596/161/1/012021~012021~Numerical Calculation of the Force on some Generalized Casimir Pistons~N~","PHYSICAL REVIEW A~2007~76~Schaden, M; Zhao, KF; Wu, Z~10.1103/PhysRevA.76.06250~http://wok-ws.isiknowledge.com/WoS?recid=159967707#000251985900048~Effects of diffusion and surface interactions on the line shape of electron paramagnetic resonances in the presence of a magnetic field gradient~Y~","PHYSICAL REVIEW A~2008~77~Schaden, M; Zhao, KF; Wu, Z~10.1103/PhysRevA.77.04990~http://wok-ws.isiknowledge.com/WoS?recid=162407861#000255457100211~Effects of diffusion and surface interactions on the line shape of electron paramagnetic resonances in the presence of a magnetic field gradient (vol 76, artn 062502, 2007)~Y~","PHYSICAL REVIEW A~2008~78~Zhao, KF; Schaden, M; Wu, Z~10.1103/PhysRevA.78.03490~http://wok-ws.isiknowledge.com/WoS?recid=173568967#000259689400211~Method for measuring surface-interaction parameters of spin-polarized Rb atoms on coated Pyrex glass surfaces using edge enhancement~Y~","PHYSICAL REVIEW A~2008~78~Zhao, KF; Schaden, M; Wu, Z~10.1103/PhysRevA.78.01341~http://wok-ws.isiknowledge.com/WoS?recid=172877644#000258180300155~Nonperturbative broadening of paramagnetic resonance lines by transverse magnetic field gradients~Y~"],"startDate":"05/01/2006","title":"THE SEMICLASSICAL APPROXIMATION APPLIED TO CASIMIR EFFECTS","transType":"Continuing Grant","ueiNumber":"M1LVPE5GLSD9"},{"abstractText":"NON-TECHNICAL ABSTRACT:\r\nThe primary goals of this research are to use superfluid and normal helium to investigate the motion of droplets on specially prepared weak substrates made of cesium and to use an optical probe technique called ellipsometry to study wetting and long range forces between a molecule and a solid surface. An apparatus will be constructed that will provide optical access to an experimental cell with a base temperature of approximately 0.35 K. Since surface forces are particularly sensitive to surface contamination, a high\r\npower pulsed laser will be purchased and used to clean substrates in situ at low temperature and to form novel high quality substrates using laser ablation. In the droplet studies, the motion of superfluid drops on these surfaces will be observed using high speed video. The experiments will measure the net force on a superfluid droplet and will determine whether superfluid drops move with zero friction. Our recently developed cryogenic ellipsometer will be used to monitor the growth and wetting of helium films on a variety of substrates, particularly those that are inaccessible to conventional microbalance methods, including bulk rubidium and lithium. The ellipsometer will also be used to monitor the helium film thickness on conventional strong substrates, which can be prepared with atomically flat surfaces, such as cleaved alkali halide crystals, graphite, mica and gold. The goal of these experiments will be to eliminate the effects of surface\r\nroughness on measurements of delicate forces which control the thickness of thin films. In all of these cases, substrates will be cleaned or deposited using energy delivered by a laser pulse. Laser ablation will also be explored as a method of producing cesium with a monolayer of cesium oxide, which is a candidate for a superweak substrate.