The consequences of source charge and surface modulation are studied within the framework of the Poisson-Boltzmann theory of electrolyte solutions. Through a consideration of various examples, it is found that inherent modulation can lead to both like-charge attraction and overcharging effects.

We describe an analytic model for polycrystalline thin film growth based on competition between grains with conic geometries. This model is valid for all film thicknesses and is verified using level set simulations in $2+1$ dimensions. We study the effects of nonuniform initial grain distributions on growth statistics. These results provide a possible explanation for discrepancies between experimentally measured and theoretical scaling laws.

We present stochastic, finite-population formulations of the Crow-Kimura and Eigen models of quasispecies theory, for fitness functions that depend in an arbitrary way on the number of mutations from the wild type. We include back mutations in our description. We show that the fluctuation of the population numbers about the average values is exceedingly large in these physical models of evolution. We further show that horizontal gene transfer reduces by orders of magnitude the fluctuations in the population numbers and reduces the accumulation of deleterious mutations in the finite population due to Muller’s ratchet. Indeed, the population sizes needed to converge to the infinite population limit are often larger than those found in nature for smooth fitness functions in the absence of horizontal gene transfer. These analytical results are derived for the steady state by means of a field-theoretic representation. Numerical results are presented that indicate horizontal gene transfer speeds up the dynamics of evolution as well.

In recent years, many network perturbation techniques, such as topological perturbations and service perturbations, were employed to study and improve the robustness of complex networks. However, there is no general way to evaluate the network robustness. In this paper, we propose a global measure for a network, the reconstructability coefficient $\theta$, defined as the maximum number of eigenvalues that can be removed, subject to the condition that the adjacency matrix can be reconstructed exactly. Our main finding is that a linear scaling law, $E\left[\theta \right]=aN$, seems universal in that it holds for all networks that we have studied.

The present study shows that diffusive connections with two long-time delays can induce the stabilization of a steady state in network oscillators. A linear stability analysis shows that, if the two delay times retain a proportional relation with a certain bias, the stabilization can be achieved independent of the delay times. Furthermore, a simple systematic procedure for designing the coupling strength and the delay times in the connections is proposed. The procedure has the following two advantages: one can employ time delays as long as one wants and the stabilization can be achieved independently of its network topology. Our analytical results are applied to the well-known double-scroll circuit model on a small-world network.

Emulsion stability simulations are used to estimate the coalescence time of one drop of hexadecane pressed by buoyancy against a planar water/hexadecane interface. In the present simulations, the homophase is represented by a big drop of oil at least 500 times larger than the approaching drop $(1–10\mu \text{m})$. Both deformable and nondeformable drops are considered along with six different diffusion tensors. In each case, van der Waals, electrostatic, steric, and buoyancy forces are taken into account. The coalescence times are estimated as the average of 1000 random walks. It is found that the repulsive potential barrier has a significant influence in the results. The experimental data can only be reproduced assuming negligible repulsive barriers, as well as nondeformable drops that move with a combination of Stokes and Taylor tensors as they approach the interface.

Biased (degree-dependent) percolation was recently shown to provide strategies for turning robust networks fragile and vice versa. Here, we present more detailed results for biased edge percolation on scale-free networks. We assume a network in which the probability for an edge between nodes $i$ and $j$ to be retained is proportional to ${\left(k_i{k}_j\right)}^{-\alpha }$ with $k_i$ and $k_j$ the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their properties by analytical and numerical means. The system is examined away from the percolation transition, where the size of the giant cluster is obtained, and close to the transition, where nonuniversal critical exponents are extracted using the generating-functions method. The theory is found to agree quite well with simulations. By presenting an extension of the Fortuin-Kasteleyn construction, we find that biased percolation is well-described by the $q\to 1$ limit of the $q$-state Potts model with inhomogeneous couplings.

