We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the $q$-states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with nonconserved order parameter. We analyze the distribution of hull-enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for $q=2$ (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit superuniversality properties.

We present a study of hydrogen at pressures higher than molecular dissociation using the coupled electron-ion Monte Carlo method. These calculations use the accurate reptation quantum Monte Carlo method to estimate the electronic energy and pressure while doing a Monte Carlo simulation of the protons. In addition to presenting simulation results for the equation of state over a large region of the phase diagram, we report the free energy obtained by thermodynamic integration. We find very good agreement with density-functional theory based molecular-dynamics calculations for pressures beyond 600 GPa and densities above $\rho =1.4\text{g}/{\text{cm}}^3$, both for thermodynamic and structural properties. This agreement provides a strong support to the different approximations employed in the density-functional treatment of the system, specifically the approximate exchange-correlation potential and the use of pseudopotentials for the range of densities considered. We find disagreement with chemical models, which suggests that a reinvestigation of planetary models—previously constructed using the Saumon-Chabrier-Van Horn equations of state—might be needed.

The present paper is devoted to mathematical description of the vascular network response to local perturbations in the cellular tissue state, being one of the basic mechanisms controlling the inner environment of human body. Keeping in mind individual organs we propose a model for distributed self-regulation of living tissue, which is regarded as an active hierarchical system without any controlling center. This model is based on the self-processing of information about the cellular tissue state and cooperative interaction of blood vessels governing redistribution of blood flow over the vascular network. The information self-processing is implemented via mass conservation, i.e., conservation of blood flow as well as special biochemical compounds called activators transported by blood. The cooperative interaction of blood vessels stems from the response of individual vessels to activators in blood flowing through them. The general regularities are used to specify the vessel behavior. The arterial and venous beds are considered to be individually of the tree form. The constructed governing equations are analyzed numerically. In particular, first, we show that the blood perfusion rate approximately (in the analyzed case within 10% accuracy) depends only on the local concentration of activators in the cellular tissue. It is due to the hierarchical structure of the vascular network rather than the ideal behavior of individual vessels accepted previously. Second, we demonstrate the distinction between the reaction thresholds of individual vessels and that of the vascular network as a whole. The latter effect is the cause for introducing the notion of activators instead of using such quantities as temperature in describing the living tissue self-regulation.

By studying a recent biophysical model of tumor growth in the presence of the immune system, here we propose that the phenomenon of evasion of tumors from immune control at a temporal mesoscale might, in some cases, be due to random fluctuations in the levels of the immune system. Bounded noises are considered, but the Gaussian approach is also used for analytical reference. After showing that in the case of bounded noises there may be multiple attractors in the space of probability densities, we numerically show that the velocity of convergence toward asymptotic density is very slow and that a transitory analysis is needed. Then, by simulations using the sine-Wiener and the Tsallis noises, we show that if the level of the noise is sufficiently large then there may be the onset of noise-induced transitions in the transitory density evaluated at realistic times. Namely, the transitions are from unimodal density centered at low values of tumor burden to bimodal densities that have a second maximum centered at higher values. However, those transitions depend on the distribution of the noise.

We report experimental results on structure identification of nonlinear systems by a steady-state control method. The idea underlying the method is to drive the nonlinear system to steady state by applying a suitable feedback control input. It turns out experimentally that this control-based structure identification method can be used for some applications, such as estimation of initial conditions and state variables of nonlinear systems and structure identification of some special elements. Two attractors of the Chua oscillator are presented to illustrate the reliability of the suggested techniques under the hypotheses of measurable state variables and physical access to the system for implementing the proportional feedback.

The capillary-dominated regime of dynamics of electrified jets of a viscous leaky dielectric liquid is studied numerically. In this regime the effective force in the direction of an applied field due to tangential electric stresses is balanced by the gradient of liquid pressure governed by the surface-tension stresses. As is characteristic of this regime, the electric current and the characteristic jet radius are dependent on the surface-tension coefficient and not on viscosity. In the scope of this work, the conditions of the existence of this regime are determined. A qualitative order-of-magnitude analysis gives the power-law dependences of the jet radius and electric current on the parameters of the problem (conductivity, applied electric field, flow rate, and surface-tension coefficient). Numerical results are obtained for low conductive liquids for a large range of the dimensionless flow rate (capillary number, Ca). The order-of-magnitude estimations of electric current are in agreement with the numerical results given a small Ca. The corresponding numerically obtained jet shapes are discussed and explained.

