4,729 research outputs found

### 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

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