Diffusive and structural properties in the binary mixture of charged particles are investigated based on the molecular dynamical simulation. It is shown that the particles with higher charge enhance or weaken the diffusion of the whole system depending on the coupling strength, and regimes of subdiffusion as well as normal diffusion are identified. The nonmonotonous diffusion, i.e., the diffusion at first is increased and then is decreased with increasing the higher charged particles, is strongest close to the phase from liquidlike state to solidlike state. Stronger coupling and lower concentration of higher charged particles are in favor of the formation of ordered shells centered at the higher charged particles.

We study the thermal breakage of a discrete one-dimensional string, with open and fixed ends, in the heavily damped regime. Basing our analysis on the multidimensional Kramers escape theory, we are able to make analytical predictions on the mean breakage rate and on the breakage propensity with respect to the breakage location on the string. We then support our predictions with numerical simulations.

In the literature, there are five distinct fragmented sets of analytic predictions for the scaling behavior at the phase transition in the random-site Ising model in four dimensions. Here, the scaling relations for logarithmic corrections are used to complete the scaling pictures for each set. A numerical approach is then used to confirm the leading scaling picture coming from these predictions and to discriminate between them at the level of logarithmic corrections.

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear “fast” diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

The inelastic thermal spike model is applied to liquid water in relation to high-energy ${{}^{12}\text{C}}^{6+}$ beams (hundreds of MeV/u) used for cancer therapy. The goal of this project is to calculate the heat transfer in the vicinity of the incident-ion track. Thermal spike calculations indicate a very large temperature increase in the vicinity of ion tracks near the Bragg peak during the time interval from ${10}^{-15}$ to ${10}^{-9}\text{s}$ after the ion’s passage and an increase in pressure, as large as tens of MPa, can be induced during that time. These effects suggest a possibility of thermomechanical pathways to disruption of irradiated DNA. An extension of the model for hydrogen, beryllium, argon, krypton, xenon, and uranium ions around the Bragg peak is presented as well.

Several types of biological networks have recently been shown to be accurately described by a maximum entropy model with pairwise interactions, also known as the Ising model. Here we present an approach for finding the optimal mappings between input signals and network states that allow the network to convey the maximal information about input signals drawn from a given distribution. This mapping also produces a set of linear equations for calculating the optimal Ising-model coupling constants, as well as geometric properties that indicate the applicability of the pairwise Ising model. We show that the optimal pairwise interactions are on average zero for Gaussian and uniformly distributed inputs, whereas they are nonzero for inputs approximating those in natural environments. These nonzero network interactions are predicted to increase in strength as the noise in the response functions of each network node increases. This approach also suggests ways for how interactions with unmeasured parts of the network can be inferred from the parameters of response functions for the measured network nodes.

We show that heterogeneous degree distributions in observed scale-free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a physical interpretation of hyperbolic distances as energies of links. The hidden space curvature affects the heterogeneity of the degree distribution, while clustering is a function of temperature. We embed the internet into the hyperbolic plane and find a remarkable congruency between the embedding and our hyperbolic model. Besides proving our model realistic, this embedding may be used for routing with only local information, which holds significant promise for improving the performance of internet routing.

We present experimental heat transport measurements of turbulent Rayleigh-Bénard convection with rotation about a vertical axis. The fluid, water with a Prandtl number $\left(\sigma \right)$ of about 6, was confined in a cell with a square cross section of $7.3\times 7.3{\text{cm}}^2$ and a height of 9.4 cm. Heat transport was measured for Rayleigh numbers $2\times {10}^5<\text{Ra}<5\times {10}^8$ and Taylor numbers $0<\text{Ta}<5\times {10}^9$. We show the variation in normalized heat transport, the Nusselt number, at fixed dimensional rotation rate ${\Omega }_D$, at fixed Ra varying Ta, at fixed Ta varying Ra, and at fixed Rossby number Ro. The scaling of heat transport in the range of ${10}^7$ to about ${10}^9$ is roughly 0.29 with a Ro-dependent coefficient or equivalently is also well fit by a combination of power laws of the form $a{\text{Ra}}^{1/5}+b{\text{Ra}}^{1/3}$. The range of Ra is not sufficient to differentiate single power law or combined power-law scaling. The data are roughly consistent with an assumption that the enhancement of heat transport owing to rotation is proportional to the number of vortical structures penetrating the boundary layer. We also compare indirect measures of thermal and Ekman boundary layer thicknesses to assess their potential role in controlling heat transport in different regimes of Ra and Ta.

