The temperature field inside an evaporating two-dimensional droplet resting on curved or flat isothermal substrates is studied under various evaporation conditions. An analytical solution for the temperature is derived, which can be directly used in the cases of pinned and depinned contact lines as well as in stick-slip evaporation modes. It is found that the temperature drop at the free surface of a droplet on a convex, hydrophobic substrate is far greater than that for flat or concave substrates of the same hydrophobicity. The analytical solution for the temperature field allows the direct estimate of the local temperature gradient and, hence, of the local surface tension gradient that gives rise to Marangoni flow directed from the contact lines to the top of the droplet.

We perform Monte Carlo simulations of a simplified two-dimensional model for colloidal hard spheres in an external uniaxial ac electric field. Experimentally, the external field induces dipole moments in the colloidal particles, which in turn form chains. We therefore approximate the system as composed of well-formed chains of dipolar hard spheres of a uniform length. The dipolar interaction between colloidal spheres gives rise to an effective interaction between the chains, which we treat as disks in a plane, that includes a short-range attraction and long-range repulsion. Hence, the system favors finite clustering over bulk phase separation, and indeed we observe at low temperature and density that the system does form a cluster phase. As the density increases, percolation is accompanied by a pressure anomaly. The percolated phase, despite being composed of connected, locally crystalline domains, does not bear the typical signatures of a hexatic phase. At very low densities, we find no indication of a “void phase” with a cellular structure seen recently in experiments.

The trembling shear behavior of electrorheological (ER) fluids has been investigated by using a computer simulation method, and a shear-slide boundary model is proposed to understand this phenomenon. A thiourea-doped Ba-Ti-O ER fluid which shows a trembling shear behavior was first prepared and then systematically studied by both theoretical and experimental methods. The shear curves of ER fluids in the dynamic state were simulated with shear rates from 0.1 to 1000 s${}^{-1}$ under different electric fields. The simulation results of the flow curves match the experimental results very well. The trembling shear curves are divided into four regions and each region can be explained by the proposed model.

We study the dynamics of a one-dimensional fluid of orientable hard rectangles with a non-coarse-grained microscopic mechanism of facilitation. The length occupied by a rectangle depends on its orientation, which is a discrete variable coupled to an external field. The equilibrium properties of our model are essentially those of the Tonks gas, but at high densities the orientational degrees of freedom become effectively frozen due to jamming. This is a simple analytically tractable model of the glassy phase. Under a cyclic variation of the pressure, hysteresis is observed. Following a pressure quench, the orientational persistence exhibits a two-stage decay characteristic of glassy systems.

Efforts are currently under way to produce nanoparticle samples with a size dispersion as low as possible, using deposition of preformed clusters on a substrate. However, even for diluted cluster films, contact or coalescence between neighboring clusters cannot be totally avoided due to the random nature of the deposition process. Consequently, the incident particle-size distribution will necessarily be degraded, with the statistical formation of multimers (dimers, trimers, or more generally $n$mers). In this article, we consider diluted assemblies of nanoparticles (with a narrow size distribution) randomly deposited on a surface and develop theoretical tools to assess the various multimer proportions. We establish simple and reliable analytical approximations of the probability for a cluster to form an $n$mer and the subsequent multimer proportion. These results can be applied in the analysis of experimental samples: They constitute a convenient tool for experimentalists in the design of their nanoparticle sample and the interpretation of experimental measurements.

We study the out-of-equilibrium relaxation of surface steps after thermal quenches using numerical simulations of the terrace-step-kink model for a vicinal surface. We analyze both single and interacting steps in a situation where the temperature is suddenly changed at a given quench time. We focus on a physically relevant range of temperatures and show that the relaxation of the roughness is compatible with a power-law behavior with an effective relaxation exponent close to $\gamma =1/2$ in all cases. This value is consistent with a one-dimensional Edwards-Wilkinson equation. In particular, this means that, although the case of interacting steps is effectively a two-dimensional system, its relaxation is dominated by short length-scale fluctuations, where steps are not interacting.

We apply the method developed [Chernyshuk and Lev, Phys. Rev. E 81, 041701 (2010)] for theoretical investigation of colloidal elastic interactions between axially symmetric particles in the confined nematic liquid crystal near one wall and in the nematic cell with thickness $L$. Both cases of homeotropic and planar director orientations are considered. Particularly, dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions of the one particle with the wall and within the nematic cell are found as well as corresponding two particle elastic interactions. A set of results has been predicted: The effective power of repulsion between two dipole particles at height $h$ near the homeotropic wall is reduced gradually from inverse 3 to 5 with an increase of dimensionless distance $r/h$; near the planar wall, the effect of dipole-dipole isotropic attraction is predicted for large distances $r>r_{\mathit{dd}}=4.76h$; maps of attraction and repulsion zones are crucially changed for all interactions near the planar wall and in the planar cell; and one dipole particle in the homeotropic nematic cell was found to be shifted by the distance ${\delta }_{\mathrm{eq}}$ from the center of the cell. The proposed theory fits very well with experimental data for the confinement effect of elastic interaction between spheres in the homeotropic cell [Vilfan et al., Phys. Rev. Lett. 101, 237801 (2008)] in the range $1-1000$ kT. The influence of the $K_{24}$ and $K_{13}$ terms as well as connection with other theoretical approaches are discussed.

