The dielectric behavior of a linear cluster of two or more living cells connected by tight junctions is analyzed using a spectral method. The polarizability of this system is obtained as an expansion over the eigenmodes of the linear response operator, showing a clear separation of geometry from electric parameters. The eigenmode with the second largest eigenvalue dominates the expansion as the junction between particles tightens, but only when the applied field is aligned with the cluster axis. This effect explains a distinct low-frequency relaxation observed in the impedance spectrum of a suspension of linear clusters.

Fairness plays a key role in explaining the emergence and maintenance of cooperation. Opponent-oriented social utility models were often proposed to explain the origins of fairness preferences in which agents take into account not only their own outcomes but are also concerned with the outcomes of their opponents. Here, we propose a payoff-oriented mechanism in which agents update their beliefs only based on the payoff signals of the previous ultimatum game, regardless of the behaviors and outcomes of the opponents themselves. Employing adaptive ultimatum game, we show that (1) fairness behaviors can emerge out even under such minimalist assumptions, provided that agents are capable of responding to their payoff signals, (2) the average game payoff per agent per round decreases with the increasing discrepancy rate between the average giving rate and the average asking rate, and (3) the belief update process will lead to 50%-50% fair split provided that there is no mutation in the evolutionary dynamics.

Resonance requires precise synchronization. Surprisingly, relativistic cyclotron instability can survive under a magnetic field with its nonuniformity larger than the requirement of synchronism. Localized eigenmode observed in a hybrid simulation is found to be consistent with that predicted by an analytical theory including both profile and eigenvalue. Half of the spatial area of the wave profile is located where the frequency mismatch is negative as against to the positive requirement generally believed. The consequence on the $\alpha$ dynamics is also demonstrated.

We introduce several infinite families of critical exponents for the random-cluster model and present scaling arguments relating them to the $k$-arm exponents. We then present Monte Carlo simulations confirming these predictions. These exponents provide a convenient way to determine $k$-arm exponents from Monte Carlo simulations. An understanding of these exponents also leads to a radically improved implementation of the Sweeny Monte Carlo algorithm. In addition, our Monte Carlo data allow us to conjecture an exact expression for the shortest-path fractal dimension $d_{\text{min}}$ in two dimensions: $d_{\text{min}}\stackrel{?}{=}\left(g+2\right)\left(g+18\right)/\left(32g\right)$, where $g$ is the Coulomb-gas coupling, related to the cluster fugacity $q$ via $q=2+2\text{cos}\left(g\pi /2\right)$ with $2\le g\le 4$.

We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The long-time behavior of the particle position is studied in the frame of a continuous-time random walk on a semi-infinite one-dimensional lattice. We formulate the conditions for anomalous diffusion, derive the diffusion laws, and analyze their dependence on the particle mass and the distribution of the random force.

With the development of quantum thermodynamics it has been shown that relaxation to thermal equilibrium and with it the concept of heat flux may emerge directly from quantum mechanics. This happens for a large class of quantum systems if embedded into another quantum environment. In this paper, we discuss the complementary question of the emergence of work flux from quantum mechanics. We introduce and discuss two different methods to assess the work source quality of a system, one based on the generalized factorization approximation, the other based on generalized definitions of work and heat. By means of those methods, we show that small quantum systems can, indeed, act as work reservoirs. We illustrate this behavior for a simple system consisting of a spin coupled to an oscillator and investigate the effects of two different interactions on the work source quality. One case will be shown to allow for a work source functionality of arbitrarily high quality.

A relativistic two-fluid temperature-dependent approach for a streaming magnetized pair plasma is considered. Such a scenario corresponds to secondary plasmas created at the polar caps of pulsar magnetospheres. In the model the generalized vorticity rather than the magnetic field is frozen into the fluid. For parallel propagation four transverse modes are found. Two are electromagnetic plasma modes which at high temperature become light waves. The remaining two are Alfvénic modes split into a fast and slow mode. The slow mode is cyclotron two-stream unstable at large wavelengths and is always subluminous. We find that the instability cannot be suppressed by temperature effects in the limit of large (finite) magnetic field. The fast Alfvén mode can be superluminous only at large wavelengths, however it is always subluminous at high temperatures. In this incompressible approximation only the ordinary mode is present for perpendicular propagation. For oblique propagation the dispersion relation is studied for finite and large strong magnetic fields and the results are qualitatively described.