By adding an array of metallic cut wires, the transmission of transverse electric (TE) waves (the electric field is parallel to the slits) through subwavelength slits in a thin metallic film is significantly enhanced. An 800-fold enhanced transmission is obtained compared to the case without the cut wires. It is demonstrated that a TE incident wave is highly confined by the cut wires, due to the excitation of the electric dipolelike resonance, and then effectively squeezed into and through the subwavelength slits.

A recently proposed model for skin cell proliferation [E. Clayton et al., Nature (London) 446, 185 (2007)] is extended to incorporate mitotic autoregulation, and hence homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a model for carcinogenesis. One way in which this can arise is homeostatic metastability, in which the cell populations escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multistage model of carcinogenesis. Homeostatic metastability offers a possible explanation for the peculiar epidemiology of lung cancer in ex-smokers.

In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a probabilistic description. The coupling of delayed rates with stochastic dynamics leads to a probability conservation equation characterizing a non-Markovian process. A systematic approximation is derived that incorporates the effect of delayed rates on the characterization of molecular noise valid in the limit of long delay time. By way of a simple example, we show that delayed reaction dynamics can only increase intrinsic fluctuations about the steady state. The method is general enough to accommodate nonlinear transition rates allowing characterization of fluctuations around a delay-induced limit cycle.

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.

This is the first of three papers devoted to the nonequilibrium thermodynamics of amorphous materials. Our focus here is on the role of internal degrees of freedom in determining the dynamics of such systems. For illustrative purposes, we study a solid whose internal degrees of freedom are vacancies that govern irreversible volume changes. Using this model, we compare a thermodynamic theory based on the Clausius-Duhem inequality to a statistical analysis based directly on the law of increase of entropy. The statistical theory is used first to derive the Clausius-Duhem inequality. We then use the theory to go beyond those results and obtain detailed equations of motion, including a rate factor that is enhanced by deformation-induced noisy fluctuations. The statistical analysis points to the need for understanding how both energy and entropy are shared by the vacancies and their environments.

We develop a theory of the effective disorder temperature in glass-forming materials driven away from thermodynamic equilibrium by external forces. Our basic premise is that the slow configurational degrees of freedom of such materials are weakly coupled to the fast kinetic-vibrational degrees of freedom and therefore that these two subsystems can be described by different temperatures during deformation. We use results from the preceding paper on the nonequilibrium thermodynamics of systems with internal degrees of freedom to derive an equation of motion for the effective temperature and to learn how this temperature couples to the dynamics of the system as a whole.

We use the internal-variable, effective-temperature thermodynamics developed in two preceding papers to reformulate the shear-transformation-zone (STZ) theory of amorphous plasticity. As required by the preceding analysis, we make explicit approximations for the energy and entropy of the STZ internal degrees of freedom. We then show that the second law of thermodynamics constrains the STZ transition rates to have an Eyring form as a function of the effective temperature. Finally, we derive an equation of motion for the effective temperature for the case of STZ dynamics.

Experimental evidence of local thickness fluctuations of a surfactant membrane, as observed by neutron scattering, is reported. A swollen lamellar structure consisting of nonionic surfactant, water, and oil was investigated by neutron spin echo spectroscopy. Different dynamical processes are recognized at three different length scales. At length scales larger than the membrane thickness, the bending motion is observed, which follows the Zilman and Granek theory [Phys. Rev. Lett. 77, 4788 (1996)]. At the length scale corresponding to the membrane thickness, a clear excess dynamics in addition to the bending motion is observed. This mode is interpreted as the local thickness fluctuations. At even shorter length scales, smaller than the membrane thickness, intramembrane dynamics such as protrusion motions may have been observed.

Using a lattice-gas model in mean-field theory, we discuss the problem of how adsorption and desorption of fluids in independent cylinderlike pores is influenced by variations in the pore diameter along the length of the pore, surface roughness of the pore walls, and chemical heterogeneity. We also consider the impact of contact with the bulk phase via the pore opening and the possibility of interactions between neighboring pores via a liquid film on the external surface of the material. We find that a combination of pore size variation along the length of the pore and surface roughness yields sorption hysteresis similar to that found in systems with three-dimensional disordered pore networks such as porous glasses. Our results are especially relevant to adsorption and desorption in porous silicon materials with independent linear pores and apparently anomalous features of the behavior in these systems can be accounted for within the context of the present model.

