The dynamics of the open or closed state region of an ion channel may be described by a probability density $p(x,t)$ which satisfies a Fokker-Planck equation. The closed state dwell-time distribution $f_c\left(t\right)$ derived from the Fokker-Planck equation with a nonlinear diffusion coefficient $D\left(x\right)\propto \exp (-\gamma x)$, $\gamma >0$ and a linear ramp potential $U_c\left(x\right)$, is in good agreement with experimental data and it may be shown analytically that if $\gamma$ is sufficiently large, $f_c\left(t\right)\propto t^{-2-\nu }$ for intermediate times, where $\nu =U_c^{\prime }∕\gamma \approx -0.3$ for a fast Cl channel. The solution of a master equation which approximates the Fokker-Planck equation exhibits an oscillation superimposed on the power law trend and can account for an empirical rate-amplitude correlation that applies to several ion channels.

We analyze a simple discrete-time stochastic process for the theoretical modeling of the evolution of protein lengths. At every step of the process, a new protein is produced as a modification of one of the proteins already existing, and its length is assumed to be a random variable that depends only on the length of the originating protein. Thus a random recursive tree is produced over the natural numbers. If (quasi) scale invariance is assumed, the length distribution in a single history tends to a log-normal form with a specific signature of the deviations from exact Gaussianity. Comparison with the very large Similarity Matrix of Proteins database shows good agreement.

Interaction of DNA with oppositely charged objects, such as multivalent ions, cationic surfactants, cationic liposomes, basic proteins, and alcohols, up to nano- or mesoscopic particles, gives rise to a very interesting and fascinating phenomenology, where the shape, size, and stability of the resulting aggregates depend on a delicate balance between different driving forces, mainly of electrostatic origin. We have studied the cationic liposome-DNA complexes during the whole complexation process, below, close to, and above the isoelectric condition, where the number of cationic lipids equals the number of phosphate groups on the DNA chain. We took advantage of the combined use of dynamic light scattering, laser Doppler electrophoretic mobility, and radio-wave dielectric relaxation measurements in order to characterize both the structural parameters (hydrodynamic radius) and the electrical parameters (charge and counterion concentration) of the resulting structures. These structures are fundamentally of two types, clusters of liposomes stuck together by DNA chains (cluster phase in low-density colloidal suspension) and coexisting DNA coils and DNA globules, according to the procedure through which interactions occur (liposomes in excess DNA solution or DNA in excess liposome suspension).

There is experimental evidence that the neuronal network in some areas of the brain cortex presents the scale-free property, i.e., the neuron connectivity is distributed according to a power law, such that neurons are more likely to couple with other already well-connected ones. From the information processing point of view, it is relevant that neuron bursting activity be synchronized in some weak sense. A coherent output of coupled neurons in a network can be described through the chaotic phase synchronization of their bursting activity. We investigated this phenomenon using a two-dimensional map to describe neurons with spiking-bursting activity in a scale-free network, in particular the dependence of the chaotic phase synchronization on the coupling properties of the network as well as its synchronization with an externally applied time-periodic signal.

We discuss some aspects of interactions of high-frequency electromagnetic waves with plasmas, assuming that the intensity of radiation is sufficiently large, so that the photon-photon interaction is more likely than the photon-plasma particle interaction. In the stationary limit, solving the kinetic equation of the photon gas, we derive a distribution function. With this distribution function at hand, we investigate the adiabatic photon self-capture and obtain the number density of the trapped photons. We employ the distribution function to calculate the thermodynamic quantities for the photon gas. Having expressions of the entropy and the pressure of the photon gas, we define the heat capacities and exhibit the existence of the ratio of the specific heats $\Gamma$, which equals $7∕6$ for nonrelativistic temperatures. In addition, we disclose the magnitude of the mean square fluctuation of the number of photons. Finally, we discuss the uniform expansion of the photon gas.

The aim of this work was to perform a complete study of the dynamic and steady-state photoinduced processes of thick bacteriorhodopsin (bR) films, taking into account all the physical parameters and the coupling of rate equations with the energy transfer equation. The theoretical approach was compared with experimental data, and good concordance was found between both sets of data. The theoretical approach shows that the values of the rate constants for solid bR films are about two or three orders of magnitude lower than those observed in solution. It can also be noted that the temperature change during the experiment had a great influence on the final values of transmittance and, consequently, on the inhomogeneous distribution along the coordinate of light propagation. The study shows that, depending on the intensity and wavelength of the pump beam, we can obtain a very inhomogeneous profile of the population densities, which implies an inhomogeneous profile of the birefringence and dichroism. Therefore, this must be taken into account in the applications described for this system.