Dielectric relaxation spectra of solutions of block polymers containing sequential type-A dipoles are considered from a theoretical correlation-function standpoint. Spectra of a specific set of block copolymers can be combined to isolate the dynamic cross-correlation between the motions of two distinct parts of the same polymer chain. Unlike past treatments of this problem, no model is assumed for the underlying polymer dynamics.

A stochastic interpretation of spontaneous action potential initiation is developed for the Morris-Lecar equations. Initiation of a spontaneous action potential can be interpreted as the escape from one of the wells of a double well potential, and we develop an asymptotic approximation of the mean exit time using a recently developed quasistationary perturbation method. Using the fact that the activating ionic channel’s random openings and closings are fast relative to other processes, we derive an accurate estimate for the mean time to fire an action potential (MFT), which is valid for a below-threshold applied current. Previous studies have found that for above-threshold applied current, where there is only a single stable fixed point, a diffusion approximation can be used. We also explore why different diffusion approximation techniques fail to estimate the MFT.

The response of a neuronal population to afferent drive can be expected to be sensitive to both the distribution and dynamics of membrane voltages within the population. Voltage fluctuations can be driven by synaptic noise, neuromodulators, or cellular inhomogeneities: processes ranging from millisecond autocorrelation times to effectively static or “frozen” noise. Here we extend previous studies of filtered fluctuations to the experimentally verified exponential integrate-and-fire model. How fast or frozen fluctuations affect the steady-state rate and firing-rate response are both examined using perturbative solutions and limits of a 1 $+$ 2 dimensional Fokker-Planck equation. The central finding is that, under conditions of a more-or-less constant population voltage variance, the firing-rate response is only weakly dependent on the fluctuation filter constant: The voltage distribution is the principal determinant of the population response. This result is unexpected given the nature of the systems underlying the extreme limits of fast and frozen fluctuations; the first limit represents a homogeneous population of neurons firing stochastically, whereas the second limit is equivalent to a heterogeneous population of neurons firing deterministically.

We study the influence of temperature and the values of basic energy parameters on the character of vibron self-trapped states in quasi-one-dimensional hydrogen-bonded molecular chains. Investigations have been carried out within the one-dimensional Holstein molecular crystal model employing the variational extension of the Lang-Firsov unitary transformation. It was found that, in the low-temperature regime, only partially dressed small-polaron states may exist. With the rise of temperature, the system enters the metastability region, where partially dressed (light and mobile) and fully dressed (heavy and practically immobile) small-polaron states may exist simultaneously.

It has been suggested that the three-dimensional structure of one particle may be reconstructed using the scattering from many identical, randomly oriented copies ab initio, without modeling or a priori information. This may be possible if these particles are frozen in either space or time, so that the conventional two-dimensional small-angle x-ray scattering (SAXS) distribution contains fluctuations and is no longer isotropic. We consider the magnitude of the correlated fluctuation SAXS (CFSAXS) signal for typical x-ray free-electron laser (XFEL) beam conditions and compare this against the errors derived with the inclusion of Poisson photon counting statistics. The resulting signal-to-noise ratio (SNR) is found to rapidly approach a limit independent of the number of particles contributing to each diffraction pattern, so that the addition of more particles to a “single-particle-per-shot” experiment may be of little value, apart from reducing solvent background. When the scattering power is significantly less than one photon per particle per Shannon pixel, the SNR grows in proportion to incident flux. We provide simulations for protein molecules in support of these analytical results, and discuss the effects of solvent background scatter. We consider the SNR dependence on resolution and particle size, and discuss the application of the method to glasses and liquids, and the implications of more powerful XFELs, smaller focused beams, and higher pulse repetition rates for this approach. We find that an accurate CFSAXS measurement may be acquired to subnanometer resolution for protein molecules if a 9-keV beam containing ${10}^{13}$ photons is focused to a $\sim$100-nm spot diameter, provided that the effects of solvent background can be reduced sufficiently.

When particles in liquid suspensions flow through channels and pipes in a laminar fashion, the resulting parabolic velocity profile gives rise to shear, which induces the particles to rotate. If flowing suspensions containing dielectric particles are immersed in an external electric field, the anisotropic polarization induced in rotating nonspherical particles will vary with the orientation of the particle with respect to the external field; what results is an uncertainty in experimental measurements that involve particle polarization. The present study establishes the limits of this uncertainty and shows that departure from spherical symmetry in individual particles can lead to a significant overlap in measurements attempting to discriminate between particle subpopulations in suspensions. For example, the uncertainty in signal amplitude for a population of activated T-lymphocytes can be as high as $20\%.$ Such concerns arise in applications like field-flow fractionation, dielectrophoretic sorting of particles, flow impedance measurements and cytometry, and, most recently, isodielectric separation, all of which are used to separate particles in a flow based on their dielectric response. This paper considers axisymmetric particles as the first departure from the approximation of spherical symmetry, shows how to calculate an estimate of the size of the population overlap, and suggests possible strategies to minimize it.

