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We derive exact results for the critical Casimir force (CCF) within the Nagle-Kardar model with periodic boundary conditions (PBC's). The model represents one-dimensional Ising chain with long-range equivalent-neighbor ferromagnetic interactions of strength $J_{l}/N>0$ superimposed on the nearest-neighbor interactions of strength $J_{s}$ which could be either ferromagnetic ($J_{s}>0$) or antiferromagnetic ($J_{s}<0$). In the infinite system limit the model exhibits in the plane $(K_s=\beta J_s,K_l=\beta J_l)$ a critical line $2 K_l=\exp{\left(-2 K_s\right)}, K_s>-\ln3/4$, which ends at a tricritical point $(K_l=-\sqrt{3}/2, K_s=-\ln3/4)$. The critical Casimir amplitudes are: $\Delta_{\rm Cas}^{\rm (cr)}=1/4$ at the critical line, and $\Delta_{\rm Cas}^{\rm (tr)}=1/3$ at the tricritical point. Quite unexpectedly, with the imposed PBC's the CCF exhibits very unusual behavior as a function of temperature and magnetic field. It is \textit{repulsive} near the critical line and tricritical point, decaying rapidly with separation from those two singular regimes fast away from them and becoming \textit{attractive}, displaying in which the maximum amplitude of the attraction exceeds the maximum amplitude of repulsion. This represents a violation of the widely-accepted ``boundary condition rule,'' which holds that the CCF is attractive for equivalent BC's and repulsive for conflicting BC's \textit{independently} of the actual bulk universality class of the phase transition under investigation., Comment: 6 pages, 3 figures; to appear in PRE as a letter

We obtain exact closed-form expressions for the partition function of the one-dimensional Ising model in the fixed-$M$ ensemble, for three commonly-used boundary conditions: periodic, antiperiodic and Dirichlet. These expressions allow for the determination of fluctuation-induced forces in the canonical ensemble, which we term Helmholtz forces. The thermodynamic expressions and the calculations flowing from them should provide insights into the nature and behavior of fluctuation induced forces in interesting and as-yet unexplored regimes., Comment: 7 pages, 6 figures. This is the version that was accepted for publication in Physical Review E Letters

Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of reaction-diffusion systems, which allow familiar techniques to be applied. The focus is largely on the appearance of soliton-like moving fronts that spread infection to previously uninfected regions. Near threshold dynamical critical behavior and a degree of universality are revealed. Extending two of the models to include a simple nonlinearity in the strength of the binary interaction between a susceptible individual and an infected one, we find the possibility of static coexistence between spatial regions with different levels of infection and an analogy with first-order transitions in thermodynamics., Comment: 37 pages, 12 figures

Single-stranded (ss) RNA viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization. However, during the self-assembly of complete viral particles in the cytoplasm of an infected cell, the viral genome molecules must be selected from a large pool of very similar host messenger RNA molecules and it is not known whether this also can be understood by free energy minimization. We address this question using a simple mathematical model recently proposed for the assembly of small ssRNA viruses (submitted to PLOS Biocomputation). We present a statistical physics analysis of the properties of the model finding an effect kinetic RNA selection mechanism with selection taking place during the formation of the nucleation complex. Surprisingly, kinetic selectivity is greatly enhanced by a modest level of supersaturation and by reduced protein to RNA concentration ratios. The mechanism is related to the Hopfield kinetic proofreading scenario., Comment: 23 pages, 23 figures. This is a significantly modified version of a previously posted manuscript, "The spanning Tree Model and the Assembly of RNA viruses", arXiv:2108.05472, in that here all assembly pathways-rather than a selected pathway-consistent with a minimum energy scenario are taken into account. arXiv admin note: text overlap with arXiv:2108.05472

