Department of Physics Papers
The aim of physicists is to discover the most fundamental principles of nature. Their tools are mathematics and experiment. The physical world as we perceive it is very complex, yet the principles of Physics are inherently simple. A physicist's forte is the ability to analyze a problem, reduce its complexity, and arrive at an understanding of the underlying patterns of nature in terms of simple relationships among constituent elements. Learning to do this gives Physics majors an intellectual versatility that can serve them well in a variety of future activities ranging from research and teaching in Physics or related sciences to careers in law, the health professions, and high-technology companies.
PublicationLow-Frequency Response Functions of Random Magnetic Systems(1977-07-01) Harris, A. Brooks; Kirkpatrick, Scott RThe frequencies of long-wavelength spin waves in random magnets are studied through their relation to the static magnetic elastic constants A, the domain-wall stiffness, and (for antiferromagnets) χ⊥, the perpendicular susceptibility. We treat the classical limit of large spin and low temperature. In the case of random dilution A and χ⊥ are evaluated numerically as a function of magnetic concentration p for common lattices. Exact analytic results for the static susceptibility, χ(q), where q is the wave vector, are given for some models of disorder in one dimension and, for higher dimensionality, in the limit of low concentrations of vacancies. One general conclusion is that local fluctuations in the spin magnitude significantly affect χ⊥, causing it to diverge for isotropic random systems in two or fewer dimensions. If critical exponents are defined for p→pc by A~|p−pc|σ, χ⊥~|p−pc|−τ, P~|p−pc|β, and ξ~|p−pc|−ν, where pc is the percolation threshold, P is the percolation probability, and ξ is the correlation length, then our numerical results in three dimensions yield σ=1.6±0.1 and τ=0.5±0.2. A simple physical argument shows that τ≥σ−β+(2−d)ν. Our data are consistent with the possibility that this is an equality. Using mean-field-theory values for the exponents in this relation leads to a critical dimensionality dc=6. We study pc, A, and χ⊥ in diluted YIG and mixed garnets and give a detailed discussion of the regime near angular momentum compensation, where a low-frequency optical mode with both ω∝q and ω∝q2 regimes occurs. Our work contradicts the common assumption of a concentration-independent relationship between Tc and A or D, the spin-wave stiffness. We also present nonlinear calculations which allow us to study the dependence of χ⊥ on magnetic field. Our calculations agree with the experimental results on diluted KMnF3 and K2MnF4 and show that the observed nonlinearity is largely the result of local ferrimagnetic fluctuations. A novel configuration for elastic neutron scattering in the presence of a transverse magnetic field is proposed to permit direct observation of the magnitude and characteristic length scale of these fluctuations. PublicationResistance Fluctuations in Randomly Diluted Networks(1987-03-01) Blumenfeld, Raphael; Meir, Yigal; Aharony, Amnon; Harris, A. BrooksThe resistance R(x,x’) between two connected terminals in a randomly diluted resistor network is studied on a d-dimensional hypercubic lattice at the percolation threshold pc. When each individual resistor has a small random component of resistance, R(x,x’) becomes a random variable with an associated probability distribution, which contains information on the distribution of currents in the individual resistors. The noise measured between the terminals may be characterized by the cumulants Mq(x,x’) of R(x,x’). When averaged over configurations of clusters, M¯q(x,x’)~‖x-x’‖ψ̃(q). We construct low-concentration series for the generalized resistive susceptibility, χ(q), associated with M¯q, from which the critical exponents ψ̃(q) are obtained. We prove that ψ̃(q) is a convex monotonically decreasing function of q, which has the special values ψ̃(0)=DB, ψ̃(1)=ζ̃R, and ψ̃(∞)=1/ν. (DB is the fractal dimension of the backbone, ζ̃R is the usual scaling exponent for the average resistance, and ν is the correlation-length exponent.) Using the convexity property and the accepted values of these three exponents, we construct two approximant functions for ψ(q)=ψ̃(q)ν, both of which agree with the series results for all q>1 and with existing numerical simulations. These approximants enabled us to obtain explicit approximate forms for the multifractal functions α(q) and f(q) which, for a given q, characterize the scaling with size of the dominant value of the current and the number of bonds having this current. This scaling description fails for sufficiently large negative q, when the dominant (small) current decreases exponentially with size. In this case χ(q) diverges at a lower threshold p*(q), which vanishes as q→-∞. PublicationSpontaneous Expulsion of Giant Lipid Vesicles Induced by Laser Tweezers(1997) Moroz, J David; Nelson, Philip C; Bar-Ziv, Roy; Moses, ElishaIrradiation of a giant unilamellar lipid bilayer vesicle with a focused laser spot leads to a tense pressurized state which persists indefinitely after laser shutoff. If the vesicle contains another object it can then be gently and continuously expelled from the tense outer vesicle. Remarkably, the inner object can be almost as large as the parent vesicle; its volume is replaced during the exit process. We offer a qualitative theoretical model to explain these and related phenomena. The main hypothesis is that the laser trap pulls in lipid and ejects it in the form of submicron objects, whose osmotic activity then drives the expulsion. PublicationThe Dilaton Equation in Semirigid String Theory(1991-12-01) Distler, Jacques; Nelson, Philip CWe show how to obtain explicit integration measures on ordinary moduli space corresponding to the correlation functions of pure 2-dimensional topological gravity. In particular our prescription tells how to remove the zero modes of the βγ system. We then use our formula to derive the “dilaton equation” introduced by E. Verlinde and H. Verlinde,a relation between the N-point and (N − 1)-point correlations of this theory. Just as incritical string theory we use the fact that certain brst-exact states fail to decouple. Instead they build up ˇ Cech classes, in this instance the Euler class of an N-times punctured surface. Throughout we use the “semirigid” formulation of topological gravity. Thus theLiouville