Physics Commons^™

Mathematical And Physical Aspects Of Complex Symmetric Operators, Stephan Ramon Garcia, Emil Prodan, Mihai Putinar

Pomona Faculty Publications and Research

Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugate-linear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics, and complex variables.

Entropy Driven Crystal Formation On Highly Strained Substrates, John R. Savage, Stefan F. Hopp, Rajesh Ganapathy, Sharon J. Gerbode, Andreas Heuer, Itai Cohen

All HMC Faculty Publications and Research

In heteroepitaxy, lattice mismatch between the deposited material and the underlying surface strongly affects nucleation and growth processes. The effect of mismatch is well studied in atoms with growth kinetics typically dominated by bond formation with interaction lengths on the order of one lattice spacing. In contrast, less is understood about how mismatch affects crystallization of larger particles, such as globular proteins and nanoparticles, where interparticle interaction energies are often comparable to thermal fluctuations and are short ranged, extending only a fraction of the particle size. Here, using colloidal experiments and simulations, we find particles with short-range attractive interactions form …

3d Imaging And Mechanical Modeling Of Helical Buckling In Medicago Truncatula Plant Roots, Jesse L. Silverberg, Roslyn D. Noar, Michael S. Packer, Maria J. Harrison, Christopher L. Henley, Itai Cohen, Sharon J. Gerbode

All HMC Faculty Publications and Research

We study the primary root growth of wild-type Medicago truncatula plants in heterogeneous environments using 3D time-lapse imaging. The growth medium is a transparent hydrogel consisting of a stiff lower layer and a compliant upper layer. We find that the roots deform into a helical shape just above the gel layer interface before penetrating into the lower layer. This geometry is interpreted as a combination of growth-induced mechanical buckling modulated by the growth medium and a simultaneous twisting near the root tip. We study the helical morphology as the modulus of the upper gel layer is varied and demonstrate that …

Black Hole Thermalization, D0 Brane Dynamics, And Emergent Spacetime, Paul L. Riggins '12, Vatche Sahakian

All HMC Faculty Publications and Research

When matter falls past the horizon of a large black hole, the expectation from string theory is that the configuration thermalizes and the information in the probe is rather quickly scrambled away. The traditional view of a classical unique spacetime near a black hole horizon conflicts with this picture. The question then arises as to what spacetime does the probe actually see as it crosses a horizon, and how does the background geometry imprint its signature onto the thermal properties of the probe. In this work, we explore these questions through an extensive series of numerical simulations of D0 branes. …

How The Cucumber Tendril Coils And Overwinds, Sharon J. Gerbode, Joshua R. Puzey, Andrew G. Mccormick, L. Mahadevan

All HMC Faculty Publications and Research

The helical coiling of plant tendrils has fascinated scientists for centuries, yet the underlying mechanism remains elusive. Moreover, despite Darwin’s widely accepted interpretation of coiled tendrils as soft springs, their mechanical behavior remains unknown. Our experiments on cucumber tendrils demonstrate that tendril coiling occurs via asymmetric contraction of an internal fiber ribbon of specialized cells. Under tension, both extracted fiber ribbons and old tendrils exhibit twistless overwinding rather than unwinding, with an initially soft response followed by strong strain-stiffening at large extensions. We explain this behavior using physical models of prestrained rubber strips, geometric arguments, and mathematical models of elastic …

Evolution Of Spur-Length Diversity In Aquilegia Petals Is Achieved Solely Through Cell-Shape Anisotropy, Joshua R. Puzey, Sharon J. Gerbode, Scott A. Hodges, Elena M. Kramer, L. Mahadevan

All HMC Faculty Publications and Research

The role of petal spurs and specialized pollinator interactions has been studied since Darwin. Aquilegia petal spurs exhibit striking size and shape diversity, correlated with specialized pollinators ranging from bees to hawkmoths in a textbook example of adaptive radiation. Despite the evolutionary significance of spur length, remarkably little is known about Aquilegia spur morphogenesis and its evolution. Using experimental measurements, both at tissue and cellular levels, combined with numerical modelling, we have investigated the relative roles of cell divisions and cell shape in determining the morphology of the Aquilegia petal spur. Contrary to decades-old hypotheses implicating a discrete meristematic zone …

