The main aim of the paper is to incorporate the nonlinear kinetic term into non-Markovian transport equations described by a continuous time random walk (CTRW) with nonexponential waiting time distributions. We consider three different CTRW models with reactions. We derive nonlinear Master equations for the mesoscopic density of reacting particles corresponding to CTRW with arbitrary jump and waiting time distributions. We apply these equations to the problem of front propagation in the reaction-transport systems with Kolmogorov-Petrovskii-Piskunov kinetics and anomalous diffusion. We have found an explicit expression for the speed of a propagating front in the case of subdiffusive transport.

We examine the coevolution of $N$ cycles and force chains as part of a broader study which is designed to quantitatively characterize the role of the laterally supporting contact network to the evolution of force chains. Here, we elucidate the rheological function of these coexisting structures, especially in the lead up to failure. In analogy to force chains, we introduce the concept of force cycles: $N$ cycles whose contacts each bear above average force. We examine their evolution around force chains in a discrete element simulation of a dense granular material under quasistatic biaxial loading. Three-force cycles are shown to be stabilizing structures that inhibit relative particle rotations and provide strong lateral support to force chains. These exhibit distinct behavior from other cycles. Their population decreases rapidly during the initial stages of the strain-hardening regime—a trend that is suddenly interrupted and reversed upon commencement of force chain buckling prior to peak shear stress. Results suggest that the three-force cycles are called upon for reinforcements to ward off failure via shear banding. Ultimately though, the resistance to buckling proves futile; buckling wins under the combined effects of dilatation and increasing compressive load. The sudden increase in three-force cycles may thus be viewed as an indicator of imminent failure via shear bands.

Using particle tracking microrheology, we studied the glass transition in dense suspensions of thermosensitive microgel particles. These suspensions can be tuned reversibly between the glass state at low temperature and the liquid state at high temperature. In the glass state, the ensemble averaged mean squared displacements (MSDs) of added fluorescent tracer particles depend on the age of the suspension. We also determine the local viscoelastic moduli, $G^{\prime }$ and $G^{″}$, from the MSDs using the Generalized Stokes-Einstein Relation and compare them to the bulk moduli, measured using conventional rheometry. With particle tracking, one probes the viscoelastic moduli in a lower frequency range than with macrorheology, which makes it possible to determine the mean relaxation time that is inaccessible with macrorheology. In the glass state, the mean relaxation time increases linearly with the age of the sample and the short time particle displacement distributions are non-Gaussian, indicating inhomogeneity of the system. The observed difference between conventional and microrheology is explained quantitatively assuming that the tracer particles are surrounded by a viscoelastic liquid shell, different from the bulk.

In this article the influence of deformation on the coalescence rates of oil-in-water (O/W) emulsions is analyzed. Calculations for doublets and many-particles systems were performed based on a Brownian dynamics algorithm. Extensional and bending energies were included in order to quantify the effect of the changes in the surface geometry on the coalescence rates. Also, the hydrodynamic resistance due to the flat film was included through a correction to the diffusion coefficient in the lubrication limit. Results of two particles calculations were compared with previous analytical evaluations of the coalescence time in absence of highly repulsive barriers [Danov et al., Langmuir 9, 1731 (1993)]. Lifetime of doublets was calculated as a function of the particle radius from 100 nm to $100\mu \text{m}$. It was found that the doublets lifetime strongly depends on the interplay between the potential of interaction between the droplets and the hydrodynamic resistance. Depending on the repulsive barrier either a monotonous increase of the lifetime with the droplet size or a maximum value is observed. Finally, the evolution of O/W emulsions with a volume fraction of $\varphi =0.10$ was studied. For these many-particle systems, the results show a sensitive dependence of the aggregation behavior on the interfacial tension. The procedure reported here allows us to include Derjaguin-Landau-Verwey-Overbeek (DLVO) and non-DLVO forces and the film drainage velocity of many different systems.

Recent research on nanofluids has offered particle clustering as a possible mechanism for the abnormal enhancement of the effective thermal conductivity $\left(k\right)$ when nanoparticles are dispersed in liquids. This paper was devoted to verify experimentally and theoretically the significance of the effect by altering the cluster structure, size distribution, and thermal conductivity of solid particles in water. Starting with well dispersed ${\text{SiO}}_2$ sols in water as a reference system, we control the aggregation kinetics by adjusting $p\text{H}$. Contrary to previous model predictions, the present experiment showed that clustering did not show any discernable enhancement in the thermal conductivity even at high volume loading. A series of fractal model calculations not only suggested that the conductive benefit due to clustering might be completely compensated by the reduced convective contribution due to particle growth, but also recommended the need for higher thermal conductivity and optimized fractal dimension of particles for maximizing the clustering effect.

