We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single-component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth, and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-“liquid” as well as vapor-“solid” coexistence. For the vapor-liquid phase separation we observe that $\ell$, the average domain length, grows with time ($t$) as $t^{1/2}$, a behavior that has connection with hydrodynamics. At low-enough temperature, a sharp crossover of this time dependence to a much slower, temperature-dependent, growth is identified within the timescale of our simulations, implying “solid”-like final state of the high-density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data collapse with respect to $\ell /{\ell }_w, \ell$, and ${\ell }_w$ being the average domain lengths at times $t$ and $t_w$ ($\le t$), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: $\sim {(\ell /{\ell }_w)}^{-\lambda }$ for $t\gg t_w$. The decay exponent $\lambda$, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.

We study stability and chaotic-transport features of paradigmatic nonequilibrium many-body systems, i.e., periodically kicked and interacting particles, for arbitrary number of particles, nonintegrability strength unbounded from above, and different interaction cases. We rigorously show that under the latter general conditions and in strong nonintegrability regimes there exist fully stable orbits, accelerator-mode (AM) fixed points, performing ballistic motion in momentum. These orbits exist despite of the completely and strongly chaotic phase space with generally fast Arnol'd diffusion. It is numerically shown that an “isolated chaotic zone” (ICZ), separated from the rest of the phase space, remains localized around an AM fixed point for long times even when this point is partially stable in only a few phase-space directions. This localization should reflect an Arnol'd diffusion in an ICZ much slower than that in the rest of phase space. The time evolution of the mean kinetic energy of an initial ensemble containing an ICZ exhibits superdiffusion instead of normal chaotic diffusion.

The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. The DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity over the relevant state space and fails when this property is not satisfied. This failure becomes severe in situations where the direction of selection switches sign. Here we employ the WKB (Wentzel-Kramers-Brillouin) large-deviations method, which requires only the logarithm of a given quantity to be smooth over its state space. Combining the WKB scheme with asymptotic matching techniques, we show how to derive the diffusion approximation in a controlled manner and how to produce better approximations, applicable for much wider regimes of parameters. We also introduce a scalable (independent of population size) WKB-based numerical technique. The method is applied to a central problem in population genetics and evolution, finding the chance of ultimate fixation in a zero-sum, two-types competition.

Like genes and proteins, cells can use biochemical networks to sense and process information. The differentiation of the cell state in colonic crypts forms a typical unidirectional phenotypic transitional cascade, in which stem cells differentiate into the transit-amplifying cells (TACs), and TACs continue to differentiate into fully differentiated cells. In order to quantitatively describe the relationship between the noise of each compartment and the amplification of signals, the gain factor is introduced, and the gain-fluctuation relation is obtained by using the linear noise approximation of the master equation. Through the simulation of these theoretical formulas, the characters of noise propagation and amplification are studied. It is found that the transmitted noise is an important part of the total noise in each downstream cell. Therefore, a small number of downstream cells can only cause its small inherent noise, but the total noise may be very large due to the transmitted noise. The influence of the transmitted noise may be the indirect cause of colon cancer. In addition, the total noise of the downstream cells always has a minimum value. As long as a reasonable value of the gain factor is selected, the number of cells in colonic crypts will be controlled within the normal range. This may be a good method to intervene the uncontrollable growth of tumor cells and effectively control the deterioration of colon cancer.

Hydrogels are sponge-like materials that can absorb or expel significant amounts of water. Swelling up from a dried state, they can swell up more than a hundredfold in volume, with the kinetics and the degree of swelling depending sensitively on the physicochemical properties of both the polymer network and the aqueous solvent. In particular, the presence of dissolved macromolecules in the background liquid can have a significant effect, as the macromolecules can exert an additional external osmotic pressure on the hydrogel material, thereby reducing the degree of swelling. In this paper, we have submerged dry hydrogel particles in polymer solutions containing large and small macromolecules. Interestingly, for swelling in the presence of large macromolecules we observe a concentration-dependent overshoot behavior, where the particle volume first continuously increases toward a maximum, after which it decreases again, reaching a lower, equilibrium value. In the presence of smaller macromolecules we do not observe this intriguing overshoot behavior, but instead observe a rapid growth followed by a slowed-down growth. To account for the observed overshoot behavior, we realize that the macromolecules entering the hydrogel network not only lead to a reduction of the osmotic pressure difference, but their presence within the network also affects the swelling behavior through a modification of the solvent-polymer interactions. In this physical picture of the swelling process, the net amount of volume change should thus depend on the magnitudes of both the reduction in osmotic pressure and the change in effective solvent quality associated with the macromolecules entering the pores of the hydrogel network. We develop a phenomenological model that incorporates both of these effects. Using this model we are able to account for both the swelling and compression kinetics of hydrogels within aqueous polymer solutions, as a function of the size of the dissolved macromolecules and of their effect on the effective solvent quality.

