Criticality in multicomponent spherical models : results and cautions

To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an \ns-species hard core lattice gas. On introducing \ns spherical constraints, the free energy may be expressed generally in terms of an \ns\times\ns matrix describing the species interactions. For binary systems, thermodynamic properties have simple expressions, while all the pair correlation functions are combinations of just two eigenmodes. When only hard-core and short-range overall attractive interactions are present, a choice of variables relates the behavior to that of one-component systems. Criticality occurs on a locus terminating a coexistence surface; however, except at some special points, an unexpected ``demagnetization effect'' suppresses the normal divergence of susceptibilities at criticality and distorts two-phase coexistence. This effect, unphysical for fluids, arises from a general lack of symmetry and from the vectorial and multicomponent character of the spherical model. Its origin can be understood via a mean-field treatment of an XY spin system below criticality.Comment: 4 figure

The Force Exerted by a Molecular Motor

The stochastic driving force exerted by a single molecular motor (e.g., a kinesin, or myosin) moving on a periodic molecular track (microtubule, actin filament, etc.) is discussed from a general viewpoint open to experimental test. An elementary "barometric" relation for the driving force is introduced that (i) applies to a range of kinetic and stochastic models, (ii) is consistent with more elaborate expressions entailing explicit representations of externally applied loads and, (iii) sufficiently close to thermal equilibrium, satisfies an Einstein-type relation in terms of the velocity and diffusion coefficient of the (load-free) motor. Even in the simplest two-state models, the velocity-vs.-load plots exhibit a variety of contrasting shapes (including nonmonotonic behavior). Previously suggested bounds on the driving force are shown to be inapplicable in general by analyzing discrete jump models with waiting time distributions.Comment: submitted to PNA

Extended Kinetic Models with Waiting-Time Distributions: Exact Results

Inspired by the need for effective stochastic models to describe the complex behavior of biological motor proteins that move on linear tracks exact results are derived for the velocity and dispersion of simple linear sequential models (or one-dimensional random walks) with general waiting-time distributions. The concept of ``mechanicity'' is introduced in order to conveniently quantify departures from simple ``chemical,'' kinetic rate processes, and its significance is briefly indicated. The results are extended to more elaborate models that have finite side-branches and include death processes (to represent the detachment of a motor from the track).Comment: 17 pages, 2 figure

Screening in Ionic Systems: Simulations for the Lebowitz Length

Simulations of the Lebowitz length, $\xi_{\text{L}}(T,\rho)$, are reported for t he restricted primitive model hard-core (diameter $a$) 1:1 electrolyte for densi ties $\rho\lesssim 4\rho_c$ and $T_c \lesssim T \lesssim 40T_c$. Finite-size eff ects are elucidated for the charge fluctuations in various subdomains that serve to evaluate $\xi_{\text{L}}$. On extrapolation to the bulk limit for $T\gtrsim 10T_c$ the low-density expansions (Bekiranov and Fisher, 1998) are seen to fail badly when $\rho > {1/10}\rho_c$ (with $\rho_c a^3 \simeq 0.08$). At highe r densities $\xi_{\text{L}}$ rises above the Debye length, \xi_{\text{D}} \prop to \sqrt{T/\rho}, by 10-30% (upto $\rho\simeq 1.3\rho_c$); the variation is portrayed fairly well by generalized Debye-H\"{u}ckel theory (Lee and Fisher, 19 96). On approaching criticality at fixed $\rho$ or fixed $T$, $\xi_{\text{L}}(T, \rho)$ remains finite with $\xi_{\text{L}}^c \simeq 0.30 a \simeq 1.3 \xi_{\text {D}}^c$ but displays a weak entropy-like singularity.Comment: 4 pages 5 figure

Criticality in Charge-asymmetric Hard-sphere Ionic Fluids

Phase separation and criticality are analyzed in $z$:1 charge-asymmetric ionic fluids of equisized hard spheres by generalizing the Debye-H\"{u}ckel approach combined with ionic association, cluster solvation by charged ions, and hard-core interactions, following lines developed by Fisher and Levin (1993, 1996) for the 1:1 case (i.e., the restricted primitive model). Explicit analytical calculations for 2:1 and 3:1 systems account for ionic association into dimers, trimers, and tetramers and subsequent multipolar cluster solvation. The reduced critical temperatures, $T_c^*$ (normalized by $z$), \textit{decrease} with charge asymmetry, while the critical densities \textit{increase} rapidly with $z$. The results compare favorably with simulations and represent a distinct improvement over all current theories such as the MSA, SPB, etc. For $z$$\ne$1, the interphase Galvani (or absolute electrostatic) potential difference, $\Delta \phi(T)$, between coexisting liquid and vapor phases is calculated and found to vanish as $|T-T_c|^\beta$ when $T\to T_c-$ with, since our approximations are classical, $\beta={1/2}$. Above $T_c$, the compressibility maxima and so-called $k$-inflection loci (which aid the fast and accurate determination of the critical parameters) are found to exhibit a strong $z$-dependence.Comment: 25 pages, 14 figures; last update with typos corrected and some added reference

The heat capacity of the restricted primitive model electrolyte

The constant-volume heat capacity, C_V(T, rho), of the restricted primitive model (RPM) electrolyte is considered in the vicinity of its critical point. It is demonstrated that, despite claims, recent simulations for finite systems do not convincingly indicate the absence of a divergence in C_V(T, rho)--which would point to non-Ising-type criticality. The strong qualitative difference between C_V for the RPM and for a Lennard-Jones fluid is shown to result from the low critical density of the former. If one considers the theoretically preferable configurational heat-capacity density, C_V/V, the finite-size results for the two systems display qualitatively similar behavior on near-critical isotherms.Comment: 5 Pages, including 5 EPS figures. Also available as PDF file at http://pallas.umd.edu/~luijten/erikpubs.htm