In this paper, we study particle plasmons associated with a chain of metal nanospheres by the method of multiple scattering. The extinction efficiency is used to identify the resonant modes in nanoparticle chains. Special emphasis is placed upon the multipolar nature of particle plasmons at two major resonant modes by studying the associated field patterns, surface charges, and distributions of the field enhancement. Effects of the number of particles, interparticle spacing, and particle alignment are investigated by examining the frequency shift, bandwidth, and the number of resonant modes.

We present a control algorithm to eliminate spurious density fluctuations associated with the coupling of atomistic and continuum descriptions for dense liquids. A Schwartz domain decomposition algorithm is employed to couple molecular dynamics for the simulation of the atomistic system with a continuum solver for the simulation of the Navier-Stokes equations. The lack of periodic boundary conditions in the molecular dynamics simulations hinders the proper accounting for the virial pressure leading to spurious density fluctuations at the continuum-atomistic interface. An ad hoc boundary force is usually employed to remedy this situation. We propose the calculation of this boundary force using a control algorithm that explicitly cancels the density fluctuations. The results demonstrate that the present approach outperforms state-of-the-art algorithms. The conceptual and algorithmic simplicity of the method makes it suitable for any type of coupling between atomistic and continuum descriptions of dense fluids.

An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried out. The calculation is based on an $ϵ$ expansion in the correlation exponent: $C\left(t\right)={\mid t\mid }^{-1+ϵ}$. The fixed point of the theory is associated with stretched exponential scaling of the distribution; analytical expressions have been provided in the preasymptotic regime. Also, the permanence time distribution appears to be characterized by stretched exponential scaling. The conditions for application of the theory to non-Gaussian processes have been analyzed and the relations with the issue of return times in the case of multifractal measures have been discussed.

The friction coefficient of a particle can depend on its position, as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show that the requirement that a particle’s distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number of examples with spatially varying diffusion coefficients. We also derive a path integral representation for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

For large energy barrier systems the lattice vibrations can play an important role in the diffusion of a guest component inside channeled structures. Here, quantum corrections to the guest diffusion are studied within a semiclassical framework in which the guest behaves classically and the lattice quantum mechanically. The permeability is expressed in terms of correlation functions that are calculated using path integrals. Forward-backward path integrals for propagators are combined, and, using the Martin-Siggia-Rose formalism [Phys. Rev. A. 8, 423 (1973)], are transformed into a set of generalized Langevin equations that reduce to the classical equation of motion at high temperatures. The random initial conditions to these equations are specified by the density matrix from which an approximate expression for the quantum mechanical potential of mean force is derived. The quantum potential of mean force and activation energy obtained for the guest inside the lattice is slightly higher than the one for the fully classical system, and the diffusion of the guest in the quantum lattice is slower compared to its fully classical counterpart. The macroscopic intrinsic permeability of $\alpha$-quartz towards neon is reported, $P_{\mathrm{qtm}}^{\prime }\left(300\mathrm{K}\right)=9.91\times {10}^8\mathrm{s}∕\left(\mathrm{mkg}\right)$ within the semiclassical approximation and is lower than $P_{\mathrm{class}}^{\prime }\left(300\mathrm{K}\right)=1.26\times {10}^9\mathrm{s}∕\left(\mathrm{mkg}\right)$ obtained in the classical case at $300\mathrm{K}$ for the same potential model.

It is a fundamental physical problem how a state is selected in a nonequilibrium steady state where the energy is continuously dissipated. This problem is common to phase transitions in liquids under shear flow and those in solids under deformation or electric current. In particular, soft matter often exhibits a strong nonlinear response to an external field, since its structural susceptibility to the external field is extremely large due to its softness and flexibility. Here we study the nucleation and growth process of the lamellar phase from the sponge phase under shear flow in a bilayer-forming surfactant system. We found an interesting shape selection of lamellar nuclei under shear flow between multilamellar vesicles (onions) and cylinders (leeks). These two types of behavior are separated sharply at a critical shear rate: a slight change of the shear rate is enough to switch one behavior to the other. We also found that, under a sufficiently strong shear flow, nucleated onions decrease their size with time, and eventually transform into leeks. This suggests that leeks may be the stable morphology under steady shear flow. However, the stability is limited only to the lamellar-sponge coexistence region. When a system enters into the lamellar phase region by further cooling, leeks lose their stability and break up into rather monodisperse onions, presumably via Rayleigh-like instability of a fluid tube. On the basis of these results, we draw a dynamic state diagram of smectic membrane organization under shear flow.