Single-stranded (ss) RNA viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and the viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization of rather simple models. However, during the self-assembly of complete viral particles in the cytoplasm of an infected cell, the viral genome molecules must be selected from a large pool of very similar host messenger RNA molecules. It is known that the assembly process takes the form of preferential heterogeneous nucleation of capsid proteins on viral RNA molecules ("selective nucleation"). Recently, a simple mathematical model was proposed for the selective nucleation of small ssRNA viruses. In this paper we present a statistical physics analysis of the thermal equilibrium and kinetic properties of that model and show that it can account, at least qualitatively, for numerous observations of the self-assembly of small ssRNA viruses., Comment: 19 pages, 26 figures. Submitted to Physical Review E. arXiv admin note: text overlap with arXiv:2102.03941

We present a simple kinetic model for the assembly of small single-stranded RNA viruses that can be used to carry out analytical packaging contests between different types of RNA molecules. The RNA selection mechanism is purely kinetic and based on small differences between the assembly energy profiles. RNA molecules that win these packaging contests are characterized by having a minimum "Maximum Ladder Distance" and a maximum "Wrapping Number".The former is a topological invariant that measures the "branchiness" of the genome molecule while the latter measures the ability of the genome molecule to maximally associate with the capsid proteins. The model can also be used study the applicability of the theory of nucleation and growth to viral assembly, which breaks down with increasing strength of the RNA-protein interaction., Comment: 18 pages, 25 figures

The Landau theory of phase transitions has been productively applied to phase transitions that involve rotational symmetry breaking, such as the transition from an isotropic fluid to a nematic liquid crystal. It even can be applied to the orientational symmetry breaking of simple atomic or molecular clusters that are not true phase transitions. In this paper we address fundamental problems that arise with the Landau theory when it is applied to rotational symmetry breaking transitions of more complex particle clusters that involve order parameters characterized by larger values of the $l$ index of the dominant spherical harmonic that describes the broken symmetry state. The problems are twofold. First, one may encounter a thermodynamic instability of the expected ground state with respect to states with lower symmetry. A second problem concerns the proliferation of quartic invariants that may or may not be physical. We show that the combination of a geometrical method based on the analysis of the space of invariants, developed by Kim to study symmetry breaking of the Higgs potential, with modern visualization tools provides a resolution to these problems. The approach is applied to the outcome of numerical simulations of particle ordering on a spherical surface and to the ordering of protein shells., Comment: 32 pages, 50 figures

We present an analytical solution of an effective field theory which, in one of its formulations, is equivalent to the Ginzburg's $\Psi$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point. We consider three versions of the theory, depending on the way one determines its parameters from the experimental measurements. We present exact results for the behavior of the order parameter profiles and of the Casimir force within this theory, which is characterized by $d=3$, $\nu=2/3$ and $\beta=1/3$, where $d$ is the bulk spatial dimension and $\nu$ and $\beta$ are the usual critical exponents. In addition, we revisit relevant experiments \cite{GC99} and \cite{GSGC2006} in terms of our findings. We find reasonably good agreement between our theoretical predictions and the experimental data. We demonstrate analytically that our calculated force is attractive. The position of the extremum is predicted to be at $x_{\rm min}=\pi$, with $x=(L/\xi_0)(T/T_\lambda-1)^{1/\nu}$, which value effectively coincides with the experimental finding $x_{\rm min}=3.2\pm 0.18$. Here $L$ is the thickness of the film, $T_\lambda$ is the bulk critical temperature and $\xi_0$ is the correlation length amplitude of the system for temperature $T>T_\lambda$. The theoretically predicted position of the minimum does not depend on the one adjustable parameter, $M$, entering the theory., Comment: 18 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1803.08998

We present an analytical solution of the Ginzburg's $\Psi$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point, and we revisit the corresponding experiments in light of our findings. We find reasonably good agreement between the $\Psi$-theory predictions and the experimental data. Our calculated force is attractive, and the largest absolute value of the scaling function is $1.848$, while experiment yields $1.30$. The position of the extremum is predicted to be at $x=(L/\xi_0)(T/T_\lambda-1)^{1/\nu}=\pi$, while experiment is consistent with $x=3.8$. Here $L$ is the thickness of the film, $T_\lambda$ is the bulk critical temperature and $\xi_0$ is the correlation length amplitude of the system for $T>T_\lambda$., Comment: 8 pages, 3 figures, submitted to Phys. Rev. E