Effect Of Substrate Composition And Alignment On Corneal Cell Phenotype, Donna Phu '09, Lindsay S. Wray '08, Robert V. Warren '10, Richard C. Haskell, Elizabeth J. Orwin

All HMC Faculty Publications and Research

Corneal blindness is a significant problem treated primarily by corneal transplants. Donor tissue supply is low, creating a growing need for an alternative. A tissue-engineered cornea made from patient-derived cells and biopolymer scaffold materials would be widely accessible to all patients and would alleviate the need for donor sources. Previous work in this lab led to a method for electrospinning type I collagen scaffolds for culturing corneal fibroblasts ex vivo that mimics the microenvironment in the native cornea. This electrospun scaffold is composed of small-diameter, aligned collagen fibers. In this study, we investigate the effect of scaffold nanostructure and composition …

Evidence Of The Harmonic Faraday Instability In Ultrasonic Atomization Experiments With A Deep, Inviscid Fluid, Andrew P. Higginbotham '09, Aaron Guillen '11, Nathan C. Jones '10, Thomas D. Donnelly, Andrew J. Bernoff

All HMC Faculty Publications and Research

A popular method for generating micron-sized aerosols is to submerge ultrasonic (ω~MHz) piezoelectric oscillators in a water bath. The submerged oscillator atomizes the fluid, creating droplets with radii proportional to the wavelength of the standing wave at the fluid surface. Classical theory for the Faraday instability predicts a parametric instability driving a capillary wave at the subharmonic (ω/2) frequency. For many applications it is desirable to reduce the size of the droplets; however, using higher frequency oscillators becomes impractical beyond a few MHz. Observations are presented that demonstrate that smaller droplets may also be created by …

Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu

Pomona Faculty Publications and Research

The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their …

Dislocations And Vacancies In Two-Dimensional Mixed Crystals Of Spheres And Dimers, Sharon J. Gerbode, Desmond C. Ong, Chekesha M. Liddell, Itai Cohen

All HMC Faculty Publications and Research

In colloidal crystals of spheres, dislocation motion is unrestricted. On the other hand, recent studies of relaxation in crystals of colloidal dimer particles have demonstrated that the dislocation dynamics in such crystals are reminiscent of glassy systems. The observed glassy dynamics arise as a result of dislocation cages formed by certain dimer orientations. In the current study, we use experiments and simulations to investigate the transition that arises when a pure sphere crystal is doped with an increasing concentration of dimers. Specifically, we focus on both dislocation caging and vacancy motion. Interestingly, we find that any nonzero fraction of dimers …

Glassy Dislocation Dynamics In 2d Colloidal Dimer Crystals, Sharon J. Gerbode, Ugmang Agarwal, Desmond C. Ong, Chekesha M. Liddell, Fernando Escobedo, Itai Cohen

All HMC Faculty Publications and Research

Although glassy relaxation is typically associated with disorder, here we report on a new type of glassy dynamics relating to dislocations within 2D crystals of colloidal dimers. Previous studies have demonstrated that dislocation motion in dimer crystals is restricted by certain particle orientations. Here, we drag an optically trapped particle through such dimer crystals, creating dislocations. We find a two-stage relaxation response where initially dislocations glide until encountering particles that cage their motion. Subsequent relaxation occurs logarithmically slowly through a second process where dislocations hop between caged configurations. Finally, in simulations of sheared dimer crystals, the dislocation mean squared displacement …

Kinematic Evidence For Superfast Locomotory Muscle In Two Species Of Teneriffiid Mites, Grace C. Wu, Jonathan C. Wright, Dwight L. Whitaker, Anna N. Ahn

All HMC Faculty Publications and Research

Locomotory muscles typically operate over a narrow range of contraction frequencies, characterized by the predominant fiber types and functional roles. The highest documented frequencies in the synchronous sound-producing muscles of insects (550 Hz) and toadfish (200 Hz) far exceed the contraction frequencies observed in weight-bearing locomotory muscles, which have maximum documented frequencies below 15-30 Hz. Laws of scaling, however, predict that smaller arthropods may employ stride frequencies exceeding this range. In this study we measured running speed and stride frequency in two undescribed species of teneriffiid mites from the coastal sage scrub of southern California. Relative speeds of both species …