The swelling and compression of hydrogels in polymer solutions can be understood by considering hydrogel-osmolyte-solvent interactions which determine the osmotic pressure difference between the inside and the outside of a hydrogel particle and the changes in effective solvent quality for the hydrogel network. Using the theory of poroelasticity, we find the exact solution to hydrogel dynamics in a dilute polymer solution, which quantifies the effect of diffusion and partitioning of osmolyte and the related solvent quality change to the volumetric changes of the hydrogel network. By making a dominant-mode assumption, we propose a model for the swelling and compression dynamics of (spherical) hydrogels in concentrated polymer solutions. Osmolyte diffusion induces a biexponential response in the size of the hydrogel radius, whereas osmolyte partitioning and solvent quality effects induce monoexponential responses. Comparison of the dominant-mode model to experiments provides reasonable values for the compressive bulk modulus of a hydrogel particle, the permeability of the hydrogel network, and the diffusion constant of osmolyte molecules inside the hydrogel network. Our model shows that hydrogel-osmolyte interactions can be described in a conceptually simple manner, while still capturing the rich (de)swelling behaviors observed in experiments. We expect our approach to provide a roadmap for further research into and applications of hydrogel dynamics induced by, for example, changes in the temperature and the $p\mathrm{H}$.

A general theory of liquid crystals is presented, starting from the group-theory symmetry analysis of the constituting molecules. A particular attention is paid to the type of elastic free-energies and their relationships with the molecular symmetries. The orientational order-parameter tensors are identified for each molecular symmetry, in a consideration of consistently keeping the leading, characteristic elastic free energies in a model. The order parameters are expressed in terms of symmetric traceless tensors, some of high orders, for all major molecular symmetries, including seven groups of axial symmetries and seven groups of polyhedral symmetries. For spatially inhomogeneous liquid crystals, the couplings of these tensors in the elastic energies are derived by expanding the interaction energies between these molecules. The aim is to provide a general view of the molecular symmetries of individual molecules, orientational order parameters characterizing the orientational distribution functions, and the elastic free energies, all under one single group-theory approach.

We consider a fluid interface in contact with an elastic membrane and study the static profiles of the interface and the membrane. Equilibrium conditions are derived by minimizing the total energy of the system with volume constraints. The total energy consists of surface energies and the Willmore energy; the latter penalizes the bending of the membrane. It is found that, while the membrane is locally flat at the contact line with the contact angle satisfying the Young-Dupré equation, the gradient of the mean curvature of the membrane exhibits a jump across the contact line. This jump balances the surface tension of the fluid interface in the normal direction of the membrane. Asymptotic solutions are obtained for two-dimensional systems in the limits as the reduced bending modulus $\nu$ tends to $+\infty$ and 0, respectively. In the stiff limit as $\nu \to +\infty$, the leading-order solution is given by that of a droplet sitting on a rigid substrate with the contact angle satisfying the Young-Dupré equation; in contrast, in the soft limit as $\nu \to 0$, a transition layer appears near the contact line and the interfaces have constant curvatures in the outer region with apparent contact angles obeying Neumann's law. These solutions are validated by numerical experiments.

During the past few years, researchers have been proposing time-dependent injection strategies for stabilizing or manipulating the development of viscous fingering instabilities in radial Hele-Shaw cells. Most of these studies investigate the displacement of Newtonian fluids and are entirely based on linear stability analyses. In this work, linear stability theory and variational calculus are used to determine closed-form expressions for the proper time-dependent injection rates $Q\left(t\right)$ required to either minimize the interface disturbances or to control the number of emerging fingers. However, this is done by considering that the displacing fluid is non-Newtonian and has a time-varying viscosity. Moreover, a perturbative third-order mode-coupling approach is employed to examine the validity and effectiveness of the controlling protocols dictated by these $Q\left(t\right)$ beyond the linear regime and at the onset of nonlinearities.