\r\n\r\nTECHNICAL ABSTRACT:\r\nThe primary goals of this research are to use superfluid and normal helium to investigate the motion of droplets on cesiated surfaces and to use ellipsometry to study wetting and long range forces on a variety of substrates. An apparatus will be constructed that will provide optical access to an experimental cell with a base temperature of approximately\r\n0.35 K. A high power pulsed laser will be purchased and used to clean substrates in situ at low temperature and to form novel high quality substrates using laser ablation. In the droplet studies, the goal will be to make cesium surfaces with finite values of both the advancing and receding contact angle and to observe the motion of superfluid drops on these surfaces using high speed video. The experiments will measure the net force on a superfluid droplet and will determine whether low velocity motion of superfluid drops is essentially dissipationless or if moving contact lines generate intrinsic dissipation. Our recently developed cryogenic ellipsometer will be used to monitor the growth and wetting of helium films on a variety of substrates, particularly those that are inaccessible to conventional microbalance methods, including bulk rubidium and lithium. On this type of intermediate strength substrate, superfluidity and prewetting appear to be entangled, and the superfluid transition is not well described by the standard Kosterlitz-Thouless model. The ellipsometer will also be used to monitor the helium film thickness on conventional strong substrates, which can be prepared with atomically flat surfaces, such as cleaved alkali halide crystals, graphite, mica and gold. The goal of these experiments will be to eliminate the effects of surface roughness on measurements of the Casimir force and other possible finite size contributions to the free energy of a thin film. In all of these cases, substrates will be cleaned or deposited using energy delivered by a laser pulse. Laser ablation will also be explored as a method of producing cesium with a monolayer of cesium oxide, which has the lowest known work function and is a candidate for a superweak substrate.\r\n\r\n","activeAwd":"false","agency":"NSF","awardAgencyCode":"4900","awardee":"UNIVERSITY OF CALIFORNIA IRVINE","awardeeAddress":"160 ALDRICH HALL","awardeeCity":"IRVINE","awardeeCountryCode":"US","awardeeDistrict":"47","awardeeDistrictCode":"CA47","awardeeName":"University of California-Irvine","awardeePhone":"9498247295","awardeeStateCode":"CA","awardeeZipCode":"926970001","cfdaNumber":"47.049","date":"06/15/2005","dirAbbr":"MPS","divAbbr":"DMR","estimatedTotalAmt":"0","expDate":"12/31/2009","fundAgencyCode":"4900","fundProgramName":"CONDENSED MATTER PHYSICS","fundsObligated":["FY 2005 = $200,000.00","FY 2006 = $200,000.00","FY 2007 = $170,000.00","FY 2008 = $170,000.00","FY 2009 = $7,000.00"],"fundsObligatedAmt":"747000","histAwd":"false","id":"0509685","initAmendmentDate":"06/15/2005","jrnl":[{"artTitl":"Cryogenic vacuum tribology of diamond and diamond-like carbon films","auth":"Aggleton, M; Burton, JC; Taborek, P","authIndCode":"Y","dgtlObjId":"10.1063/1.315833","jrnlTitl":"JOURNAL OF APPLIED PHYSICS","jrnlVol":"106","jrnlYr":"2009","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=182359592#000268065000031"},{"artPageNum":"924","artTitl":"The PCP pathway Instructs the Planar Orientation of Ciliated Cells in Xenopus Larval Skin","auth":"B. Mitchell, J.L. Stubbs, F Huisman, P. Taborek , C. Yu, and C. Kintner","authIndCode":"N","jrnlTitl":"Current