We present both exact and numerical results for the behavior of the Casimir force in $O(n)$ systems with a finite extension in one direction when the system is subjected to surface fields that induce helicity in the order parameter. We show that for such systems the Casimir force in certain temperature ranges is of the order of $L^{-2}$, both above and below the critical temperature, $T_c$, of the bulk system. An example of such a system would be one with chemically modulated bounding surfaces, in which the modulation couples directly to the system's order parameter. We demonstrate that, depending on the parameters of the system, the Casimir force can be either attractive or repulsive. The exact calculations presented are for the one dimensional $XY$ and Heisenberg models under twisted boundary conditions resulting from finite surface fields that differ in direction by a specified angle and the three dimensional Gaussian model with surface fields in the form of plane waves that are shifted in phase with respect to each other. Additionally, we present exact and numerical results for the mean field version of the three dimensional $O(2)$ model with finite surface fields on the bounding surfaces. We find that all significant results are consistent with the expectations of finite size scaling., Comment: 23 pages, 24 figures

We present a generalized Landau-Brazovskii free energy for the solidification of chiral molecules on a spherical surface in the context of the assembly of viral shells. We encounter two types of icosahedral solidification transitions. The first type is a conventional first-order phase transition from the uniform to the icosahedral state. It can be described by a single icosahedral spherical harmonic of even $l$. The chiral pseudo-scalar term in the free energy creates secondary terms with chiral character but it does not affect the thermodynamics of the transition. The second type, associated with icosahedral spherical harmonics with odd $l$, is anomalous. Pure odd $l$ icosahedral states are unstable but stability is recovered if admixture with the neighboring $l+1$ icosahedral spherical harmonic is included, generated by the non-linear terms. This is in conflict with the principle of Landau theory that symmetry-breaking transitions are characterized by only a \textit{single} irreducible representation of the symmetry group of the uniform phase and we argue that this principle should be removed from Landau theory. The chiral term now directly affects the transition because it lifts the degeneracy between two isomeric mixed-$l$ icosahedral states. A direct transition is possible only over a limited range of parameters. Outside this range, non-icosahedral states intervene. For the important case of capsid assembly dominated by $l=15$, the intervening states are found to be based on octahedral symmetry.

We present a generalized Landau-Brazovskii theory for the solidification of chiral molecules on a spherical surface. With increasing sphere radius one encounters first intervals where robust achiral density modulations appear with icosahedral symmetry via first-order transitions. Next, one en- counters intervals where fragile but stable icosahedral structures still can be constructed but only by superposition of multiple irreducible representations. Chiral icoshedral structures appear via continuous or very weakly first-order transitions. Outside these parameter intervals, icosahedral symmetry is broken along a three-fold axis or a five-fold axis. The predictions of the theory are compared with recent numerical simulations.

The proceeding comment raises a few points concerning our paper Dantchev \textit{et al.}, Phys. Rev. E. {\bf 89}, 042116 (2014). In this reply we stress that while Refs. Diehl \textit{et al.} EPL {\bf 100}, 10004 (2012) and Phys. Rev. E. {\bf 89}, 062123 (2014) use three different models to study the the Casimir force for the $O(n \rightarrow \infty)$ model with free boundary conditions we study a single model over the entire range of temperatures, from above the bulk critical temperature, $T_c$, to absolute temperatures down to $T=0$. The use of a single model renders more transparent the crossover from effects dominated by critical fluctuations in the vicinity of the bulk transition temperature to effects controlled by Goldstone modes at low temperatures. Contrary to the assertion in the comment, we make no claim for the superiority of our model over any of those considered by Diehl \textit{et al}. We also present additional evidence supporting our conclusion in Dantchev \textit{et al.}, Phys. Rev. E. {\bf 89}, 042116 (2014) that the temperature range in which our low-temperature analytical expansion for the Casimir force increases as $L$ grows and remains accurate for values of the ratio $T/T_c$ that become closer and closer to unity, while $T$ remains well outside of the critical region., Comment: 3 pages, 1 table

