We have developed a model for studying the axial propagation of elliptically polarized electromagnetic waves in a spatially random helical media. We start by writing Maxwell equations for a structurally chiral medium whose dielectric permittivities, polar, and helical angles contain both a stochastic contribution and a deterministic one. We write the electromagnetic equations into a Marcuvitz-Schwigner representation to transform them afterward in a simpler expression by using the Oseen transformation. We exhibit that in the Oseen frame the Marcuvitz-Schwigner equations turns out to be a linear vector stochastic system of differential equations with multiplicative noise. Applying to the resulting equation a formalism for treating stochastic differential equations, we find the governing equations for the first moments of the electromagnetic field amplitudes for a general autocorrelation function for the system diffractive indexes, and calculate their corresponding band structure for a particular spectral noise density. We have shown that the average resulting electromagnetic fields exhibit a decaying exponential dependence which stems from by dissipation and the presence of qualitative modifications in the band structure including a considerable widening of the band gap and the existence of new local maxima for the modes without a band gap.

We present a model of bidirectional vesicular transport between two intracellular organelles, which takes into account intermediate stages of transport that occur between vesicular budding from one organelle and subsequent fusion with the other organelle. These are incorporated into the model by associating with each organelle a donor pool of newly budded vesicles and an acceptor pool of transported vesicles ready for fusion. By constructing a system of differential equations that keeps track of the distribution of vesicles and protein concentrations within the various pools and along cytoskeletal tracks, we show how a stable steady state can emerge that consists of organelles that maintain different protein concentrations in spite of the continuous exchange of materials. In particular, exploiting the fact that the surface area of individual vesicles is much smaller than the surface area of organelles, we use an adiabatic approximation to eliminate the vesicular variables. This results in a major simplification of the dynamics and provides a systematic procedure for deriving phenomenological models of cooperative transport.

Pathogen-host relationships are the result of an ongoing coevolutionary race where the immune system of the host attempts to eliminate the pathogen, while the successful pathogen mutates to become invisible for the host's immune system. We here propose a minimal pathogen-host evolution model that takes into account cross immunization and allows for evolution of a spatially heterogeneous immune status of a population of hosts. With only the mutation rate as a determining parameter, the model allows us to produce an evolutionary tree of diseases which is highly branched, but hardly ever splits into separate long-lived trunks. Side branches remain short lived and seldom diverge to the extent of losing all cross immunizations.

The role of diffraction is investigated for two-dimensional area-preserving maps with sharply or almost sharply divided phase space, in relation to the issue of dynamical tunneling. The diffraction effect is known to appear in general when the system contains indifferentiable or discontinuous points. We find that it controls the quantum transition between regular and chaotic regions in mixed phase space in the case where the border between these regions is set to be sharp. However, its manifestation is rather subtle: it would be possible to identify the diffraction effect under suitable coordinates if the support of the wave function contains indifferentiable or discontinuous points, whereas it is mixed with the tunneling effect and the whole process becomes hybrid if the support does not contain the sources of diffraction. We make detailed analyses, including the semiclassical treatment of edge contributions of the one-step propagator, to clarify the nature of diffraction in mixed phase space. Our result implies that chaos does not play any roles in the regular-to-chaotic transition process when the phase space is sharply divided.

The decay of the plasma grating formed at the intersection of two femtosecond filaments is measured in several molecular and atomic gases. The grating evolution is ruled by ambipolar diffusion in atomic gases and by a combination of ambipolar diffusion and collision-assisted free electron recombination in molecular gases. Electron diffusion and recombination coefficients are extracted for Ne, Ar, Kr, Xe, N${}_2$, O${}_2$, CO${}_2$, and air at 1 bar.

We study the critical behavior of Boolean variables on scale-free networks with competing interactions (Ising spin glasses). Our analytical results for the disorder–network-decay-exponent phase diagram are verified using Monte Carlo simulations. When the probability of positive (ferromagnetic) and negative (antiferromagnetic) interactions is the same, the system undergoes a finite-temperature spin-glass transition if the exponent that describes the decay of the interaction degree in the scale-free graph is strictly larger than 3. However, when the exponent is equal to or less than 3, a spin-glass phase is stable for all temperatures. The robustness of both the ferromagnetic and spin-glass phases suggests that Boolean decision problems on scale-free networks are quite stable to local perturbations. Finally, we show that for a given decay exponent spin glasses on scale-free networks seem to obey universality. Furthermore, when the decay exponent of the interaction degree is larger than 4 in the spin-glass sector, the universality class is the same as for the mean-field Sherrington-Kirkpatrick Ising spin glass.

