arXiv subjects

Joseph Rudnick

Publications and source records attributed to Joseph Rudnick.

At least 37 records · Page 2Linked to original sources

arXiv2011

Casimir force in the rotor model with twisted boundary conditions

We investigate the three dimensional lattice XY model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is $α$ where $0 \le α\le π$. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film---and the Casimir force it generates---as a function of the temperature $T$, the angle $α$, and the thickness $L$ of the system. Among the results of that calculation are a Casimir force that depends in a continuous way on both the parameter $α$ and the temperature and that can be attractive or repulsive. In particular, by varying $α$ and/or $T$ one controls \underline{both} the sign \underline{and} the magnitude of the Casimir force in a reversible way. Furthermore, for the case $α=π$, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors.

cond-mat.stat-mech↗

arXiv2010

Spherical spin-glass - Coulomb gas duality: solution beyond mean-field theory

We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlevé $τ^{IV} [n]$ function in the $n\to 0$ limit. The large $N$ thermodynamics exactly recovers that of Kosterlitz, Thouless and Jones \cite{ktjonesPRL}. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.

cond-mat.dis-nn↗

arXiv2010

Boundary conditions and the critical Casimir force on an Ising model film: exact results in one and two dimensions

Finite size effect in critical systems can be interpreted as universal Casimir forces. Here we compare the Casimir force for free, periodic and antiperiodic boundary conditions in the exactly calculable case of the Ising model in one and two dimensions. We employ a new procedure which allows us to calculate the Casimir force with periodic and antiperiodic boundary conditions analytically in a transparent manner. Quite interestingly, we find an attractive Casimir force for the case of periodic boundary condition but a repulsive Casimir force for the anti-periodic one.

cond-mat.stat-mech↗

arXiv2009

Electrostatic interactions between discrete helices of charge

We analytically examine the pair interaction for parallel, discrete helices of charge. Symmetry arguments allow for the energy to be decomposed into a sum of terms, each of which has an intuitive geometric interpretation. Truncated Fourier expansions for these terms allow for accurate modeling of both the axial and azimuthal terms in the interaction energy and these expressions are shown to be insensitive to the form of the interaction. The energy is evaluated numerically through application of an Ewald-like summation technique for the particular case of unscreened Coulomb interactions between the charges of the two helices. The mode structures and electrostatic energies of flexible helices are also studied. Consequences of the resulting energy expressions are considered for both F-actin and A-DNA aggregates.

cond-mat.soft↗

arXiv2009

Finite-size effects in presence of gravity: The behavior of the susceptibility in $^3He$ and $^4He$ films near the liquid-vapor critical point

We study critical point finite-size effects on the behavior of susceptibility of a film placed in the Earth's gravitational field. The fluid-fluid and substrate-fluid interactions are characterized by van der Waals-type power law tails, and the boundary conditions are consistent with bounding surfaces that strongly prefer the liquid phase of the system. Specific predictions are made with respect to the behavior of $^3$He and $^4$He films in the vicinity of their respective liquid-gas critical points. We find that for all film thicknesses of current experimental interest the combination of van der Waals interactions and gravity leads to substantial deviations from the behavior predicted by models in which all interatomic forces are very short ranged and gravity is absent. In the case of a completely short-ranged system exact mean-field analytical expressions are derived, within the continuum approach, for the behavior of both the local and the total susceptibilities.

cond-mat.stat-mech↗

arXiv2008

Anderson transition of the plasma oscillations of 1D disordered Wigner lattices

We report the existence of a localization-delocalization transition in the classical plasma modes of a one dimensional Wigner Crystal with a white noise potential environment at T=0. Finite size scaling analysis reveals a divergence of the localization length at a critical eigenfrequency. Further scaling analysis indicates power law behavior of the critical frequency in terms of the relative interaction strength of the charges. A heuristic argument for this scaling behavior is consistent with the numerical results. Additionally, we explore a particular realization of random-bond disorder in a one dimensional Wigner lattice in which all of the collective modes are observed to be localized.

cond-mat.dis-nn↗

arXiv2008

Disorder induced transition into a one-dimensional Wigner glass

The destruction of quasi-long range crystalline order as a consequence of strong disorder effects is shown to accompany the strict localization of all classical plasma modes of one-dimensional Wigner crystals at T=0. We construct a phase diagram that relates the structural phase properties of Wigner crystals to a plasmon delocalization transition recently reported. Deep inside the strictly localized phase of the strong disorder regime, we observe ``glass-like'' behavior. However, well into the critical phase with a plasmon mobility edge, the system retains its crystalline composition. We predict that a transition between the two phases occurs at a critical value of the relative disorder strength. This transition has an experimental signature in the AC conductivity as a local maximum of the largest spectral amplitude as a function of the relative disorder strength.

cond-mat.dis-nn↗

arXiv2008

Conformation of single-stranded RNA in a virus capsid: implications of dimensional reduction

The statistical mechanics of a treelike polymer in a confining volume is relevant to the packaging of the genome in RNA viruses. Making use of the mapping of the grand partition function of this system onto the statistical mechanics of a hard-core gas in two fewer spatial dimensions and of techniques developed for the evaluation of the equilibrium properties of a one-dimensional hard rod gas, we show how it is possible to determine the density and other key properties of a collection of rooted excluded-volume tress confined between two walls, both in the absence and in the presence of a one-dimensional external potential. We find, somewhat surprisingly, that in the case of key quantities, the statistical mechanics of the excluded volume, randomly branched polymer map exactly into corresponding problems for an unrestricted linear polymer.

cond-mat.stat-mech↗

arXiv2008

The confinement free energies of non-ideal branched polymers and ideal unbranched polymers are the same