A model system inspired by recent experiments on the dynamics of a folded protein under the influence of a sinusoidal force is investigated and found to replicate many of the response characteristics of such a system. The essence of the model is a strongly over-damped oscillator described by a harmonic restoring force for small displacements that reversibly yields to stress under sufficiently large displacement. This simple dynamical system also reveals unexpectedly rich behavior, exhibiting a series of dynamical transitions and analogies with equilibrium thermodynamic phase transitions. The effects of noise and of inertia are briefly considered and described., Comment: 19 pages, 38 figures

We study elasticity-driven morphological transitions of soft spherical core shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response is dominated by bending. To generate the transitions, we consider the case where the surface area of the liquid layer is increased for a fixed amount of interior elastic material. We find that generically there is a critical excess surface area at which the isotropic sphere becomes unstable to buckling. At this point it adopts a lower symmetry wrinkled structure that can be described by a spherical harmonic deformation. We study the dependence of the buckled sphere and critical excess area of the transition on the elastic parameters and size of the system. We also relate our results to recent experiments on the wrinkling of gel-filled vesicles as their interior volume is reduced. The theory may have broader applications to a variety of related structures from the macroscopic to the microscopic, including the wrinkling of dried peas, raisins, as well as the cell nucleus., Comment: 12 pages, 8 figures, REVTeX 4.1

We present results for the temperature behavior of the Casimir force for a system with a film geometry with thickness $L$ subject to free boundary conditions and described by the $n\to\infty$ limit of the $O(n)$ model. These results extend over all temperatures, including the critical regime near the bulk critical temperature $T_c$, where the critical fluctuations determine the behavior of the force, and temperatures well below it, where its behavior is dictated by the Goldstone's modes contributions. The temperature behavior when the absolute temperature, $T$, is a finite distance below $T_c$, up to a logarithmic-in-$L$ proximity of the bulk critical temperature, is obtained both analytically and numerically; the critical behavior follows from numerics. The results resemble - but do not duplicate - the experimental curve behavior for the force obtained for $^4$He films., Comment: 16 pages, 3 figures, accepted for publication in Physical Review E. Abstract and author order changed to reflect the manuscript as rewritten, and comments changed to reflect the current status of the manuscript. Now published

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 $\alpha$ where $0 \le \alpha \le \pi$. 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 $\alpha$, 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 $\alpha$ and the temperature and that can be attractive or repulsive. In particular, by varying $\alpha$ 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 $\alpha=\pi$, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors., Comment: 14 pages, 9 figures

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 Painlev\'e $\tau^{IV} [n]$ 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., Comment: 4 pages, 2 figures, revtex 4.1, revised version shows no disrepancy between large N results and KTJ

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., Comment: 18 page, 10 figures

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.

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., Comment: pdflatex, 19 pages; some changes in the main text, including in few figures, and new references added; version to be published in PRE

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.

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., Comment: 12 pages, no figures

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., Comment: 15 pages, 3 figures

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.

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., Comment: 5 pages, revtex. Typo regarding localization length exponent corrected. Should read 1 / \delta

Experiments on $^4$He films reveal an attractive Casimir-like force at the bulk $\lambda$-point, and in the superfluid regime. Previous work has explained the magnitude of this force at the $\lambda$ transition and deep in the superfluid region but not the substantial attractive force immediately below the $\lambda$-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., Comment: 4 pages

We explore various properties of classical one-dimensional Wigner solids in the presence of disorder at T=0 in the context of a recently discovered Anderson transition of plasma modes in the random potential system. The extent to which the Wigner lattice is really a ``crystal'' rather than an amorphous solid is discussed for two types of disorder. We investigate the way in which zero point quantum fluctuations that would normally destroy the long range positional order are affected by the disorder. The probability density of particle spacings is examined analytically within a weak disorder approximation and compared to numerical calculations for two different realizations of disorder. We also discuss the multifractal character of the eigenmodes, the compressibility of the electrons, and the AC conductivity., Comment: 11 pages, 10 figures, revised section on crystalline order

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., Comment: 17 pages, revtex