Biology","jrnlVol":"19","jrnlYr":"2009"},{"artTitl":"Bifurcation from Bubble to Droplet Behavior in Inviscid Pinch-off","auth":"Burton, JC; Taborek, P","authIndCode":"Y","dgtlObjId":"10.1103/PhysRevLett.101.21450","jrnlTitl":"PHYSICAL REVIEW LETTERS","jrnlVol":"101","jrnlYr":"2008","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=174764519#000261141500021"},{"artTitl":"Two-dimensional inviscid pinch-off: An example of self-similarity of the second kind","auth":"Burton, JC; Taborek, P","authIndCode":"Y","dgtlObjId":"10.1063/1.280038","jrnlTitl":"PHYSICS OF FLUIDS","jrnlVol":"19","jrnlYr":"2007","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=158950346#000250589600014"},{"artPageNum":"1","artTitl":"Helium Adsorption on Lithium Substrates","auth":"E. Van Cleve, P. Taborek, and J.E. Rutledge","authIndCode":"N","jrnlTitl":"Journal of Low Temperature Physics","jrnlVol":"150","jrnlYr":"2008"},{"artPageNum":"036311","artTitl":"Fluid Pinch-off in Normal and Superfluid Helium","auth":"J.C. Burton, J.E. Rutledge, and P. Taborek","authIndCode":"N","jrnlTitl":"Phys. Rev. E","jrnlVol":"75","jrnlYr":"2007"},{"artPageNum":"151","artTitl":"Superfluid onset and capillary condensation","auth":"Lazarowich, RJ; Taborek, P","authIndCode":"Y","dgtlObjId":"10.1007/s10909-007-9506-","endPageNum":"155","jrnlTitl":"JOURNAL OF LOW TEMPERATURE PHYSICS","jrnlVol":"149","jrnlYr":"2007","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=158367626#000249819200003"},{"artPageNum":"924","artTitl":"The PCP Pathway Instructs the Planar Orientation of Ciliated Cells in the Xenopus Larval Skin","auth":"Mitchell, B; Stubbs, JL; Huisman, F; Taborek, P; Yu, C; Kintner, C","authIndCode":"Y","dgtlObjId":"10.1016/j.cub.2009.04.01","endPageNum":"929","jrnlTitl":"CURRENT BIOLOGY","jrnlVol":"19","jrnlYr":"2009","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=181390933#000266891900026"},{"artPageNum":"024512","artTitl":"Superfluid Transitions and Capillary Condensation in Porous Media","auth":"R.J. Lazarowich and P. Taborek","authIndCode":"N","jrnlTitl":"Phys. Rev. B","jrnlVol":"74","jrnlYr":"2006"},{"artPageNum":"101","artTitl":"Wetting, Prewetting and Superfluidity","auth":"Taborek, P","authIndCode":"Y","dgtlObjId":"10.1007/s10909-009-9906-","endPageNum":"110","jrnlTitl":"JOURNAL OF LOW TEMPERATURE PHYSICS","jrnlVol":"157","jrnlYr":"2009","srceUri":"http://wok-ws.isiknowledge.com/WoS?recid=183830874#000270385000003"}],"latestAmendmentDate":"04/03/2009","managingPec":"171000","orgCodeDir":"03000000","orgCodeDiv":"03070000","orgLongName":"Directorate for Mathematical and Physical Sciences","orgLongName2":"Division Of Materials Research","orgUrl":"http://www.nsf.gov/div/index.jsp?div=dmr","parentUeiNumber":"GH98ZGGP6RR5","pdPIName":"Peter Taborek","perfAddress":"160 ALDRICH HALL","perfCity":"IRVINE","perfCountryCode":"US","perfDistrict":"47","perfDistrictCode":"CA47","perfLocation":"University of California-Irvine","perfStateCode":"CA","perfZipCode":"926970001","pi":["Peter Taborek ptaborek@uci.edu"],"piEmail":"ptaborek@uci.edu","piFirstName":"Peter","piId":"000181941","piLastName":"Taborek","poEmail":"","poName":"Wendy W. Fuller-Mora","poPhone":"","primaryProgram":["app-0105","app-0106","app-0107","01000809DB NSF RESEARCH & RELATED ACTIVIT","01000910DB NSF RESEARCH & RELATED ACTIVIT"],"progEleCode":"171000","program":"SINGLE DIVISION/UNIVERSITY, UNDERGRADUATE EDUCATION, REU SUPP-Res Exp for Ugrd Supp, ADVANCED MATERIALS & PROCESSING PROGRAM, SCIENCE, MATH, ENG & TECH EDUCATION","progRefCode":"9161, 9178, 9251, AMPP, SMET","publicAccessMandate":"0","publicationResearch":["JOURNAL OF APPLIED PHYSICS~2009~106~Aggleton, M; Burton, JC; Taborek, P~10.1063/1.315833~http://wok-ws.isiknowledge.com/WoS?recid=182359592#000268065000031~Cryogenic vacuum tribology of diamond and diamond-like carbon films~Y~","Current Biology~2009~19~B. Mitchell, J.L. Stubbs, F Huisman, P. Taborek , C. Yu, and C. Kintner~924~The PCP pathway Instructs the Planar Orientation of Ciliated Cells in Xenopus Larval Skin~N~","PHYSICAL REVIEW LETTERS~2008~101~Burton, JC; Taborek, P~10.1103/PhysRevLett.101.21450~http://wok-ws.isiknowledge.com/WoS?recid=174764519#000261141500021~Bifurcation from Bubble to Droplet Behavior in Inviscid Pinch-off~Y~","PHYSICS OF FLUIDS~2007~19~Burton, JC; Taborek, P~10.1063/1.280038~http://wok-ws.isiknowledge.com/WoS?recid=158950346#000250589600014~Two-dimensional inviscid pinch-off: An example of self-similarity of the second kind~Y~","Journal of Low Temperature Physics~2008~150~E. Van Cleve, P. Taborek, and J.E. Rutledge~1~Helium Adsorption on Lithium Substrates~N~","Phys. Rev. E~2007~75~J.C. Burton, J.E. Rutledge, and P. Taborek~036311~Fluid Pinch-off in Normal and Superfluid Helium~N~","JOURNAL OF LOW TEMPERATURE PHYSICS~2007~149~Lazarowich, RJ; Taborek, P~10.1007/s10909-007-9506-~151~155~http://wok-ws.isiknowledge.com/WoS?recid=158367626#000249819200003~Superfluid onset and capillary condensation~Y~","CURRENT BIOLOGY~2009~19~Mitchell, B; Stubbs, JL; Huisman, F; Taborek, P; Yu, C; Kintner, C~10.1016/j.cub.2009.04.01~924~929~http://wok-ws.isiknowledge.com/WoS?recid=181390933#000266891900026~The PCP Pathway Instructs the Planar Orientation of Ciliated Cells in the Xenopus Larval Skin~Y~","Phys. Rev. B~2006~74~R.J. Lazarowich and P. Taborek~024512~Superfluid Transitions and Capillary Condensation in Porous Media~N~","JOURNAL OF LOW TEMPERATURE PHYSICS~2009~157~Taborek, P~10.1007/s10909-009-9906-~101~110~http://wok-ws.isiknowledge.com/WoS?recid=183830874#000270385000003~Wetting, Prewetting and Superfluidity~Y~"],"startDate":"07/01/2005","title":"Drops, Bubbles and Wetting Phenomena in Superfluid and Normal Helium","transType":"Continuing Grant","ueiNumber":"MJC5FCYQTPE6"}],"metadata":{"offset":0,"rpp":25,"totalCount":29}}}
![\"Casimir](\"/por/images/Reports/POR/2022/2019288/2019288_10576079_1672511864212_Torque_image--rgov-66x44.jpg\")
\n\n\nDepiction of the Casimir torque.\nJeremy Munday\nCopyrighted\nJeremy Munday\nCasimir torque\n \n![\"Casimir](\"/por/images/Reports/POR/2022/2019288/2019288_10576079_1672511864212_Torque_image--rgov-214x142.jpg\")
![\"Casimir](\"/por/images/Reports/POR/2019/1506047/1506047_10389859_1546974859607_Munday_Torque_01--rgov-214x142.jpg\")
![\"Schematic](\"/por/images/Reports/POR/2019/1506047/1506047_10389859_1546975015305_Munday_Torque_03--rgov-214x142.jpg\")
![\"Optical](\"/por/images/Reports/POR/2019/1506047/1506047_10389859_1546975549661_Torque_Angle_Data--rgov-214x142.jpg\")
![\"MCMC](\"/por/images/Reports/POR/2018/1520293/1520293_10388870_1533822120335_MCMCPhysics--rgov-214x142.jpg\")
![\"Physics](\"/por/images/Reports/POR/2018/1520293/1520293_10388870_1533824088356_2018_Physics_Commencement_02--rgov-214x142.jpg\")
![\"Physics](\"/por/images/Reports/POR/2018/1520293/1520293_10388870_1533824370204_Middlebury_Physics_Graduation_2017_0528_cropped--rgov-214x142.jpg\")