We use the method of dimensional reduction to show that a branching polymer with excluded volume interaction confined between two flat plates has, in the thermodynamic limit, a confinement free energy and density profile that is the same as that of an ideal linear polymer with the same number of monomers and the same monomer-plate interaction potential. Condensation due to branching is exactly compensated by swelling due to excluded volume interaction.

cond-mat.stat-mech↗

arXiv2007

Nucleosome Switching

We present a statistical-mechanical analysis of the positioning of nucleosomes along one of the chromosomes of yeast DNA as a function of the strength of the binding potential and of the chemical potential of the nucleosomes. We find a significant density of two-level nucleosome switching regions where, as a function of the chemical potential, the nucleosome distribution undergoes a "micro" first-order transition. The location of these nucleosome switches shows a strong correlation with the location of transcription-factor binding sites.

cond-mat.soft↗

arXiv2007

Effect of external stress on the thermal melting of DNA

We discuss the effects of external stress on the thermal denaturation of homogeneous DNA. Pulling double-stranded DNA at each end exerts a profound effect on the thermal denaturation, or melting, of a long segment of this molecule. We discuss the effects on this transition of a stretching force applied to opposite ends of one of the DNA strands, including full consideration of the consequences of excluded volume, the analysis of which is greatly simplified in this case. We also discuss the interplay of thermal denaturation and force-generated separation when the tension is generated by a force at the end of the duplexed strands and an equal and opposite force is applied to the other end of the second strand.

cond-mat.soft↗

arXiv2007

Exact longitudinal plasmon dispersion relations for one and two dimensional Wigner crystals

We derive the exact longitudinal plasmon dispersion relations, $ω(k)$ of classical one and two dimensional Wigner crystals at T=0 from the real space equations of motion, of which properly accounts for the full unscreened Coulomb interactions. We make use of the polylogarithm function in order to evaluate the infinite lattice sums of the electrostatic force constants. From our exact results we recover the correct long-wavelength behavior of previous approximate methods. In 1D, $ω(k) \sim | k |\log ^{1/2} (1/k)$, validating the known RPA and bosonization form. In 2D $ω(k) \sim \sqrt k$, agreeing remarkably with the celebrated Ewald summation result. Additionally, we extend this analysis to calculate the band structure of tight-binding models of non-interacting electrons with arbitrary power law hopping.

cond-mat.str-el↗

arXiv2007

Thinning of superfluid films below the critical point

Experiments on $^4$He films reveal an attractive Casimir-like force at the bulk $λ$-point, and in the superfluid regime. Previous work has explained the magnitude of this force at the $λ$ transition and deep in the superfluid region but not the substantial attractive force immediately below the $λ$-point. Utilizing a simple mean-field calculation renormalized by critical fluctuations we obtain an effective Casimir force that is qualitatively consistent with the scaling function $\vartheta$ obtained by collapse of experimental data.

cond-mat.stat-mech↗

arXiv2006

Finite-size effects on the behavior of the susceptibility in van der Waals films under $+,+$ boundary conditions

We study critical point finite-size effects in the case of the susceptibility of a film in which interactions are characterized by a van der Waals-type power law tail. The geometry is appropriate to a slab-like system with two bounding surfaces. Boundary conditions are consistent with surfaces that both prefer the same phase in the low temperature, or broken symmetry, state. We take into account both interactions within the system and interactions between the constituents of the system and the material surrounding it. Specific predictions are made with respect to the behavior of a $^3$He and $^4$He films in the vicinity of their respective liquid-vapor critical points.

cond-mat.stat-mech↗

arXiv2005

Soft elasticity of RNA gels and negative Poisson ratio

We propose a model for the elastic properties of RNA gels. The model predicts anomalous elastic properties in the form of a negative Poisson ratio and shape instabilities. The anomalous elasticity is generated by the non-Gaussian force-deformation relation of single-stranded RNA. The effect is greatly magnified by broken rotational symmetry produced by double-stranded sequences and the concomitant soft modes of uniaxial elastomers.

cond-mat.soft↗

arXiv2004

Casimir forces, surface fluctuations, and thinning of superfluid films

Recent experiments on the wetting of $^{4}$He have shown that the film becomes thinner at the $λ$ transition, and in the superfluid phase. The difference in thickness above and below the transition has been attributed to a Casimir interaction which is a consequence of a broken continuous symmetry in the bulk superfluid. However, the observed thinning of the film is larger than can be accounted by this Casimir force. We show that surface fluctuations give rise to an additional force, similar in form but larger in magnitude, which may explain the observations.

cond-mat.stat-mech↗

arXiv2003

Anomalous Buckling of Charged Rods

Unscreened electrostatic interactions exert a profound effect on the onset of the buckling instability of a charged rod. When this interaction is unscreened, the threshold value of the compressional force needed to induce buckling is independent of rod length for sufficiently long rods. In the case of rods of intermediate length, the critical buckling force crosses over from the classic inverse-square length dependence to asymptotic length-independent form with increasing rod length. It is suggested that this effect might lead to the possibility of the ``electromechanical'' stiffening of nanotubes, which would allow relatively long segments of them to be used as atomic force probes.

cond-mat.soft↗

arXiv2003

Cohesive energy, stability and structural transitions in polyelectrolyte bundles

A lattice of uniformly charged, infinitesimally thin, rods decorated with an ordered array of counterions exhibits anomalous behavior as the spacing between the rods is varied. In particular, the counterion lattice undergoes a sequence of structural shearing, or "tilting," phase transformations as the spacing between the rods decreases. The potential implications of this behavior with respect to the packaging of biologically relevant polyelectrolytic molecules are commented upon.

cond-mat.soft↗