An $O\left(N\text{log}N\right)$ treecode algorithm is presented for computing pairwise interactions of electrostatic free energy for reaction potentials with polarization effects due to the macroscopic solvent. A multipole expansion for a cluster is used to account for particles inside the cluster, where a spatial difference is applied to obtain the expansion coefficients of the polarization function. Numerical tests are performed to illustrate the accuracy and efficiency of the approach. The algorithm is significant in speeding up generalized Born methods for biomolecular simulations under the framework of macroscopically treating solvents.

In order to model the evolution of concentration profiles induced by ion beam mixing in thick layers, Monte Carlo simulations were performed to study in detail the transition probability controlling the evolution of this profile within the binary collision approximation. We demonstrate that this transition probability can be factorized in two distinct functions. The first one can be understood as a scale factor. The second one controls the dynamics of ion beam mixing which can be analyzed as a Levy flight. The power law form of the tail of this function closely linked to the cross section of a collision event is responsible for long tails of concentration profiles. We demonstrate that the Levy flight nature of ion beam mixing induces an enhancement of the evolution of the initial concentration profile.

We investigate the phenomenon of extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state $n=0$ is a repelling (scenario A) or attracting (scenario B) point of the deterministic rate equation. In scenario A the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point $n=0$. In scenario B there is an intermediate repelling point $n=n_1$ between the attracting point $n=0$ and another attracting point $n=n_2$ in the vicinity of which the metastable population resides. The crux of the theory is a dissipative variant of WKB (Wentzel-Kramers-Brillouin) approximation which assumes that the typical population size in the metastable state is large. Starting from the master equation, we calculate the quasistationary probability distribution of the population sizes and the (exponentially long) mean time to extinction for each of the two scenarios. When necessary, the WKB approximation is complemented (i) by a recursive solution of the quasistationary master equation at small $n$ and (ii) by the van Kampen system-size expansion, valid near the fixed points of the deterministic rate equation. The theory yields both entropic barriers to extinction and pre-exponential factors, and holds for a general set of multistep processes when detailed balance is broken. The results simplify considerably for single-step processes and near the characteristic bifurcations of scenarios A and B.

Liquid water, at ambient conditions, has short-range density correlations which are well known in literature. Surprisingly, large scale molecular-dynamics simulations reveal an unusually long-distance correlation in “longitudinal” part of dipole-dipole orientational correlations. It is nonvanishing even at $75\text{Å}$ and falls off exponentially with a correlation length of about $24\text{Å}$ beyond solvation region. Numerical evidence suggests that the long-range nature of dipole-dipole correlation is due to underlying fluctuating network of hydrogen bonds in the liquid phase. This correlation is shown to give a shape dependant attraction between two hydrophobic surfaces at large distances of separation and the range of this attractive force is in agreement with experiments. In addition it is seen that quadrupolar fluctuations vanish within the first solvation peak $\left(3\text{Å}\right)$.

The quasi-two-dimensional deposition of ferromagnetic materials by electrochemical process under the influence of a magnetic field applied in the plane of the growth leads to a surprising symmetry breaking in the dendritic structures found. The reasons for these features are still not completely understood. The original dense circular envelope becomes rectangular, as well as the sparse figures have their shapes elongated. This paper reports the results of a diffusion-limited aggregation (DLA) -like simulation. The model proposed here, a modification of the original DLA model, can deal with ferromagnetic particles under the influence of an electric field and the dipolar interactions between particles, submitted to an applied magnetic field in the plane of growth of such structures. The results were produced varying the applied magnetic field and the magnetic moment of the particles and show that the balance between these interactions is an important mechanisms that can be responsible for the changes in shape of the aggregates observed in the experiments.