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., Comment: 4 pages, 3 figures, Typo for the localization length corrected. Should read 1 / \nu

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., Comment: 10 pages, 17 figures

Recent experiments on the wetting of $^{4}$He have shown that the film becomes thinner at the $\lambda$ 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., Comment: 4 pages, 1 figure

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., Comment: 4 pages, 4 figures

We show that a viscoelastic dispersion relation for shear waves in normal $^{3}$He at low temperatures follows directly from the Landau theory of normal Fermi liquids. This theoretical result is in accord with the experimental observations of propagating high frequency shear waves that identify normal $^{3}$He as a viscoelastic substance., Comment: 3 pages, RevTeX4 file

We study the dynamics of the passage of a stiff chain through a pore into a cell containing particles that bind reversibly to it. Using Brownian Molecular Dynamics simulations we investigate the mean-first-passage time as a function of the length of the chain inside, for different concentrations of binding particles. As a consequence of the interactions with these particles, the chain experiences a net force along its length whose calculated value from the simulations accounts for the velocity at which it enters the cell. This force can in turn be obtained from the solution of a generalized diffusion equation incorporating an effective Langmuir adsorption free energy for the chain plus binding particles. These results suggest a role of binding particles in the translocation process which is in general quite different from that of a Brownian ratchet. Furthermore, non-equilibrium effects contribute significantly to the dynamics, \emph{e.g.}, the chain often enters the cell faster than particle binding can be saturated, resulting in a force several times smaller than the equilibrium value., Comment: 7 pages, 4 figures

Recent studies reveal that certain viruses package a portion of their genome in a manner that mirrors the icosahedral symmetry of the protein container, or capsid. Graph theoretical constraints forbid exact realization of icosahedral symmetry. This paper proposes a model for the determination of quasi-icosahedral genome structures and discusses the connection between genomic structure and viral assembly kinetics., Comment: 4 pages revtex, 4 eps figures

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rodlike limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with its linear charge density and the Debye screening of its self-interaction. An alternative definition of the electrostatic persistence length is proposed based on matching of the maximum of the distribution with that of an effective wormlike chain, as opposed to the traditional matching of the first or the second moments of the distributions. It is shown that this definition provides a more accurate probe of the affinity of the distribution to that of the wormlike chains, as compared to the traditional definition. It is also found that the length of a polyelectrolyte segment can act as a crucial parameter in determining its elastic properties., Comment: 15 pages, 19 figures

The protein shells, or capsids, of all sphere-like viruses adopt icosahedral symmetry. In the present paper we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral capsids constructed from structurally identical protein subunits and that this symmetry requires (at least) two internal "switching" configurations of the protein. Our results indicate that icosahedral symmetry is not a generic consequence of free energy minimization but requires optimization of internal structural parameters of the capsid proteins., Comment: pdf file, 13 pages, three figures

We report on a study of the shape of a stiff, charged rod that is subjected to equal and opposite force couples at its two ends. Unlike a neutral elastic rod, which forms a constant curvature configuration under such influences, the charged rod tends to flatten in the interior and accumulate the curvature in the end points, to maximally reduce the electrostatic self-repulsion. The effect of this nonuniform bending on the effective elasticity and on the statistical conformations of a fluctuating charged rod is discussed. An alternative definition for the electrostatic persistence length is suggested. This new definition is found to be consistent with a corresponding length that can be deduced from the end-to-end distribution function of a fluctuating polyelectrolyte., Comment: RevTeX 4, 10 pages, 11 eps figures

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., Comment: 10 pages, 7 eps figures, revtex4 file with assocated .bbl file

Charge transfer along the base-pair stack in DNA is modeled in terms of thermally-assisted tunneling between adjacent base pairs. Central to our approach is the notion that tunneling between fluctuating pairs is rate-limited by the requirement of their optimal alignment. We focus on this aspect of the process by modeling two adjacent base pairs in terms of a classical damped oscillator subject to thermal fluctuations as described by a Fokker-Planck equation. We find that the process is characterized by two time scales, a result that is in accord with experimental findings., Comment: original file is revtex4, 10 pages, three eps figures