Free-energy differences computed from fast-switching simulations or measurements according to the Jarzynski equation are independent of the particular protocol specifying how the control parameter is changed in time. In contrast, the average work carried out on the system as well the accuracy of the resulting free energy strongly depend on the protocol. Recently, Schmiedl and Seifert [Phys. Rev. Lett. 98, 108301 (2007)] found that protocols that minimize the average work for a given duration of the switching process have discrete steps at the beginning and the end. Here we determine numerically the protocols that minimize the statistical error in the free energy estimate and find that such minimum error protocols have similar discrete jumps. Our analysis shows that the reduction in computational effort achieved by the use of steplike protocols can be considerable. Such large savings of computing time, however, typically occur for parameter ranges in which an application of the Jarzynski equation is impractical due to large statistical errors arising from the exponential work average.

A solid-on-solid model is generalized to study the formation of Ge pyramid islands bounded by (105) facets on Si(100) substrates in two dimensions. Each atomic column is not only characterized by the local surface height but also by two deformation state variables dictating the local surface tilt and vertical extension. These local deformations phenomenologically model surface reconstructions in (105) facets and enable the formation of islands which better resemble faceted pyramids. We apply the model to study a kinetic limited growth regime. Transitions from stepped mounds into faceted islands under deposition conditions are demonstrated. It is shown that a significantly reduced growth rate after faceting leads to a continuous nucleation of new islands until overcrowding occurs. The island size distribution is now dominated by fluctuations in the initial island size during faceting and the increased diversity in the ages of the islands. This multistate model may find applications in kinetic simulations of other nanostructures or nanoclusters involving arbitrary high-index surfaces.

The orientational order parameters $⟨P_2⟩$ and $⟨P_4⟩$ in the nematic liquid crystal 4-pentyl-4'-cyanobipheny (5CB) have been determined by means of the two completely different techniques: polarized Raman spectroscopy and x-ray scattering. In particular, the values of $⟨P_2⟩$ and $⟨P_4⟩$ obtained using two different Raman methods, proposed by Jen et al. [J. Chem. Phys 66, 4635 (1977)] and Jones et al. [J. Mol. Struct. 708, 145 (2004)], respectively, are compared with the results of x-ray measurements. A good agreement between the experimental values of $⟨P_2⟩$ and $⟨P_4⟩$ and the results of the Humphries-James-Luckhurst mean field theory has been found whenever they were determined using either x-ray measurement or following the Jen et al. method. In addition, a study of the influence of the intensity of the exiting laser source on the apparent values of the order parameters has been performed. Therefore, it was found that the discrepancies of the value of $⟨P_4⟩$ determined following Jen et al. and Jones et al. could be determined by nonlinear effects.

The rheological properties of polymer melts and other complex macromolecular fluids are often successfully modeled by phenomenological constitutive equations containing fractional differential operators. We suggest a molecular basis for such fractional equations in terms of the generalized Langevin equation (GLE) that underlies the renormalized Rouse model developed by Schweizer [J. Chem. Phys. 91, 5802 (1989)]. The GLE describes the dynamics of the segments of a tagged chain under the action of random forces originating in the fast fluctuations of the surrounding polymer matrix. By representing these random forces as fractional Gaussian noise, and transforming the GLE into an equivalent diffusion equation for the density of the tagged chain segments, we obtain an analytical expression for the dynamic shear relaxation modulus $G\left(t\right)$, which we then show decays as a power law in time. This power-law relaxation is the root of fractional viscoelastic behavior.

We have analyzed the statistical thermodynamics of peeling single-stranded DNA (ssDNA) from the surface of graphite. Using recently measured parameters, we represent ssDNA as a polymer chain strongly adsorbed to a frictionless substrate using the freely jointed chain, wormlike chain, and rotational isomeric state models. All three models predict steady peeling force under force control, in agreement with single-molecule experiments. We predict that, for finite-length chains, the force response has measurable spikes under displacement control. These force spikes carry information about the underlying sequence of ssDNA, which might thus be measurable with a sufficiently stiff loading system. For the freely jointed chain model, under force control, we have obtained several exact closed-form results and provide relations between the measured peel force and the underlying adhesion free energy.

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.

Consider a large finite scale-free network consisting of $M⪢1$ nodes and $N⪢1$ links, in which the degree distribution of links per bond is governed by a power-law $P\left(n\right)\simeq n^{-1-\alpha }$ with exponent $0<\alpha <1$. A subset of $m⪡M$ nodes is sampled arbitrarily, yielding the empirical sample mean $\eta$: the average number of links per node, within the sampled subset. We explore the statistics of the sample mean $\eta$ and show that its fluctuations around the network mean $\nu =N/M$ are extremely broad and strongly skewed—yielding typical values, which are systematically and significantly smaller than the network mean $\nu$. Applying these results to the case of bipartite scale-free networks, we show that the sample means of the two parts of these networks generally differ—a fact we refer to as the “matchmaking paradox.”