From Surface Operators To Non-Abelian Volume Operators In Puff Field Theory, Vatche Sahakian

All HMC Faculty Publications and Research

Puff field theory (PFT) is a low energy decoupling regime of string theory that still retains the nonlocal attributes of the parent theory—while preserving isotropy for its nonlocal degrees of freedom. It realizes an extended holographic dictionary at strong coupling and dynamical nonlocal states akin to defects or the surface operators of local gauge theories. In this work, we probe the nonlocal features of PFT using D3 branes. We find supersymmetric configurations that end on defects endowed with non-Abelian degrees of freedom. These are 2+1 dimensional defects in the 3+1 dimensional PFT that may be viewed as volume operators. We …

Kinematic Evidence For Superfast Locomotory Muscle In Two Species Of Teneriffiid Mites, Grace C. Wu, Jonathan C. Wright, Dwight L. Whitaker, Anna N. Ahn

Pomona Faculty Publications and Research

Locomotory muscles typically operate over a narrow range of contraction frequencies, characterized by the predominant fiber types and functional roles. The highest documented frequencies in the synchronous sound-producing muscles of insects (550 Hz) and toadfish (200 Hz) far exceed the contraction frequencies observed in weight-bearing locomotory muscles, which have maximum documented frequencies below 15-30 Hz. Laws of scaling, however, predict that smaller arthropods may employ stride frequencies exceeding this range. In this study we measured running speed and stride frequency in two undescribed species of teneriffiid mites from the coastal sage scrub of southern California. Relative speeds of both species …

Direct Measurements Of Island Growth And Step-Edge Barriers In Colloidal Epitaxy, Rajesh Ganapathy, Mark R. Buckley, Sharon J. Gerbode, Itai Cohen

All HMC Faculty Publications and Research

Epitaxial growth, a bottom-up self-assembly process for creating surface nano- and microstructures, has been extensively studied in the context of atoms. This process, however, is also a promising route to self-assembly of nanometer- and micrometer-scale particles into microstructures that have numerous technological applications. To determine whether atomic epitaxial growth laws are applicable to the epitaxy of larger particles with attractive interactions, we investigated the nucleation and growth dynamics of colloidal crystal films with single-particle resolution. We show quantitatively that colloidal epitaxy obeys the same two-dimensional island nucleation and growth laws that govern atomic epitaxy. However, we found that in colloidal …

Self-Organized Criticality In Sheared Suspensions, L. Corté, Sharon J. Gerbode, W. Man, D. J. Pine

All HMC Faculty Publications and Research

Recent studies reveal that suspensions of neutrally buoyant non-Brownian particles driven by slow periodic shear can undergo a dynamical phase transition between a fluctuating irreversible steady state and an absorbing reversible state. Using a computer model, we show that such systems exhibit self-organized criticality when a finite particle sedimentation velocity v_s is introduced. Under periodic shear, these systems evolve, without external intervention, towards the shear-dependent critical concentration ϕ_c as v_s is reduced. This state is characterized by power-law distributions in the lifetime and size of fluctuating clusters. Experiments exhibit similar behavior and, as v_s is reduced, …

How Much Can Guided Modes Enhance Absorption In Thin Solar Cells?, Peter N. Saeta, Vivian E. Ferry, Domenico Pacifici, Jeremy N. Munday, Harry A. Atwater

All HMC Faculty Publications and Research

Absorption enhancement in thin metal-backed solar cells caused by dipole scatterers embedded in the absorbing layer is studied using a semi-analytical approach. The method accounts for changes in the radiation rate produced by layers above and below the dipole, and treats incoherently the subsequent scattering of light in guided modes from other dipoles. We find large absorption enhancements for strongly coupled dipoles, exceeding the ergodic limit in some configurations involving lossless dipoles. An antireflection-coated 100-nm layer of a-Si:H on Ag absorbs up to 87% of incident above-gap light. Thin layers of both strong and weak absorbers show similar strongly enhanced …

Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori

All HMC Faculty Publications and Research

Analysis of acoustic phonons modulated due to the surfaces of a free-standing semiconductor plate and their deformation-potential interaction with electrons are presented. The form factor for electron-modulated acoustic phonon interaction is formulated and analyzed in detail. The form factor at zero in-plane phonon wave vector satisfies sum rules regardless of electron wave function. The form factor is larger than that calculated using bulk phonons, leading to a higher scattering rate and lower electron mobility. When properly normalized, the form factors lie on a universal curve regardless of plate thickness and material.