We study the complex shear modulus $G$ of two side-chain liquid-crystal polymers (SCLCPs), a methoxy-phenylbenzoate substituted polyacrylate (thereafter called ${\text{PAOCH}}_3$), and a cyanobiphenyl substituted polyacrylate supplied by Merck (thereafter called LCP105) using a piezoelectric rheometer. Two methods of filling the cell are used: (a) a capillary method, which can be used only at high temperature because of the low value of the viscosity, and (b) the classical one, thereafter called compression method, which consists in placing the sample between the two slides of the cell and to bring them closer. By filling the cell at high temperature either with the compression or the capillary method, we show that the response of both compounds is liquidlike ($G^{\prime }\sim f^2$ and $G^{″}\sim f$, where $f$ is the frequency) for temperatures higher than a certain temperature $T_0$ and gel-like $\left(G^{\prime }\sim \text{const},G^{″}\sim f\right)$ below $T_0$. This change in behavior from the conventional flow response to a gel-like response, when approaching the glass transition, is observed for nonsliding conditions and for very weak-imposed shear strains. It can be explained by a percolation-type mechanism of preglassy elastic clusters, which correspond to long-range and long-lived density fluctuations that are frozen at the time scale of the experiment. The sample response is therefore the sum of two contributions: one is due to the flow response of the polymer melt and the other to the elastic response of the network formed by the preglassy elastic clusters. By filling the cell below $T_0$ with the compression method, both compounds exhibit a gel-type behavior by gently bringing closer the slides of the cell and an anomalous low-frequency behavior characterized by $G^{\prime }=\text{const}$ and $G^{″}=\text{const}$ by increasing the pressure used to bring closer the slides of the cell. A compression-assisted aggregation of the preglassy elastic clusters can explain both the increase in the low-frequency elastic plateau when the sample thickness is decreased and the anomalous low-frequency behavior. Further evidence for the existence of these elastic clusters is provided by the following results: (a) the nonlinear response of the samples as a function of the strain amplitude, which can be explained by the Payne effect, and (b) the aggregation effects, which can be mimicked by a polydimethylsiloxane melt filled with silica particles, the silica particles playing the role of the preglassy elastic clusters. All these observations show that ${\text{PAOCH}}_3$ is not a macroscopically solidlike material with an unconventional type of elasticity, as claimed by Mendil et al. [Phys. Rev. Lett. 96, 077801 (2006)]. The gel-type behavior observed here on two SCLCPs (${\text{PAOCH}}_3$ and LCP105) and previously on some conventional flexible polymers (atactic polystyrene, poly-$n$-butylacrylate) seems to be a generic effect of the glass transition. The presence of the preglassy elastic clusters questions the widely accepted hypothesis of ergodicity in the supercooled state.

Extensive studies on polymer thin films to date have revealed their interesting but unusual properties such as film thickness dependence of glass transition temperature $T_{\text{g}}$ and thermal expansivity. Recent studies have shown that the lower $T_{\text{g}}$ is not always related to the higher mobility in polymer thin films, which contradicts our current understanding of the glass transition process. In this work, we report the results of inelastic neutron-scattering measurements on polystyrene thin films using two spectrometers with different energy resolutions as well as ellipsometry measurements. The results are interpreted in terms of cooperatively rearranging region and motional slowing down due to the surface effect that explain plausibly the anomalous relationship between the glass transition temperature $T_{\text{g}}$ and the molecular mobility in thin films.

Molecular dynamics (MD) simulations are used to study the interaction of an anionic palmitoyl-oleoyl-phosphatidylglycerol (POPG) bilayer with the cationic antimicrobial peptide bovine lactoferricin (LFCinB) in a 100 mM NaCl solution at 310 K. The interaction of LFCinB with a POPG bilayer is employed as a model system for studying the details of membrane adsorption selectivity of cationic antimicrobial peptides. Seventy eight 4 ns MD production run trajectories of the equilibrated system, with six restrained orientations of LFCinB at 13 different separations from the POPG membrane, are generated to determine the free energy profile for the peptide as a function of the distance between LFCinB and the membrane surface. To calculate the profile for this relatively large system, a variant of constrained MD and thermodynamic integration is used. A simplified method for relating the free energy profile to the LFCinB-POPG membrane binding constant is employed to predict a free energy of adsorption of $-5.4\pm 1.3\text{kcal}/\text{mol}$ and a corresponding maximum adsorption binding force of about 58 pN. We analyze the results using Poisson-Boltzmann theory. We find the peptide-membrane attraction to be dominated by the entropy increase due to the release of counterions and polarized water from the region between the charged membrane and peptide, as the two approach each other. We contrast these results with those found earlier for adsorption of LFCinB on the mammalianlike palmitoyl-oleoyl-phosphatidylcholine membrane.