The dynamic behavior of swirling premixed flames generated by the effect of the gravitational orientation has been experimentally and numerically investigated. When the gravitational direction relative to the flame front is changed, i.e., in inverted gravity $\left(-1G\right)$, an unstable flame is formed in a limited domain of equivalence ratio and swirl number. The time history of flame front fluctuation shows that high-energy chaotic motion is superimposed on a periodic oscillation generated by unstable vortex motion in the combustion products. This results in the dynamic motion of the unstable flame becoming deterministically chaotic. This is clearly demonstrated by sophisticated nonlinear time series analysis, which has not been widely applied to the investigation of combustion phenomena.

We report Monte Carlo studies of a two-dimensional soft colloidal crystal confined in a strip geometry by parallel walls. The wall-particle interaction has corrugations along the length of the strip. Compressing the crystal by decreasing the distance between the walls induces a structural transition characterized by the sudden appearance of a one-dimensional array of extended defects each of which span several lattice parameters, a “soliton staircase.” We obtain the effective interaction between the solitons. A Lindemann criterion shows that the reduction in dimensionality causes the finite soliton lattice to readily melt as the temperature is raised.

We calculate short-time diffusion properties of suspensions of porous colloidal particles as a function of their permeability, for the full fluid-phase concentration range. The particles are modeled as spheres of uniform permeability with excluded volume interactions. Using a precise multipole method encoded in the HYDROMULTIPOLE program, results are presented for the hydrodynamic function, $H\left(q\right)$, sedimentation coefficient, and self-diffusion coefficients with a full account of many-body hydrodynamic interactions. While self-diffusion and sedimentation are strongly permeability dependent, the wave-number dependence of the hydrodynamic function can be reduced by appropriate shifting and scaling, to a single master curve, independent of permeability. Generic features of the permeable sphere model are discussed.

A generic dynamical model with saturation for neural signal transduction at the synaptic stage is presented. Analysis of this model of a synaptic pathway demonstrates its ability to give rise to stochastic resonance or improvement by noise, at this stage of signal transmission. Beyond the case of the intrinsic threshold nonlinearity of the neuron response, the results extend the feasibility of stochastic resonance to neural saturating dynamics at the synaptic stage. The present results also constitute the exposition of a new type of nonlinear (saturating) dynamics capable of stochastic resonance.

We study the velocity correlations of a tagged particle in an infinite assembly of interacting particles with a given density in one dimension. The assembly is in contact with a heat bath, and the particles interact via a hard-core repulsion with each other. We evaluate the two-time velocity correlation function exactly as function of time when an ensemble average is taken over initial conditions. This correlation function decays rapidly with time and becomes negative, with the rate of decay increasing with the density. This is followed by a slow decay toward zero through a power-law behavior of the form $-t^{-3/2}$ at large times for all densities. We also consider mobility of the assembly in the presence of a constant force acting on the particles, as well as the mobility of a tagged particle when only the tagged particle is driven by the force. The power spectrum of velocity fluctuations is also presented.

The relativistic equilibrium velocity distribution plays a key role in describing several high-energy and astrophysical effects. Recently, computer simulations favored Jüttner’s as the relativistic generalization of Maxwell’s distribution for $d=1,2,3$ spatial dimensions and pointed to an invariant temperature. In this work, we argue an invariant temperature naturally follows from manifest covariance. We present a derivation of the manifestly covariant Jüttner’s distribution and equipartition theorem. The standard procedure to get the equilibrium distribution as a solution of the relativistic Boltzmann’s equation, which holds for dilute gases, is here adopted. However, contrary to previous analysis, we use Cartesian coordinates in $d+1$ momentum space, with $d$ spatial components. The use of the multiplication theorem of Bessel functions turns crucial to regain the known invariant form of Jüttner’s distribution. Since equilibrium kinetic-theory results should agree with thermodynamics in the comoving frame to the gas the covariant pseudonorm of a vector entering the distribution can be identified with the reciprocal of temperature in such comoving frame. Then by combining the covariant statistical moments of Jüttner’s distribution a form of the equipartition theorem is advanced which also accommodates the invariant comoving temperature and it contains, as a particular case, a previous not manifestly covariant form.