A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a continuously varying order parameter as a transfer matrix calculation allows for the application of methods based on the Density Matrix Renormalization Group (DMRG) to the calculation of the free energy of the O(1) model. The essence of both the mapping and the DMRG calculation is laid out, along with results that validate this strategy. This method forms the basis of a unified approach to the crossover from three to two dimensions in an O(1) system with a slab-like geometry., Comment: ReVTeX, 7 pages, 4 figures in eps format

As sections of a strand duplexed DNA denature when exposed to high temperature, the excess linking number is taken up by the undenatured portions of the molecule. The mechanical energy that arises because of the overwinding of the undenatured sections can, in principle, alter the nature of the thermal denaturation process. Assuming that the strains associated with this overwinding are not relieved, we find that a simple model of strain-altered melting leads to a suppression of the melting transition when the unaltered transition is continuous. When the melting transition is first order in the absence of strain associated with overwinding, the modification is to a third order phase transition., Comment: 4 pages, 5 figures, RevTeX

We investigate the mechanical stability of a segment of DNA wrapped around a histone in the nucleosome configuration. The assumption underlying this investigation is that the proper model for this packaging arrangement is that of an elastic rod that is free to twist and that writhes subject to mechanical constraints. We find that the number of constraints required to stabilize the nuclesome configuration is determined by the length of the segment, the number of times the DNA wraps around the histone spool, and the specific constraints utilized. While it can be shown that four constraints suffice, in principle, to insure stability of the nucleosome, a proper choice must be made to guarantee the effectiveness of this minimal number. The optimal choice of constraints appears to bear a relation to the existence of a spiral ridge on the surface of the histone octamer. The particular configuration that we investigate is related to the 30 nanometer spiral, a higher-order organization of DNA in chromatin., Comment: ReVTeX, 15 pages, 18 figures

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in a rodlike configuration. We investigate the validity of the concept of electrostatic persistence length for uniformly charged wormlike chains for both screened and unscreened Coulomb interactions. We find that the distribution function of a polyelectrolyte often differs significantly from the distribution function of a wormlike chain., Comment: RevTeX 4, 7 pages, 6 figures

We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above $T_c$, finite-size contributions due to the {\it subleading} term in the interaction that are {\it dominant} in this region decaying algebraically as a function of $L$. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems., Comment: The version to be printed

A numerical algorithm based on the finite element methods has been developed to accurately determine the shape of the boundary of a domain containing ``boojum'' textures. Within the context of the simple model we adopt, the effects of both bulk elastic anisotropy and line-tension anisotropy on the domain boundary can be examined. It is found that line-tension anisotropy must be present in order to account for domains with protruding features. Both elastic anisotropy and anisotropic line-tension can result in domains with indentations. The numerical algorithm has been extended to investigate the problem of a bubble in extended region ordered phase., Comment: 13 pages, 16 eps figures included, submitted to Phys. Rev. E

A modified renormalization group equation for the inverse extrapolation length $c$ is derived by considering the phase shifts of order parameter fluctuations. The resulting non-linear equation is also derived using standard methods and some additional assumptions. The associated renormalized flow $c(l)$ exhibits the correct behavior near both the special and ordinary fixed points and in particular yields a canonical scaling of $c$ with cross-over exponent $\phi_{\rm ord} = -\nu$ near the ordinary transition., Comment: 5 pages, REVTEX, submitted to Phys. Rev. Lett

Domains and bubbles in tilted phases of Langmuir monolayers contain a class of textures knows as boojums. The boundaries of such domains and bubbles may display either cusp-like features or indentations. We derive analytic expressions for the textures within domains and surrounding bubbles, and for the shapes of the boundaries of these regions. The derivation is perturbative in the deviation of the bounding curve from a circle. This method is not expected to be accurate when the boundary suffers large distortions, but it does provide important clues with regard to the influence of various energetic terms on the order-parameter texture and the shape of the domain or bubble bounding curve. We also look into the effects of thermal fluctuations, which include a sample-size-dependent effective line tension., Comment: replaced with published version, 21 pages, 16 figures included