sector of other approaches never enters. PublicationStress Tensor Perturbations in Conformal Field Theory(1991-11-01) Campbell, Marc; Nelson, Philip C; Wong, EugeneWe reconsider the problem of deforming a conformal ﬁeld theory to a neighboring theory which is again critical. An invariant formulation of this problem is important for understanding the underlying symmetry of string theory. We give a simple derivation of A. Sen’s recent formula for the change in the stress tensor and show that, when correctly interpreted, it is coordinate-invariant. We give the corresponding superconformal perturbation for superﬁeld backgrounds and explain why it has no direct analog for spin-ﬁeld backgrounds. PublicationKinetics of Gravity-Driven Water Channels Under Steady Rainfall(2014-10-21) Cejas, Cesare M; Wei, Yuli; Barrois, Rémi; Frétigny, Christian; Durian, Douglas J; Dreyfus, RémiWe investigate the formation of fingered flow in dry granular media under simulated rainfall using a quasi-two-dimensional experimental setup composed of a random close packing of monodisperse glass beads. Using controlled experiments, we analyze the finger instabilities that develop from the wetting front as a function of fundamental granular (particle size) and fluid properties (rainfall, viscosity). These finger instabilities act as precursors for water channels, which serve as outlets for water drainage. We look into the characteristics of the homogeneous wetting front and channel size as well as estimate relevant time scales involved in the instability formation and the velocity of the channel fingertip. We compare our experimental results with that of the well-known prediction developed by Parlange and Hill [D. E. Hill and J. Y. Parlange, Soil Sci. Soc. Am. Proc. 36, 697 (1972)]. This model is based on linear stability analysis of the growth of perturbations arising at the interface between two immiscible fluids. Results show that, in terms of morphology, experiments agree with the proposed model. However, in terms of kinetics we nevertheless account for another term that describes the homogenization of the wetting front. This result shows that the manner we introduce the fluid to a porous medium can also influence the formation of finger instabilities. The results also help us to calculate the ideal flow rate needed for homogeneous distribution of water in the soil and minimization of runoff, given the grain size, fluid density, and fluid viscosity. This could have applications in optimizing use of irrigation water. PublicationColloidal Particle Motion as a Diagnostic of DNA Conformational Transitions(2007-12-01) Nelson, Philip CTethered particle motion is an experimental technique to monitor conformational changes in single molecules of DNA in real time, by observing the position fluctuations of a micrometer-size particle attached to the DNA. This article reviews some recent work on theoretical problems inherent in the interpretation of TPM experiments, both in equilibrium and dynamical aspects. PublicationOrientational Phases for M3C60(1993-10-15) Yildirim, Taner; Harris, A. Brooks; Mele, Eugene J; Hong, SuklyunThe mechanism of the orientational ordering of C60 in alkali-metal-doped fullerenes M3C60 is studied. Since the M-C60 (M=K,Rb) interactions cause the C60 molecules to assume one of two standard orientations, this model is equivalent to a generalized Ising model on a fcc lattice. The Ising interactions depend on two type of energies: (1) the direct interaction, i.e., the orientationally dependent part of interactions between nearest-neighboring C60 molecules (each carrying charge -3e), and (2) the band energy of the electrons transferred from M+ ions to the C603- ions. It is shown that the contribution to the pairwise interaction from the direct orientational interaction is ferromagnetic and dominantly nearest neighbor. However, contributions from the band (kinetic) energy of the conduction electrons are found to be antiferromagnetic for first- and third-nearest neighbors, ferromagnetic for second- and fourth-nearest neighbors, and negligible for further neighbors. The total first-neighbor interaction is probably antiferromagnetic. a non-negligible four-spin interaction is also obtained. The implication of these results for the orientational structure is discussed. PublicationSeries Analysis of Randomly Diluted Nonlinear Resistor Networks(1986-09-01) Meir, Yigal; Blumenfeld, Raphael; Aharony, Amnon; Harris, A. BrooksThe behavior of a randomly diluted network of nonlinear resistors, for each of which the voltage-current relationship is |V|=r|I|α, is studied with use of series expansions in the concentration p of conducting bonds on d-dimensional hypercubic lattices. The average nonlinear resistance 〈R〉 between pairs of sites separated by the percolation correlation length, scales as |p-pc|−ζ(α). The exponent ζ(α) was evaluated for 0<α<∞ and d=2, 3, 4, 5, and 6, found to decrease monotonically from the exponent describing the minimal length, at α=0, via that of the linear resistance, at α=1, to the exponent characterizing the singly connected bonds, ξ(∞)≡1. Our results agree with known results for α=0 and α=1, also with recent results for general α at d=6-ε dimensions. The second moment 〈R2〉 was found to diverge as 〈R⟩2 (for all α and d), indicating a scaling form for the probability distribution of R. PublicationFirst-Principles Calculation of DNA Looping in Tethered Particle Experiments(2009-07-01) Towles, Kevin; Beausang, John; Garcia, Hernan; Phillips, Rob; Nelson, Philip CWe calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in tethered particle motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. It assumes a harmonic elastic energy function (or wormlike chain type elasticity), but our Monte Carlo calculation scheme is flexible enough to accommodate arbitrary elastic energy functions. We show how to compute both the 'looping J factor' (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on TPM, and then compare to our model's predictions. In particular, we present a new method to correct observed data for finite camera shutter time and other experimental effects. Although the currently available experimental data give large uncertainties, our first-principles predictions for the looping free energy change are confirmed to within about 1 k(B)T, for loops of length around 300 basepairs. More significantly, our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical 'open' conformation of the LacI tetramer.