The Wiener-Khinchin theorem for the Fourier-Laplace transformation (WKT-FLT) provides a robust method to obtain the single-side Fourier transforms of arbitrary time-domain relaxation functions (or autocorrelation functions). Moreover, by combining an on-the-fly algorithm with the WKT-FLT, the numerical calculations of various complex spectroscopic data in a wide frequency range become significantly more efficient. However, the discretized WKT-FLT equation, obtained simply by replacing the integrations with the discrete summations, always produces two artifacts in the frequency-domain relaxation function. In addition, the artifacts become more apparent in the frequency-domain response function converted from the relaxation function. We find the sources of these artifacts that are associated with the discretization of the WKT-FLT equation. Taking these sources into account, we derive discretized WKT-FLT equations designated for both the frequency-domain relaxation and response functions with the artifacts removed. The use of the discretized WKT-FLT equations with the on-the-fly algorithm is illustrated by a flow chart. We also give application examples for the wave-vector-dependent dynamic susceptibility in an isotropic amorphous polyethylene and the frequency-domain response functions of the orientation vectors in an $n$-alkane crystal.

We investigate the distribution of bubble lifetimes and bubble lengths in DNA at physiological temperature, by performing extensive molecular dynamics simulations with the Peyrard-Bishop-Dauxois (PBD) model, as well as an extended version (ePBD) having a sequence-dependent stacking interaction, emphasizing the effect of the sequences' guanine-cytosine (GC)/adenine-thymine (AT) content on these distributions. For both models we find that base pair-dependent (GC vs AT) thresholds for considering complementary nucleotides to be separated are able to reproduce the observed dependence of the melting temperature on the GC content of the DNA sequence. Using these thresholds for base pair openings, we obtain bubble lifetime distributions for bubbles of lengths up to ten base pairs as the GC content of the sequences is varied, which are accurately fitted with stretched exponential functions. We find that for both models the average bubble lifetime decreases with increasing either the bubble length or the GC content. In addition, the obtained bubble length distributions are also fitted by appropriate stretched exponential functions and our results show that short bubbles have similar likelihoods for any GC content, but longer ones are substantially more likely to occur in AT-rich sequences. We also show that the ePBD model permits more, longer-lived, bubbles than the PBD system.

The persistence exponent $\theta$, which characterizes the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. So far, anomalous values of the persistence exponent ($\theta \ne 1/2$) were obtained, but only for anomalous processes (i.e., with Hurst exponent $H\ne 1/2$). Here we exhibit examples of ageing processes which, even if they display asymptotically a normal diffusive scaling ($H=1/2$), are characterized by anomalous persistent exponents that we determine analytically. Based on this analysis, we propose the following general criterion: The persistence exponent of asymptotically diffusive processes is anomalous if the increments display ageing and depend on the observation time $T$ at all timescales.

The spin-1/2 Hamiltonian for two coupled isosceles Heisenberg triangles, which is well suited for describing the ${\mathrm{V}}_6$-type magnetic molecules, is studied by exact diagonalization. The quantum phase transition diagram, at zero temperature, is obtained as a function of the theoretical parameters. The zero temperature magnetization is also obtained as a function of the external magnetic field. The thermodynamic behavior of the magnetization, entropy, susceptibility, and specific heat, as a function of temperature, are also computed and the corresponding magnetocaloric effect analyzed for various values of the Hamiltonian parameters.

We study the spectrum of generalized Wishart matrices, defined as $\mathbf{F}=(\mathbf{X}{\mathbf{Y}}^{\top }+\mathbf{Y}{\mathbf{X}}^{\top })/2T$, where $\mathbf{X}$ and $\mathbf{Y}$ are $N\times T$ matrices with zero mean, unit variance independent and identically distributed entries and such that $\mathbb{E}\left[{\mathbf{X}}_{it}{\mathbf{Y}}_{jt}\right]=c{\delta }_{i,j}$. The limit $c=1$ corresponds to the Marčenko-Pastur problem. For a general $c$, we show that the Stieltjes transform of $\mathbf{F}$ is the solution of a cubic equation. In the limit $c=0, T\gg N$, the density of eigenvalues converges to the Wigner semicircle.