We address the issue of the self energy of the mobile ions in electrolyte solutions within a general Gaussian renormalized fluctuation theory using a field-theoretic approach. We introduce the Born radii of the ions in the form of a charge distribution allowing for different Born radii between the cations and anions. The model thus automatically yields a theory free of divergences and accounts for the solvation of the ions at the level of continuous dielectric media. In an inhomogeneous dielectric medium, the self energy is in general position dependent and differences in the self energy between cations and anions can give rise to local charge separation in a macroscopically neutral system. Treating the Born radius $a$ as a smallness parameter, we show that the self energy can be split into an $O\left(a^{-1}\right)$ nonuniversal contribution and an $O\left(a^0\right)$ universal contribution that depends only on the ion concentration, valency, and the spatially varying dielectric constant. For a weakly inhomogeneous dielectric medium, the nonuniversal part of the self energy is shown to have the form of the Born energy with the local dielectric constant. This self energy is incorporated into the Poisson-Boltzmann equation as a simple means of including this local fluctuation effect in a mean-field theory. We illustrate the phenomenon of charge separation by considering cations and anions of difference sizes and valencies in a periodic dielectric medium.

In this paper we report on the influence of different geometric and boundary constraints on nonlocal (spatially inhomogeneous) effects in wormlike micellar systems. In a previous paper, nonlocal effects were observable by measuring the local rheological flow curves of micelles flowing in a microchannel under different pressure drops, which appeared to differ from the flow curve measured using conventional rheometry. Here we show that both the confinement and the boundary conditions can influence those nonlocal effects. The role of the nature of the surface is analyzed in detail using a simple scalar model that incorporates inhomogeneities, which captures the flow behavior in both wide and confined geometries. This leads to an estimate for the nonlocal “diffusion” coefficient (i.e., the shear curvature viscosity) which corresponds to a characteristic length from 1 to 10 μm.

We analyze here displacement controlled peeling of a flexible adherent off a thin layer of elastic adhesive, the elastic modulus of which does not remain uniform but varies periodically along the direction of peeling. Calculation shows that with progressive peeling, the crack front does not propagate continuously at the interface but intermittently with crack arrests and subsequent initiations. The crack gets arrested close to the location of the minimum shear modulus of the layer and initiates again only at a sufficiently large peel off load. This effect is very similar to the peeling experiment off surface patterned and microchannel embedded adhesives which results in significant enhancement of fracture toughness of the interface over smooth adhesive layers. The fracture toughness of the interface increases with the increase in thickness of the layer and the amplitude of variation in modulus. Fracture toughness is calculated to be high also for the larger value of critical stress at the opening of the crack. With the wavelength of modulus variation, it varies nonmonotonically, maximizing at an intermediate value. These results define the criterion for designing adhesive layers with spatially modulated physical properties useful for variety of applications.

We demonstrate the ability of pulsed electron double resonance (PELDOR) experiments to determine the orientation of spin labels in biological macromolecules. Thus, the distance information usually obtained from PELDOR data can be complemented by the mutual orientation of macromolecular domains. A method to determine the angle $\beta$ between the spin label normal and the interspin axis is proposed and analyzed mathematically. The obtained analytical expression allows extraction of angles $\beta$ without a fitting procedure if these angles are equal for both nitroxide of biradical. The method was applied to the experimental data gathered on ten spin-labeled DNA samples. The angles estimated from the PELDOR data are in excellent agreement with literature values.

We investigate a tracer particle moving on a two-dimensional square lattice created by network formers (NF). The positions of all network formers are randomly displaced by a small amount from the nodes of the network. Each NF can be in a “floppy” or “rigid” state, depending on the number of bonds connecting it to neighboring network formers. The NF that have more than a specified number of m bonds are in rigid state, the remaining ones are in a floppy state. The energy of the tracer particle depends on its distance from those of the four nearest NF that are in “rigid” state. The NF in floppy state do not contribute to the energy. We here demonstrate that the a priori increase in the diffusion coefficient with the concentration of the floppy states goes through a crossover point, after which the increase is much sharper.

We study the linear stability of an air front pushing on a viscoelastic upper convected Mawxell fluid inside a Hele-Shaw cell. Both theory and experiments involving several viscoelastic fluids prove that a unique dimensionless time parameter $\tilde{\lambda }$ controls all elastic effects. For small values of $\tilde{\lambda }$, Newtonian behavior dominates, while for higher values of $\tilde{\lambda }$ viscoelastic effects appear. We show that the linear growth rate of a small initial perturbation diverges for a critical value $\tilde{\lambda }=\widetilde{{\lambda }_{\mathbf{c}}}\simeq \mathbf{1}\mathbf{0}$. Experiments prove that this divergence is associated to a fracturelike pattern instability of the interface. We conclude that the observed fractures come from the Saffman-Taylor instability and that they directly emerge from the linear regime of it.