We extend the definition of nonadiabatic entropy production given for Markovian systems by Esposito and Van den Broeck [Phys. Rev. Lett. 104, 090601 (2010)], to arbitrary non-Markov ergodic dynamics. We also introduce a notion of stability characterizing non-Markovianity. For stable non-Markovian systems, the nonadiabatic entropy production satisfies an integral fluctuation theorem, leading to the second law of thermodynamics for transitions between nonequilibrium steady states. This quantity can also be written as a sum of products of generalized fluxes and forces, thus being suitable for thermodynamics. On the other hand, the generalized fluctuation-dissipation relation also holds, clarifying that the conditions for it to be satisfied are ergodicity and stability instead of Markovianity. We show that in spite of being counterintuitive, the stability criterion introduced in this work may be violated in non-Markovian systems even if they are ergodic, leading to a violation of the fluctuation theorem and the generalized fluctuation-dissipation relation. Stability represents then a necessary condition for the above properties to hold and explains why the generalized fluctuation-dissipation relation has remained elusive in the study of non-Markov systems exhibiting nonequilibrium steady states.

We address the investigation of the solvation properties of the minimal orientational model for water originally proposed by [Bell and Lavis, J. Phys. A 3, 568 (1970)]. The model presents two liquid phases separated by a critical line. The difference between the two phases is the presence of structure in the liquid of lower density, described through the orientational order of particles. We have considered the effect of a small concentration of inert solute on the solvent thermodynamic phases. Solute stabilizes the structure of solvent by the organization of solvent particles around solute particles at low temperatures. Thus, even at very high densities, the solution presents clusters of structured water particles surrounding solute inert particles, in a region in which pure solvent would be free of structure. Solute intercalates with solvent, a feature which has been suggested by experimental and atomistic simulation data. Examination of solute solubility has yielded a minimum in that property, which may be associated with the minimum found for noble gases. We have obtained a line of minimum solubility (TmS) across the phase diagram, accompanying the line of maximum density. This coincidence is easily explained for noninteracting solute and it is in agreement with earlier results in the literature. We give a simple argument which suggests that interacting solute would dislocate TmS to higher temperatures.

We consider a model fluid with long-range $r^{-6}$ (dispersion) interparticle potentials confined between competing parallel walls. One wall is solvophilic and would be completely wet at bulk liquid-gas coexistence ${\mu }_{\text{co}}^{-}$, whereas the other is solvophobic and would be completely dry at $\mu ={\mu }_{\text{co}}^{+}$. When the wall separation $L$ is large and the system is below the bulk critical temperature $T_C$ and close to bulk liquid-gas coexistence, a delocalized interface or soft-mode phase forms with a liquid-gas interface near the center of the slit; this interacts with the walls via the power-law tails of the interparticle potentials. We use a coarse-grained effective Hamiltonian approach to derive explicit scaling expressions for the Gibbs adsorption $\Gamma$, the surface tension $\gamma$, the solvation force $f_s$, and the total susceptibility $\chi$. These quantities depend on the dimensionless scaling variable ${(L/\sigma )}^3\beta \delta \mu$, where $\beta ={\left(k_{B}T\right)}^{-1}$, $\sigma$ is the diameter of the fluid particles and $\delta \mu =\mu -{\mu }_{\text{co}}$ is the chemical potential deviation from bulk coexistence. Using a nonlocal density functional theory, we calculate density profiles for the asymmetrically confined fluid at different chemical potentials and for sufficiently large $L$ confirm the scaling predictions for the four thermodynamic quantities. Since the upper critical dimension for complete wetting with power-law potentials is less than 3, we argue that our (mean-field) scaling predictions should remain valid in treatments that incorporate the effects of interfacial fluctuations. As the wall separation $L$ is decreased at ${\mu }_{\text{co}}$, we predict a capillary evaporation transition from the delocalized interface phase to a dilute gas state with just a thin adsorbed film of liquidlike density next to the solvophilic wall. This transition is closely connected to the first-order prewetting transition that occurs at the solvophilic wall in the semi-infinite system. We compare the phase diagram for the competing walls system with the phase diagrams for the fluid confined between identical solvophilic and identical solvophobic walls. Comparisons are also made with earlier studies of asymmetric confinement for systems with short-range forces.