Suprathreshold stochastic resonance (SSR) is examined in the context of integrate-and-fire neurons, with an emphasis on the role of correlation in the neuronal firing. We employed a model based on a network of spiking neurons which received synaptic inputs modeled by Poisson processes stimulated by a stepped input signal. The smoothed ensemble firing rate provided an output signal, and the mutual information between this signal and the input was calculated for networks with different noise levels and different numbers of neurons. It was found that an SSR effect was present in this context. We then examined a more biophysically plausible scenario where the noise was not controlled directly, but instead was tuned by the correlation between the inputs. The SSR effect remained present in this scenario with nonzero noise providing improved information transmission, and it was found that negative correlation between the inputs was optimal. Finally, an examination of SSR in the context of this model revealed its connection with more traditional stochastic resonance and showed a trade-off between supratheshold and subthreshold components. We discuss these results in the context of existing empirical evidence concerning correlations in neuronal firing.

We derive expressions for the high-frequency, wave-number-dependent elastic constants of a binary hard-sphere fluid and employ Monte Carlo computer simulation to evaluate these constants in order to highlight the impact of composition and relative sphere diameter on the elastic response of this system. It is found that the elastic constant $c_{11}\left(k\right)$ exhibits oscillatory behavior as a function of $k$ whereas the high-frequency shear modulus, for example, does not. This behavior is shown to be dictated by the angular dependence (in $\vec{k}$ space) of derivatives of the interatomic force at contact. The results are related to recent measurements of the compressibility of colloidal fluids in laser trapping experiments.

Tuning one’s shower in some hotels may turn into a challenging coordination game with imperfect information. The temperature sensitivity increases with the number of agents, making the problem possibly unlearnable. Because there is in practice a finite number of possible tap positions, identical agents are unlikely to reach even approximately their favorite water temperature. We show that a population of agents with homogeneous strategies is evolutionary unstable, which gives insights into the emergence of heterogeneity, the latter being tempting but risky.

Two penalized—balanced and normalized—versions of the Newman-Girvan modularity are introduced and estimated by the non-negative eigenvalues of the modularity and normalized modularity matrix, respectively. In this way, the partition of the vertices that maximizes the modularity can be obtained by applying the $k$-means algorithm for the representatives of the vertices based on the eigenvectors belonging to the largest positive eigenvalues of the modularity or normalized modularity matrix. The proper dimension depends on the number of the structural eigenvalues of positive sign, while dominating negative eigenvalues indicate an anticommunity structure; the balance between the negative and the positive eigenvalues determines whether the underlying graph has a community, anticommunity, or randomlike structure.

In this paper the effects of inter-community links on the synchronization performance of community networks, especially on the competition between individual community and the whole network, are studied in detail. The study is organized from two aspects: the number or portion of inter-community links and the connection strategy of inter-community links between different communities. A critical point is found in the competition of global network and individual communities. Increasing the number of inter-community links will enhance the global synchronizability but degrade the synchronization performance of individual community before this point. After that the individual community will synchronize better and better as part of the whole network because the community structure is not so prominent. The critical point represents a balance region where the individual community is maximally independent while the information transmission remains effective between different communities. Among various connection strategies, connecting nodes belonging to different communities randomly rather than connecting nodes with larger degrees are the most efficient way to enhance global synchronization of the network. However, the dynamical modularity is the reverse case. A preferential connection scheme linking most of the hubs from the communities will allow rather efficient global synchronization while maintaining strong dynamical clustering of the communities. Interestingly, the observations are found to be relevant in a realistic network of cat cortex. The synchronization state is just at the critical point, which shows a reasonable combination of segregated function in individual communities and coordination among them. Our work sheds light on principles underlying the emergence of modular architectures in real network systems and provides guidance for the manipulation of synchronization in community networks.

We derive analytic expressions for the possibility, probability, and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed and undirected edges and arbitrary degree-degree correlations. Our work extends previous theoretical developments for the undirected case, and we provide numerical support for our findings by investigating an example class of networks for which we are able to obtain closed-form expressions.

The Kolmogorov-Sinai (KS) entropy is a central measure of complexity and chaos. Its calculation for many-body systems is an interesting and important challenge. In this paper, the evaluation is formulated by considering $N$-dimensional symplectic maps and deriving a transfer matrix formalism for the stability problem. This approach makes explicit a duality relation that is exactly analogous to one found in a generalized Anderson tight-binding model and leads to a formally exact expression for the finite-time KS entropy. Within this formalism there is a hierarchy of approximations, the final one being a diagonal approximation that only makes use of instantaneous Hessians of the potential to find the KS entropy. By way of a nontrivial illustration, the KS entropy of $N$ identically coupled kicked rotors (standard maps) is investigated. The validity of the various approximations with kicking strength, particle number, and time are elucidated. An analytic formula for the KS entropy within the diagonal approximation is derived and its range of validity is also explored.