We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. For quantum statistical (thermal) field theory, the stochastic variable of the statistical theory is a boundary field configuration. We explore the properties of an effective theory for such boundary configurations and apply it to the computation of the partition function of an interacting one-dimensional quantum-mechanical system at finite temperature. Plots of free energy and specific heat show excellent agreement with more involved semiclassical results. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident end points and includes nonvanishing boundary terms. An appropriately modified expansion into modified Matsubara modes is presented.

We apply the statistical measure of complexity, introduced by López-Ruiz, Mancini, and Calbet (LMC), to uniform Fermi systems. We investigate the connection between information and complexity measures with the strongly correlated behavior of various Fermi systems as nuclear matter, electron gas, and liquid helium. We examine the possibility that LMC complexity can serve as an index quantifying correlations in the specific system and to which extent could be related with experimental quantities. Moreover, we concentrate on thermal effects on the complexity of ideal Fermi systems. We find that complexity behaves, both at low and high values of temperature, in a similar way as the specific heat.

Point configurations have been widely used as model systems in condensed-matter physics, materials science, and biology. Statistical descriptors, such as the $n$-body distribution function $g_n$, are usually employed to characterize point configurations, among which the most extensively used is the pair distribution function $g_2$. An intriguing inverse problem of practical importance that has been receiving considerable attention is the degree to which a point configuration can be reconstructed from the pair distribution function of a target configuration. Although it is known that the pair-distance information contained in $g_2$ is, in general, insufficient to uniquely determine a point configuration, this concept does not seem to be widely appreciated and general claims of uniqueness of the reconstructions using pair information have been made based on numerical studies. In this paper, we present the idea of the distance space called the $\mathbb{D}$ space. The pair distances of a specific point configuration are then represented by a single point in the $\mathbb{D}$ space. We derive the conditions on the pair distances that can be associated with a point configuration, which are equivalent to the realizability conditions of the pair distribution function $g_2$. Moreover, we derive the conditions on the pair distances that can be assembled into distinct configurations, i.e., with structural degeneracy. These conditions define a bounded region in the $\mathbb{D}$ space. By explicitly constructing a variety of degenerate point configurations using the $\mathbb{D}$ space, we show that pair information is indeed insufficient to uniquely determine the configuration in general. We also discuss several important problems in statistical physics based on the $\mathbb{D}$ space, including the reconstruction of atomic structures from experimentally obtained $g_2$ and a recently proposed “decorrelation” principle. The degenerate configurations have relevance to open questions involving the famous traveling salesman problem.

The dynamic flow behavior of a hard-disk fluid under external force field in two-dimensional microchannels is investigated using an event-driven molecular dynamics simulation method. Simulations have been carried out under laminar and subsonic conditions in both slip regime and transition regime, and the effects of three main factors, Knudsen number (Kn), force field intensity, and packing fraction, on flow and heat transfer behavior have been studied. It is shown that all the factors play important roles in the velocity distribution of the flow, and the temperature profile of the gas flow may exhibit a bimodal shape with a local minimum instead of a maximum in the center. These findings verify the predictions of nonequilibrium kinetic theories on the so-called “temperature dip.” At high Kn, the two maxima of temperature shift to two walls and the temperature profile changes to a “parabola” opening upward with a minimum in the center. A slight setback of the temperature is also found before the fluid flow eventually arrives at a steady state when the shear rate is high enough.

Planar brushes of flexible, semiflexible, and rodlike diblock polyampholytes are studied using molecular dynamics simulations in a wide range of the grafting density. Simulations show linear dependence of the average thickness on the grafting density in all cases regardless of different flexibility of anchored chains and the brushes’ different equilibrium conformations. Slopes of fitted lines to the average thickness of the brushes of semiflexible and rodlike polyampholytes versus the grafting density are approximately the same and differ considerably from that of the brushes of flexible chains. The average thickness of the brush of flexible diblock polyampholytes as a function of the grafting density is also obtained using a simple scaling analysis, which is in good agreement with our simulations.