The evolution of a line of vehicles on a ring is modeled by means of first-order car-following models. Three generic models describe the speed of a vehicle as a function of the spacing ahead and the speed of the predecessor. The first model is a basic one with no delay. The second is a delayed car-following model with a strictly positive parameter for the driver and vehicle reaction time. The last model includes a reaction time parameter with an anticipation process by which the delayed position of the predecessor is estimated. Explicit conditions for the linear stability of homogeneous configurations are calculated for each model. Two methods of calculus are compared: an exact one via Hopf bifurcations and an approximation by second-order models. The conditions describe stable areas for the parameters of the models that we interpret. The results notably show that the impact of the reaction time on the stability can be palliated by the anticipation process.

An experimental study of jets and sprays formed by a spark-induced bubble collapsing near a plate with a hole is presented. A Perspex plate with a hole at its center is placed in a half-filled water tank with its top face near the air-water interface. A bubble is created using a low-voltage electrical spark below the hole in the plate. The bubble expands against the hole, which pushes the liquid present within the hole and leads to an initial primary jet of water that emerges from the other end of the hole into air. The bubble subsequently collapses and leads to a second jet that is characterized by short bursts of liquid spray followed by a thicker continuous liquid column. The impact of the sprays onto the primary jet leads to perturbations in the jet and the breakup of the latter into fine droplets. The entire phenomenon is recorded using a high-speed camera to visualize the mechanism both within and outside the hole. The results give a clearer indication of the mechanism behind a recently reported phenomenon on the formation of impacting jets caused by bubble expansion and collapse at the micrometer length scale. The variation of the jet characteristics with parameters such as the position of the water-air interface with respect to the plate and the hole geometry (i.e., the hole diameter and the plate thickness) is also presented.

Experiments have investigated shape changes of polymer films induced by asymmetric swelling by a chemical vapor. Inspired by recent work on the shaping of elastic sheets by non-Euclidean metrics [Y. Klein, E. Efrati, and E. Sharon, Science 315, 1116 (2007)], we represent the effect of chemical vapors by a change in the target metric tensor. In this problem, unlike that earlier work, the target metric is asymmetric between the two sides of the film. Changing this metric induces a curvature of the film, which may curve into a partial cylinder or a partial sphere. We calculate the elastic energy for each of these shapes and show that the sphere is favored for films smaller than a critical size, which depends on the film thickness, while the cylinder is favored for larger films.

We study the Ising model in a hierarchical small-world network by renormalization group analysis and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities, including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point.

The purpose of this study is to extend the weighted correlation approach (WCA) for inhomogeneous fluids. It now introduces a generic expression to evaluate the single-particle direct correlation function in terms of a series of pair direct correlation functions weighted by different correlation-weight functions and adjustable weight factors. When applied for practical use, however, approximations of the pair direct correlation functions have to be made, together with appropriate definitions of the weighted densities and the choices of the correlation-weight functions. The WCA approach would, then, not only help us to connect and compare different strategies and their underlying assumptions in the density functional approaches, but also enable us to propose and apply density functional theory methods to predict the density profile of, e.g., the hard-sphere fluid confined between a pair of parallel planar hard walls. Numerical results of the extended WCA approach, against the Monte Carlo (MC) simulations in a range of surface separations and bulk densities, suggest that it is capable of representing the fine features of the hard-sphere density distributions. The WCA results also agree well with the calculations from the fundamental measure theory. In addition, the thermodynamic self-consistency of the WCA approach is confirmed by its fairly good agreement with the MC fitted data for the surface tension of a hard-sphere fluid at a planar hard wall. All these tests show that a pure WCA approach can be constructed to investigate the states of ionic hard-sphere fluids.