The Initial And Final States Of Electron And Energy Transfer Processes: Diabatization As Motivated By System-Solvent Interactions, Joseph E. Subotnik, Robert J. Cave, Ryan P. Steele, Neil Shenvi

All HMC Faculty Publications and Research

For a system which undergoes electron or energy transfer in a polar solvent, we define the diabatic states to be the initial and final states of the system, before and after the nonequilibrium transfer process. We consider two models for the system-solvent interactions: A solvent which is linearly polarized in space and a solvent which responds linearly to the system. From these models, we derive two new schemes for obtaining diabatic states from ab initio calculations of the isolated system in the absence of solvent. These algorithms resemble standard approaches for orbital localization, namely, the Boys and Edmiston–Ruedenberg (ER) formalisms. …

Generation Of Mie Size Microdroplet Aerosols With Applications In Laser-Driven Fusion Experiments, Andrew P. Higginbotham '09, O. Semonin '06, S. Bruce '08, C. Chan '08, M. Maindi '07, Thomas D. Donnelly, M. Maurer, W. Bang, I. Churina, J. Osterholz, I. Kim, A. C. Bernstein, T. Ditmire

All HMC Faculty Publications and Research

We have developed a tunable source of Mie scale microdroplet aerosols that can be used for the generation of energetic ions. To demonstrate this potential, a terawatt Ti:Al₂O₃ laser focused to 2×10¹⁹ W/cm² was used to irradiate heavy water (D₂O) aerosols composed of micron-scale droplets. Energetic deuterium ions, which were generated in the laser-droplet interaction, produced deuterium-deuterium fusion with approximately 2×10³ fusion neutrons measured per joule of incident laser energy.

Thermal Links For The Implementation Of An Optical Refrigerator, John Parker, David Mar, Steven Von Der Porten, John Hankinson, Kevin Byram, Chris Lee, Michael K. Mayeda, Richard C. Haskell, Qimin Yang, Scott R. Greenfield, Richard I. Epstein

All HMC Faculty Publications and Research

Optical refrigeration has been demonstrated by several groups of researchers, but the cooling elements have not been thermally linked to realistic heat loads in ways that achieve the desired temperatures. The ideal thermal link will have minimal surface area, provide complete optical isolation for the load, and possess high thermal conductivity. We have designed thermal links that minimize the absorption of fluoresced photons by the heat load using multiple mirrors and geometric shapes including a hemisphere, a kinked waveguide, and a tapered waveguide. While total link performance is dependent on additional factors, we have observed net transmission of photons with …

Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy

All HMC Faculty Publications and Research

A thin layer of fluid flowing down a solid planar surface has a free surface height described by a nonlinear PDE derived via the lubrication approximation from the Navier Stokes equations. For thin films, surface tension plays an important role both in providing a significant driving force and in smoothing the free surface. Surfactant molecules on the free surface tend to reduce surface tension, setting up gradients that modify the shape of the free surface. In earlier work [12, 13J a traveling wave was found in which the free surface undergoes three sharp transitions, or internal layers, and the surfactant …

Constructing Diabatic States From Adiabatic States: Extending Generalized Mulliken–Hush To Multiple Charge Centers With Boys Localization, Joseph E. Subotnik, Robert J. Cave, Sina Yeganeh, Mark A. Ratner

All HMC Faculty Publications and Research

This article shows that, although Boys localization is usually applied to single-electron orbitals, the Boys method itself can be applied to many electron molecular states. For the two-state charge-transfer problem, we show analytically that Boys localization yields the same charge-localized diabatic states as those found by generalized Mulliken–Hush theory. We suggest that for future work in electron transfer, where systems have more than two charge centers, one may benefit by using a variant of Boys localization to construct diabatic potential energy surfaces and extract electronic coupling matrix elements. We discuss two chemical examples of Boys localization and propose a generalization …

Synthesis And Assembly Of Nonspherical Hollow Silica Colloids Under Confinement, Stephanie H. Lee, Sharon J. Gerbode, Bettina S. John, Angie K. Wolfgang, Fernando A. Escobedo, Itai Cohen, Chekesha M. Liddell

All HMC Faculty Publications and Research

Hard peanut-shaped colloids were synthesized and organized into a degenerate crystal (DC), a phase previously observed only in simulations. In this structure, particle lobes tile a triangular lattice while their orientations uniformly populate the three underlying crystalline directions.