The occurrence of glass transition is believed to be associated to cooperative motion with a growing length scale with decreasing temperature. We provide a route to calculate the size of cooperatively rearranging regions (CRR) of glass-forming polymers combining the Adam-Gibbs theory of the glass transition with the self-concentration concept. To do so we explore the dynamics of glass-forming polymers in different environments. The material specific parameter $\alpha$ connecting the size of the CRR to the configurational entropy is obtained in this way. Thereby, the size of CRR can be precisely quantified in absolute values. This size results to be in the range $1–3\mathrm{nm}$ at the glass transition temperature depending on the glass-forming polymer.

We study the ground state properties of classical Coulomb charges interacting with a $1∕r$ potential moving on a plane but confined either by a circular hard-wall boundary or by a harmonic potential. The charge density in the continuum limit is determined analytically and is nonuniform. Because of the nonuniform density there are both disclinations and dislocations present and their distribution across the system is calculated and shown to be in agreement with numerical studies of the ground state (or at least low-energy states) of $N$ charges, where values of $N$ up to 5000 have been studied. A consequence of these defects is that although the charges locally form into a triangular lattice structure, the lattice lines acquire a marked curvature. A study is made of conformal crystals to illuminate the origin of this curvature. The scaling of various terms which contribute to the overall energy of the system of charges, viz., the continuum electrostatic energy, correlation energy, surface energy (and so on) as a function of the number of particles $N$ is determined. “Magic number” clusters are those at special values of $N$ whose energies take them below the energy estimated from the scaling forms and are identified with charge arrangements of high symmetry.

Under inversion in any (interior) point, a catenoid transforms into a deflated compact geometry which touches at two points (its poles). The catenoid is a minimal surface and, as such, is an equilibrium shape of a symmetric fluid membrane. The conformal symmetry of the Hamiltonian implies that inverted minimal surfaces are also equilibrium shapes. However, they will exhibit curvature singularities at their poles. Such singularities are the geometrical signature of the external forces required to pull the poles together. These forces will set up stresses in the inverted shapes. Tuning the force corresponds geometrically to the translation of the point of inversion. For any fixed surface area, there will be a maximum force. The associated shape is a symmetric discocyte. Lowering the external force will induce a transition from the discocyte to a cup-shaped stomatocyte.

The determination of the flow transitions in a cavity heated from the side in low-Prandtl-number fluids has been a challenge for many years. Contrarily to the Rayleigh-Bénard situation, these transitions occur in already very intense convective flows, and the problem has been up to now mainly treated in two-dimensional situations. Thanks to a performing numerical method, the thresholds corresponding to the first flow transition in a three-dimensional (3D) parallelepipedic cavity have been determined for a wide range of aspect ratios and Prandtl number values. We obtain a kind of map of the transitions involved. Such a map of transitions is quite usual for Rayleigh-Bénard or Marangoni-Bénard situations, but completely new for 3D cavities heated from the side. The most striking result is the very frequent change of stability branches when the aspect ratios or Prandtl number are changed, which indicates different flow structures triggered at the thresholds, either steady or oscillatory, and breaking some of the symmetries of the problem.

We study cluster-cluster aggregation and fragmentation with a periodically modulated binding rate. Using the Smoluchowski mean-field equations, we derive exact solutions for the cluster size distribution for two time courses of the binding rate: (i) harmonic modulations and (ii) on-off switching of the binding rate with dwell times ${\tau }_b$ and ${\tau }_f$. In both cases, the asymptotic cluster size distribution is oscillatory in time. The formation of small-sized clusters is enhanced compared to a constant binding rate below a critical cluster size $s_c$. There is another critical cluster size $s_p$ close to which the size distribution becomes quasistationary. We calculate analytically the dependence of the critical points $s_c$ and $s_p$ on the relevant system parameters for on-off switching of the binding rate. Our results are relevant whenever clustering can be externally controlled.