Recent work has shown that in a nonthermal, multidimensional system, the trajectories in the activated complex possess different instantaneous and time-averaged reactant decay rates. Under dissipative dynamics, it is known that these trajectories, which are bound on the normally hyperbolic invariant manifold (NHIM), converge to a single trajectory over time. By subjecting these dissipative systems to thermal noise, we find fluctuations in the saddle-bound trajectories and their instantaneous decay rates. Averaging over these instantaneous rates results in the decay rate of the activated complex in a thermal system. We find that the temperature dependence of the activated complex decay in a thermal system can be linked to the distribution of the phase space resolved decay rates on the NHIM in the nondissipative case. By adjusting the external driving of the reaction, we show that it is possible to influence how the decay rate of the activated complex changes with rising temperature.

Neural field theory of the corticothalamic system is used to explore evoked response potentials (ERPs) caused by spatially localized impulse stimuli on the convoluted cortex and on a spherical cortex. Eigenfunctions are calculated analytically on the spherical cortex and numerically on the convoluted cortex via eigenfunction expansions. Eigenmodes on a convoluted cortex are similar to those of the spherical cortex, and a few such modes are found to be sufficient to reproduce the main ERP features. It is found that the ERP peak is stronger in spherical cortex than convoluted cortex, but in both cases the peak decreases monotonically with increasing distance from the stimulus point. In the convoluted case, cortical folding causes ERPs to differ between locations at the same distance from the stimulus point and spherical symmetries are only approximately preserved.

Components in many real-world complex systems depend on each other for the resources required for survival and may die of a shortage. These patterns of dependencies often take the form of a complex network whose structure potentially affects how the resources produced in the system are efficiently shared among its components, which in turn decides a network's survivability. Here we present a simple threshold model that provides insight into this relationship between the network structure and survivability. We show that, as a combined effect of local sharing and finite lifetime of resources, many components in a complex system may die of lack of resources even when a sufficient amount is available in the system. We also obtain a surprising result that although the scale-free networks exhibit a significantly higher survivability compared to their homogeneous counterparts, a vertex in the latter survives longer on average. Finally, we demonstrate that the system's survivability can be substantially improved by changing the way vertices distribute resources among the neighbors. Our work is a step towards understanding the relationship between intricate resource dependencies present in many real-world complex systems and their survivability.

Strong electric fields may deform drops and induce their oscillation or motion on the substrate. Moreover, they can initiate partial discharges (PDs) because of the enhancement of the electric field in the vicinity of the three-phase contact lines. The partial discharges affect the drop spreading which can result in unusual drop shapes. In addition, the partial discharges can also deteriorate the surface properties of the substrate, e.g., of high-voltage composite insulators. In this study the occurrence of partial discharges due to stationary or oscillating sessile drops under the influence of an alternating electric field is investigated using a generic insulator model under well-defined conditions. Drops of a yield stress fluid (a gelatin-water mixture) are used to determine the PD inception field strength for stationary drop shapes. The influence of the volume as well as the distance between the individual drops for two drop configurations on the PD inception threshold is determined. The inception field strength of the partial discharges is measured for various drop volumes, drop charges, as well as for different resonance modes of drop oscillations. Besides the electrical measurement, the location of the partial discharges is optically determined by a UV camera. The detailed knowledge of the influencing factors of the partial discharges improves the understanding of the drop behavior under the impact of strong electric fields.

Langevin dynamical simulations are performed to study the depinning dynamics of two-dimensional dusty plasmas on a one-dimensional periodic substrate. From the diagnostics of the sixfold coordinated particles $P_6$ and the collective drift velocity $V_x$, three different states appear, which are the pinning, disordered plastic flow, and moving ordered states. It is found that the depth of the substrate is able to modulate the properties of the depinning phase transition, based on the results of $P_6$ and $V_x$, as well as the observation of hysteresis of $V_x$ while increasing and decreasing the driving force monotonically. When the depth of the substrate is shallow, there are two continuous phase transitions. When the potential well depth slightly increases, the phase transition from the pinned to the disordered plastic flow states is continuous; however, the phase transition from the disordered plastic flow to the moving ordered states is discontinuous. When the substrate is even deeper, the phase transition from the pinned to the disordered plastic flow states changes to discontinuous. When the depth of the substrate further increases, as the driving force increases, the pinned state changes to the moving ordered state directly, so that the disordered plastic flow state disappears completely.