Restricted Dislocation Motion In Crystals Of Colloidal Dimer Particles, Sharon J. Gerbode, Stephanie H. Lee, Chekesha M. Liddell, Itai Cohen

All HMC Faculty Publications and Research

Received 2 April 2008; published 1 August 2008; corrected 1 October 2008

At high area fractions, monolayers of colloidal dimer particles form a degenerate crystal (DC) structure in which the particle lobes occupy triangular lattice sites while the particles are oriented randomly along any of the three lattice directions. We report that dislocation glide in DCs is blocked by certain particle orientations. The mean number of lattice constants between such obstacles is Z̅ _exp=4.6±0.2 in experimentally observed DC grains and Z̅ _sim=6.18±0.01 in simulated monocrystalline DCs. Dislocation propagation beyond these obstacles is observed to proceed through dislocation reactions. …

Designs And Optical Tests Of Thermal Links For An Optical Refrigerator, John Parker, David Mar, Steven Von Der Porten, John Hankinson, Kevin Byram, Chris Lee, Kai Mayeda, Richard C. Haskell, Qimin Yang, Scott R. Greenfield, Richard I. Epstein

All HMC Faculty Publications and Research

Dielectric mirror leakage at large angles of incidence limits the effectiveness of solid state optical refrigerators due to reheating caused by photon absorption in an attached load. In this paper, we present several thermally conductive link solutions to greatly reduce the net photon absorption. The Los Alamos Solid State Optical Refrigerator (LASSOR) has demonstrated cooling of a Yb/sup 3+/ doped ZBLANP glass to 208 K. We have designed optically isolating thermal link geometries capable of extending cooling to a typical heat load with minimal absorptive reheating, and we have tested the optical performance of these designs. A surrogate source operating …

Computer Modeling And Analysis Of Thermal Link Performance For An Optical Refrigerator, Kevin Byram, David Mar, John Parker, Steven Von Der Porten, John Hankinson, Chris Lee, Kai Mayeda, Richard C. Haskell, Qimin Yang, Scott R. Greenfield, Richard I. Epstein

All HMC Faculty Publications and Research

We have used the thermal modeling tool in COMSOL Multiphysics to investigate factors that affect the thermal performance of the optical refrigerator. Assuming an ideal cooling element and a non-absorptive dielectric trapping mirror, the three dominant heating factors are blackbody radiation from the surrounding environment, conductive heat transfer through mechanical supports, and the absorption of fluorescent photons transmitted through the thermal link. Laboratory experimentation coupled with computer modeling using Code V optical software have resulted in link designs capable of reducing the transmission to 0.04% of the fluoresced photons emitted toward the thermal link. The ideal thermal link will have …

New Mechanism For Nonlocality From String Theory: Uv-Ir Quantum Entanglement And Its Imprints On The Cmb, Gregory Minton '08, Vatche Sahakian

All HMC Faculty Publications and Research

Puff field theories (PFT) arise as the decoupling limits of D3 branes in a Melvin universe and exhibit spatially nonlocal dynamics. Unlike other realizations of nonlocality in string theory, PFTs have full SO(3) rotational symmetry. In this work, we analyze the strongly coupled regime of a PFT through gravitational holography. We find a novel mechanism at the heart of the phenomenon of nonlocality: a quantum entanglement of UV and IR dynamics. In the holographic bulk, this translates to an apparent horizon splitting the space into two regions—with the UV completion of the PFT sitting at the horizon. We unravel this …

Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski

All HMC Faculty Publications and Research

The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerateparabolic, and admits traveling wave solutions in which the …

Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg

WM Keck Science Faculty Papers

We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to …