The thermodynamic behavior of a continuous homopolymer is described using the Wang-Landau algorithm for chain lengths up to $N=561$. The coil-globule and liquid-solid transitions are analyzed in detail with traditional thermodynamic and structural quantities. The behavior of the coil-globule transition is well within theoretical and computational predictions for all chain lengths, while the behavior of the liquid-solid transition is much more susceptible to finite-size effects. Certain “magic number” lengths $\left(N=13,55,147,309,561\right)$, whose minimal energy states offer unique icosahedral geometries, are discussed along with chains residing between these special cases. The low temperature behavior near the liquid-solid transition is rich in structural transformations for certain chain lengths, showing many similarities to the behavior of classical clusters with similar interaction potentials. General comments are made on this size dependent behavior and how it affects transition behavior in this model.

Inelastic neutron scattering was employed to study photoeffects on the molecular dynamics of membranes of the photosynthetic bacterium Rhodopseudomonas viridis. The main photoactive parts of this biomolecular system are the chlorophyll molecules whose dynamics were found to be affected under illumination by visible light in a twofold manner. First, vibrational modes are excited at energies of 12(2) and $88\left(21\right){\text{cm}}^{-1}$. Second, a partial “freezing” of rotational modes is observed at energies of 1.2(3) and $2.9\left(5\right){\text{cm}}^{-1}$. These results are attributed to a possible coupling between molecular motions and particular mechanisms in the photosynthetic process.

We study the small-scale behavior of generalized two-dimensional turbulence governed by a family of model equations, in which the active scalar $\theta ={\left(-\Delta \right)}^{\alpha /2}\psi$ is advected by the incompressible flow $\mathit{u}=\left(-{\psi }_y,{\psi }_x\right)$. Here $\psi$ is the stream function, $\Delta$ is the Laplace operator, and $\alpha$ is a positive number. The dynamics of this family are characterized by the material conservation of $\theta$, whose variance $⟨{\theta }^2⟩$ is preferentially transferred to high wave numbers (direct transfer). As this transfer proceeds to ever-smaller scales, the gradient $\nabla \theta$ grows without bound. This growth is due to the stretching term $\left(\nabla \theta \cdot \nabla \right)\mathit{u}$ whose “effective degree of nonlinearity” differs from one member of the family to another. This degree depends on the relation between the advecting flow $\mathit{u}$ and the active scalar $\theta$ (i.e., on $\alpha$) and is wide ranging, from approximately linear to highly superlinear. Linear dynamics are realized when $\nabla \mathit{u}$ is a quantity of no smaller scales than $\theta$, so that it is insensitive to the direct transfer of the variance of $\theta$, which is nearly passively advected. This case corresponds to $\alpha \ge 2$, for which the growth of $\nabla \theta$ is approximately exponential in time and nonaccelerated. For $\alpha <2$, superlinear dynamics are realized as the direct transfer of $⟨{\theta }^2⟩$ entails a growth in $\nabla \mathit{u}$, thereby, enhancing the production of $\nabla \theta$. This superlinearity reaches the familiar quadratic nonlinearity of three-dimensional turbulence at $\alpha =1$ and surpasses that for $\alpha <1$. The usual vorticity equation $\left(\alpha =2\right)$ is the border line, where $\nabla \mathit{u}$ and $\theta$ are of the same scale, separating the linear and nonlinear regimes of the small-scale dynamics. We discuss these regimes in detail, with an emphasis on the locality of the direct transfer.

A generalization to the transient regime is developed for waves with a phase singularity of the screw type. These singular waves are commonly called vortices for all kind of waves as, for instance, optical vortex or acoustical vortex. We generalize the definition of vortices to get an azimuthal velocity invariant for all the frequency components contained in the broad spectrum of a short pulse. This generalization leads to a modification of the orbital angular momentum definition. Another generalization is introduced by considering helicoidal waves with a finite number of turns. We demonstrate that, in this last case, the topological charge is no longer an integer. This provides a physical interpretation to vortices of fractional charge that are involved here to take into account the diffraction occurring at both tips of the now finite helical wave front. We show that shortening the pulse implies an angular localization of the wave energy and, as a consequence, a spreading of the angular momentum amplitude due to the uncertainty principle.