A theoretical formalism to predict the structure factors observed in dipolar soft-sphere fluids based on a virial expansion of the radial distribution function is presented. The theory is able to account for cases with and without externally applied magnetic fields. A thorough comparison of the theoretical results to molecular-dynamics simulations shows a good agreement between theory and numerical simulations when the fraction of particles involved in clustering is low; i.e., the dipolar coupling parameter is $\lambda \lesssim 2$, and the volume fraction is $\phi \lesssim 0.25$. When magnetic fields are applied to the system, special attention is paid to the study of the anisotropy of the structure factor. The theory reasonably accounts for the structure factors when the Langevin parameter is smaller than 5.

In this paper, we present a theoretical description to the quantum coherence and decoherence phenomena of energy transfer in photosynthesis observed in a recent experiment [Science 316, 1462 (2007)]. As a successive two-color laser pulses with selected frequencies cast on a sample of the photosynthetic purple bacterium Rb. sphaeroides two resonant excitations of electrons in chromophores can be generated. However, this effective two-level subsystem will interact with its protein environment and decoherence is inevitable. We describe this subsystem coupled with its environment as a dynamical spin-boson model. The non-Markovian decoherence dynamics is described using a quasiadiabatic propagator path integral (QUAPI) approach. With the photon-induced effective time-dependent level splitting energy and level flip coupling coefficient between the two excited states and the environment-induced non-Markovian decoherence dynamics, our theoretical result is in good agreement with the experimental data.

We consider a noise-driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system to obtain the mean activity level for the system as a function of the mean synaptic weight, which predicts a first-order transition and hysteresis between a noise-dominated regime and a regime of persistent neural activity. Assuming Poisson firing statistics for the neurons, the plasticity dynamics of a synapse under the influence of the mean-field environment can be mapped to the dynamics of an asymmetric random walk in synaptic-weight space. Using a master equation for small steps, we predict a narrow distribution of synaptic weights that scales with the square root of the plasticity rate for the stationary state of the system given plausible physiological parameter values describing neural transmission and plasticity. The dependence of the distribution on the synaptic weight of the mean-field environment allows us to determine the mean synaptic weight self-consistently. The effect of fluctuations in the total synaptic conductance and plasticity step sizes are also considered. Such fluctuations result in a smoothing of the first-order transition for low number of afferent synapses per neuron and a broadening of the synaptic-weight distribution, respectively.

Test experiments of hybridization in DNA microarrays show systematic deviations from the equilibrium isotherms. We argue that these deviations are due to the presence of a partially hybridized long-lived state, which we include in a kinetic model. Experiments confirm the model predictions for the intensity vs free-energy behavior. The existence of slow relaxation phenomena has important consequences for the specificity of microarrays as devices for the detection of a target sequence from a complex mixture of nucleic acids.

Sengupta et al. [Phys. Rev. E 61, 1072 (2000)] presented an elegant and simple finite-size scaling method for the calculation of elastic constants and their corresponding correlation lengths, which is suitable for many finite discrete systems considered through simulations or experiments. We take into account a mathematical finite-size effect that was neglected by the authors in order to propose a more accurate method. Consequences on the authors’ results are also discussed.

We agree with Coupier et al. [Phys. Rev. E 81, 013101 (2010)] that their technique for extracting elastic constants from microscopic strain fluctuations improves upon ours because of a more accurate computation of the integral of the elastic correlation function over sub-blocks. However, we believe that their interpretation of the physical relevance of the elastic correlation length extracted from the fits is misleading.

Through the construction of suitable objective function, the parameter estimation of the dynamical system could be converted to the problem of parameter optimization. Based on the chaotic ant swarm optimization approach, we investigate the problem of parameter optimization for the dynamical systems in the presence of noise. We systematically analyze the basic relationships among the complexity of objective function, the length of time series, and the performance of the searching algorithm. Furthermore, we consider the effect of measurable additive noise on the objective function. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed methods.