Using general scaling arguments combined with mean-field theory we investigate the critical $(T\simeq T_c)$ and off-critical $(T\ne T_c)$ behavior of the Casimir forces in fluid films of thickness $L$ governed by dispersion forces and exposed to long-ranged substrate potentials which are taken to be equal on both sides of the film. We study the resulting effective force acting on the confining substrates as a function of $T$ and of the chemical potential $\mu$. We find that the total force is attractive both below and above $T_c$. If, however, the direct substrate-substrate contribution is subtracted, the force is repulsive everywhere except near the bulk critical point $(T_c,{\mu }_c)$, where critical density fluctuations arise, or except at low temperatures and $(L∕a)\left(\beta \Delta \mu \right)=O\left(1\right)$, with $\Delta \mu =\mu -{\mu }_c<0$ and $a$ the characteristic distance between the molecules of the fluid, i.e., in the capillary condensation regime. While near the critical point the maximal amplitude of the attractive force if of order of $L^{-d}$ in the capillary condensation regime the force is much stronger with maximal amplitude decaying as $L^{-1}$. In the latter regime we observe that the long-ranged tails of the fluid-fluid and the substrate-fluid interactions further increase that amplitude in comparison with systems with short-range interactions only. Although in the critical region the system under consideration asymptotically belongs to the Ising universality class with short-ranged forces, we find deviations from the standard finite-size scaling for $\xi \ln (\xi ∕{\xi }_0^{\pm })⪢L$ even for $\xi ,L⪢{\xi }_0^{\pm }$, where $\xi [t=(T-T_c)∕T_c\to \pm 0,\Delta \mu =0]={\xi }_0^{\pm }{\mid t\mid }^{-\nu }$, is the bulk correlation length. In this regime the dominant finite-size contributions to the free energy and to the force stem from the long-ranged algebraically decaying tails of the interactions; they are not exponentially small in $L$, as it is the case there in systems governed by purely short-ranged interactions, but exhibit a power law decay in $L$. Essential deviations from the standard finite-size scaling behavior are observed also within the finite-size critical region $L∕\xi =O\left(1\right)$ for films with thicknesses $L\lesssim L_{\mathrm{crit}}$, where $L_{\mathrm{crit}}={\xi }_0^{\pm }{\left(16\mid s\mid \right)}^{\nu ∕\beta }$, with $\nu$ and $\beta$ as the standard bulk critical exponents and with $s=O\left(1\right)$ as the dimensionless parameter that characterizes the relative strength of the long-ranged tail of the substrate fluid over the fluid-fluid interaction. We present the modified finite-size scaling pertinent for such a case and analyze in detail the finite-size behavior in this region. The standard finite-size scaling behavior is recovered only for $L⪢L_{\mathrm{crit}}$.

When a fluid surface adheres to a substrate, the location of the contact line adjusts in order to minimize the overall energy. This implies boundary conditions which depend on the characteristic surface deformation energies. We develop a general geometrical framework within which these conditions can be derived in a completely systematic way. We treat both adhesion to a rigid substrate and adhesion between two fluid surfaces, and illustrate our general results for several important Hamiltonians involving both curvature and curvature gradients. Some of these have previously been studied using very different techniques. With the exception of capillary phenomena, the Hamiltonian will not only be sensitive to boundary translations, but may also respond to changes in slope and even in curvature. The functional form of the additional contributions will follow readily from our treatment. We will show that the boundary conditions describing adhesion between two fluid surfaces express the balance of stresses and torques, as one would expect. At a rigid substrate, however, this simple identification will generally fail. This is because local rotations of the surface normal will be entirely “enslaved” to translations on the substrate. As a consequence, stresses and torques enter a single balance condition and cannot be disentangled.

We report computation results obtained from extensive coarse-grained molecular-dynamics simulations of amorphous ensembles of polymer chains at constant density. In our polymer model, we use bending and torsion potentials acting along the polymer backbone to control the chain stiffness. The static and dynamic properties of the polymer bulk have been analyzed over a large temperature interval in search for the onset of the glass transition. The glass transition temperatures $T_{\mathrm{g}}$, for different types of chain stiffness, have been determined from the dependence of the self-diffusion coefficient $D$ on the temperature $T$ as the limiting value where the diffusion vanishes. Increasing the chain stiffness induces an increase of the glass transition temperature. The $T_{\mathrm{g}}$ values estimated from diffusion are confirmed by analyzing the relaxation times of the autocorrelation functions for the torsion angle and for the end-to-end vector. The dependence of the diffusion coefficient $D$ on the chain length $N$ is strongly affected by temperature for chains with bending and torsion stiffness. For systems with relatively short chains $(N\le 50)$, the exponent $\nu$ from $D\propto N^{-\nu }$ increases from the value $\nu \approx 1$ expected in the Rouse regime to $\nu \approx 2$ as the temperature is lowered towards $T_{\mathrm{g}}$.