We report theory and numerical simulations that demonstrate the feasibility of simultaneous reconstruction of the three-dimensional scattering and absorption coefficients of a mesoscopic system using angularly resolved measurements of scattered light. Image reconstruction is based on the inversion of a generalized (broken ray) Radon transform relating the scattering and absorption coefficients of the medium to angularly resolved intensity measurements. Although the single-scattering approximation to the radiative transport equation (RTE) is used to devise the image reconstruction method, there is no assumption that only singly scattered light is measured. That is, no physical mechanism for separating single-scattered photons from the rest of the multiply-scattered light (e.g., time gating) is employed in the proposed experiments. Numerical examples of image reconstruction are obtained using samples of optical depth of up to 3.2. The forward data are obtained from numerical solution of the RTE, accounting for all orders of scattering.

This paper extends the three-dielectric-layer hybrid solvation model for treating electrostatic interactions in biomolecular simulations from the spherical geometry [Comm. Comp. Phys. 6, 955 (2009)] to the prolate/oblate spheroidal geometries. In the resulting model, the inner spheroidal cavity of a low dielectric constant ${\epsilon }_i$ contains an irregular-shaped solute and some explicit solvent molecules, while the unbounded outer layer is used to implicitly model the bulk solvent as a dissimilar continuum medium of a high dielectric constant ${\epsilon }_o$. The thin intermediate translation layer, which also consists of explicit solvent molecules, assumes a continuous variation of the dielectric permittivity $\epsilon \left(\mathbf{r}\right)$ changing smoothly from ${\epsilon }_i$ to ${\epsilon }_o$. In particular, the so-called quasiharmonic dielectric permittivity profile is introduced based on a harmonic interpolation, thus allowing analytical series solutions of the generalized Coulomb potential and the self-polarization energy in terms of the associated Legendre functions. A key advantage of the proposed quasiharmonic dielectric model lies in the fact that it overcomes the inherent mathematical divergence in the self-polarization energy that exists in the simple and widely used steplike dielectric model. Numerical examples are included to show some simulated behaviors of the quasiharmonic dielectric model and the corresponding analytical solution.

Single particle trajectories are investigated assuming the coexistence of two subdiffusive processes: diffusion on a fractal structure modeling spatial constraints on motion and heavy-tailed continuous time random walks representing energetic or chemical traps. The particles’ mean squared displacement is found to depend on the way the mean is taken: temporal averaging over single-particle trajectories differs from averaging over an ensemble of particles. This is shown to stem from subordinating an ergodic anomalous process to a nonergodic one. The result is easily generalized to the subordination of any other ergodic process (i.e., fractional Brownian motion) to a nonergodic one. For certain parameters the ergodic diffusion on the underlying fractal structure dominates the transport yet displaying ergodicity breaking and aging.

We consider a quantum linear oscillator coupled at an arbitrary strength to a bath at an arbitrary temperature. We find an exact closed expression for the oscillator density operator. This state is noncanonical but can be shown to be equivalent to that of an uncoupled linear oscillator at an effective temperature $T_{\text{eff}}^{\star }$ with an effective mass and an effective spring constant. We derive an effective Clausius inequality $\delta {\mathcal{Q}}_{\text{eff}}^{\star }\le T_{\text{eff}}^{\star }dS$, where $\delta {\mathcal{Q}}_{\text{eff}}^{\star }$ is the heat exchanged between the effective (weakly coupled) oscillator and the bath, and $S$ represents a thermal entropy of the effective oscillator, being identical to the von-Neumann entropy of the coupled oscillator. Using this inequality (for a cyclic process in terms of a variation of the coupling strength) we confirm the validity of the second law. For a fixed coupling strength this inequality can also be tested for a process in terms of a variation of either the oscillator mass or its spring constant. Then it is never violated. The properly defined Clausius inequality is thus more robust than assumed previously.