In this paper we address the following question: how thick is the diffusive fraction of the thermal boundary layer in highly turbulent thermal convection? We have studied this problem in a large-scale Rayleigh-Bénard experiment at fixed aspect ratio $\Gamma =1.13$ and variable Rayleigh number $5.2\times {10}^{10}<\text{Ra}<9.6\times {10}^{11}$ using air as the working fluid. By measuring profiles of the mean temperature in the vicinity of the heated bottom plate with a higher spatial resolution than in any other previous experiment and by complementing them with simultaneous independent measurements of the local heat flux, we have determined the shares of diffusive and convective vertical heat fluxes inside the thermal boundary layer. Our measurements show that the thickness of the sublayer where heat is exclusively transported by diffusion is only about 1/25 of the nominal thickness of the thermal boundary layer and depends only weakly on Ra in the parameter domain investigated here. This result implies that phenomenological theories which assume a diffusive heat transport in the whole thermal boundary layer are unlikely to be correct at very high Rayleigh numbers.

The mechanism of destruction of a central transport barrier in a dynamical model of a geophysical zonal jet current in the ocean or the atmosphere with two propagating Rossby waves is studied. We develop a method for computing a central invariant curve which is an indicator of existence of the barrier. Breakdown of this curve under a variation in the Rossby wave amplitudes and onset of chaotic cross-jet transport happen due to specific resonances producing stochastic layers in the central jet. The main result is that there are resonances breaking the transport barrier at unexpectedly small values of the amplitudes that may have serious impact on mixing and transport in the ocean and the atmosphere. The effect can be found in laboratory experiments with azimuthal jets and Rossby waves in rotating tanks under specific values of the wave numbers that are predicted in the theory.

We study pair dispersion in a three-dimensional incompressible high Reynolds number turbulent flow generated by Fourier transforming the dynamics of the Gledzer-Ohkitani-Yamada (GOY) shell model into real space. We show that GOY shell model can successfully reproduce both the Batchelor and the Richardson-Obukhov regimes of turbulent relative dispersion. We also study how the crossover time scales with the initial separations of a particle pair and compare it to the prediction by Batchelor.

The important role of interface collisions on the thermal-diode effect, of the two-segment lattices is studied. In the high-average temperature region, it is found that the thermal-diode effect may be significantly weaken and even annihilated. In the low-temperature region, where the thermal diode is inhibited in the collisionless case, an interesting reversed thermal diode is achieved. These behaviors are interpreted in terms of phonon-band mixing induced by interface collisions. The regime where a reversed thermal diode can be observed by resorting to the dependence of the heat current on the average temperature, and a critical temperature exists. The results proposed in this paper reveal that thermal-diode effect can be qualitatively influenced if the interface collisions could not be neglected.

The monitoring of the residence time difference in bistable sensors has been recently proposed as a valid scheme for improving the detection capabilities of sensors as diverse as fluxgate magnetometers, ferroelectric sensors and mechanical sensors. In this paper we propose an approach to the residence time based detection strategy based on the measurement of the slope $m$ of the sensor output integral. We demonstrate that such a method, far from degrading the detection performances can provide an easier way to realize fast and reliable sensors without the computationally demanding task related with the computation of the residence time difference. We introduce the receiver operating characteristic curve as a quantitative estimator for the comparison of the two methods and show that the detector performances increase with increasing the periodic bias amplitude $A$ up to a maximum value. This condition has potentially relevant consequences in the future detectors design.

The rheology of dense amorphous materials under large shear strain is not fully understood, partly due to the difficulty of directly viewing the microscopic details of such materials. We use a colloidal suspension to simulate amorphous materials and study the shear-induced structural relaxation with fast confocal microscopy. We quantify the plastic rearrangements of the particles in several ways. Each of these measures of plasticity reveals spatially heterogeneous dynamics, with localized regions where many particles are strongly rearranging by these measures. We examine the shapes of these regions and find them to be essentially isotropic, with no alignment in any particular direction. Furthermore, individual particles are equally likely to move in any direction other than the overall bias imposed by the strain.

We studied the local layer structure in the B2 phase of bromine-substituted bent-core liquid crystals in the cell geometry using microbeam resonant x-ray scattering. In the homochiral state of B2 phase, the 3/2 order satellite peak was observed only when the incident x-ray energy is at the K absorption edge of bromine. This result clearly indicates that the B2 homochiral domain forms two-layer superlattice in adjacent layers, the same as in the rodlike Sm-$C_{\text{A}}$ phase. The work reports on microbeam resonant x-ray scattering experiment from the local layer of the bent-core liquid crystal in the device geometry. Moreover, we can say that bromine is also useful for the analysis of the superstructure of soft materials using resonant x-ray scattering.