We demonstrate the efficiency of the multidomain sampler (MDS) in finding multiple distinct global minima and low-energy local minima in the hydrophobic-polar (HP) lattice protein model. Extending the idea of partitioning energy space in the Wang-Landau algorithm, our approach introduces an additional partitioning scheme to divide the protein conformation space into local basins of attraction. This double-partitioning design is very powerful in guiding the sampler to visit the basins of unexplored local minima. An H-residue subchain distance is used to merge the basins of similar local minima into one domain, which increases the diversity among identified minimum-energy conformations. Moreover, a visit-enhancement factor is introduced for long protein chains to facilitate jumps between basins. Results on three benchmark protein sequences reveal that our approach is capable of finding multiple global minima and hundreds of low-energy local minima of great diversity.

The first-passage-probability can be used as an unbiased method for determining the phases of motion of individual organelles within live cells. Using high speed microscopy, we observe individual lipid droplet tracks and analyze the motor protein driven motion. At short passage lengths ($<$${10}^{-2}\mu$m), a log-normal distribution in the first-passage-probability as a function of time is observed, which switches to a Gaussian distribution at longer passages due to the running motion of the motor proteins. The mean first-passage times ($\langle t_{\mathrm{FPT}}\rangle$) as a function of the passage length ($L$), averaged over a number of runs for a single lipid droplet, follow a power law distribution $\langle t_{\mathrm{FPT}}\rangle \sim L^{\alpha }$, $\alpha >2$, at short times due to a passive subdiffusive process. This changes to another power law at long times where $1<\alpha <2$, corresponding to sub-ballistic superdiffusive motion, an active process. Subdiffusive passive mean square displacements are observed as a function of time, $〈r^2〉\sim t^{\beta }$, where $0<\beta <1$ at short times again crossing over to an active sub-ballistic superdiffusive result $1<\beta <2$ at longer times. Consecutive runs of the lipid droplets add additional independent Gaussian peaks to a cumulative first-passage-probability distribution indicating that the speeds of sequential phases of motion are independent and biochemically well regulated. As a result we propose a model for motor driven lipid droplets that exhibits a sequential run behavior with occasional pauses.

The well known approach, based on Schrödinger's integral equation, to the problem of calculating the first-passage probability density in time for classical diffusion on a continuum is revisited for the case of diffusion by hopping on a discrete lattice. It turns out that a certain boundary condition central to solving the integral equation, invoked first by Schrödinger and then by others on the basis of a physical argument, needs to be modified for the discrete case. In fact, the required boundary condition turns out to be determined entirely by the normalization condition for the first-passage probability density. An explicit analytical expression is derived for the first-passage density for a three-site problem modeling escape over a barrier. The related quantum first-passage problem is also commented upon briefly.

We develop a sequence of models describing information transmission and decision dynamics for a network of individual agents subject to multiple sources of influence. Our general framework is set in the context of an impending natural disaster, where individuals, represented by nodes on the network, must decide whether or not to evacuate. Sources of influence include a one-to-many externally driven global broadcast as well as pairwise interactions, across links in the network, in which agents transmit either continuous opinions or binary actions. We consider both uniform and variable threshold rules on the individual opinion as baseline models for decision making. Our results indicate that (1) social networks lead to clustering and cohesive action among individuals, (2) binary information introduces high temporal variability and stagnation, and (3) information transmission over the network can either facilitate or hinder action adoption, depending on the influence of the global broadcast relative to the social network. Our framework highlights the essential role of local interactions between agents in predicting collective behavior of the population as a whole.

For any initially correlated network after any kind of attack where either nodes or edges are removed, we obtain general expressions for the degree-degree probability matrix and degree distribution. We show that the proposed analytical approach predicts the correct topological changes after the attack by comparing the evolution of the assortativity coefficient for different attack strategies and intensities in theory and simulations. We find that it is possible to turn an initially assortative network into a disassortative one, and vice versa, by fine-tuning removal of either nodes or edges. For an initially uncorrelated network, on the other hand, we discover that only a targeted edge-removal attack can induce such correlations.