A polymer-membrane interacting system can produce a variety of structures. Here, we theoretically study a model system in which a membrane pushes a polymer against a hard surface; we show that a first-order structural phase transition can occur. Using a Monte Carlo simulation, we reveal that the system undergoes a transition from a confined (bump) state to a strongly confined (flattened-out) state as the pressure increases. A scaling argument is also made to understand the physical mechanism behind the phase transition and the properties of each state.

The emergence of invasive and metastatic behavior in malignant tumors can often lead to fatal outcomes for patients. The collective malignant tumor behavior resulting from the complex tumor-host interactions and the interactions between the tumor cells is currently poorly understood. In this paper, we employ a cellular automaton (CA) model to investigate microenvironment-enhanced malignant behaviors and morphologies of in vitro avascular invasive solid tumors in three dimensions. Our CA model incorporates a variety of microscopic-scale tumor-host interactions, including the degradation of the extracellular matrix by the malignant cells, nutrient-driven cell migration, pressure buildup due to the deformation of the microenvironment by the growing tumor, and its effect on the local tumor-host interface stability. Moreover, the effects of cell-cell adhesion on tumor growth are explicitly taken into account. Specifically, we find that while strong cell-cell adhesion can suppress the invasive behavior of the tumors growing in soft microenvironments, cancer malignancy can be significantly enhanced by harsh microenvironmental conditions, such as exposure to high pressure levels. We infer from the simulation results a qualitative phase diagram that characterizes the expected malignant behavior of invasive solid tumors in terms of two competing malignancy effects: the rigidity of the microenvironment and cell-cell adhesion. This diagram exhibits phase transitions between noninvasive and invasive behaviors. We also discuss the implications of our results for the diagnosis, prognosis, and treatment of malignant tumors.

In microfluidics the instability of an interface between two fluids may be favorable or unfavorable. Such an instability for incompressible flows has been extensively studied in the literature; in this paper we extend it to compressible flows which slip on the solid boundary. A generalized Darcy's law taking into consideration the compressibility and velocity slip is obtained. Using a conformal-mapping method we derive an interface equation on a fixed domain, the solutions of which determine the moving interface. We also examine the linear stability of the base-state flow by perturbing the corresponding conformal map and show that the velocity slip has a stabilizing effect.

We employ Leslie's perturbation scheme coupled with renormalization group calculations to obtain the anisotropic velocity correlation tensor in the inertial range of homogeneous shear turbulence. Hence we evaluate two universal numbers associated with the anisotropic part of the equal-time correlation tensor in the leading order of the perturbative scheme. Our theoretical results for these universal numbers are found to be in fairly good agreement with experimental values as well as estimates coming from direct numerical simulations.

We show that the relativistic dissipative hydrodynamic equation derived from the relativistic Boltzmann equation by the renormalization-group method uniquely leads to the one in the energy frame proposed by Landau and Lifshitz, provided that the macroscopic-frame vector, which defines the local rest frame of the flow velocity, is independent of the momenta of constituent particles, as it should. We argue that the relativistic hydrodynamic equations for viscous fluids must be defined on the energy frame if consistent with the underlying relativistic kinetic equation.

Turbulence governed by a generalized nonlinear Schrödinger equation (GNSE) including viscous heating and nonlinear damping is numerically investigated. It is found that a large localized pulse can suffer modulational instability and then collapse into the shortest-wavelength modes, as for the classical nonlinear Schrödinger equation. However, the total energy of the nonconservative GNSE can also become constant during the collapse via local balance of energy gain and loss in the phase space. After the collapse, instead of inverse cascading into a state of strong turbulence with broad spectrum, a single-step cascade, or condensation, into modes of one predominant wavelength can occur. In fact, after attaining total energy balance the turbulent system as a whole evolves like a closed adiabatic system.

We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of nonequilibrium stochastic currents. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of parity and state probabilities, and discontinuities in the steady state statistics of currents.

Detecting unstable periodic orbits (UPOs) in chaotic systems based solely on time series is a fundamental but extremely challenging problem in nonlinear dynamics. Previous approaches were applicable but mostly for low-dimensional chaotic systems. We develop a framework, integrating approximation theory of neural networks and adaptive synchronization, to address the problem of time-series-based detection of UPOs in high-dimensional chaotic systems. An example of finding UPOs from the classic Mackey-Glass equation is presented.

By combining total internal reflection fluorescence cross-correlation spectroscopy with Brownian dynamics simulations, we were able to measure the hydrodynamic boundary condition of water flowing over a smooth solid surface with exceptional accuracy. We analyzed the flow of aqueous electrolytes over glass coated with a layer of poly(dimethylsiloxane) (advancing contact angle Θ $=$ 108°) or perfluorosilane (Θ $=$ 113°). Within an error of better than 10 nm the slip length was indistinguishable from zero on all surfaces.

An investigation of the distribution of finite time trajectory divergence is performed on an atmospheric global circulation model. The distribution of the largest local Lyapunov exponent shows a significant probability for negative values over time spans up to 10 days. This effect is present for resolutions up to wave numbers $\ell =42$ ($\approx$250 km). The probability for a negative local largest Lyapunov exponent decreases over time, similarly to the predictions of the fluctuation theorem for entropy production. The model used is hydrostatic with variable numbers of vertical levels and different horizontal resolutions.

We propose a modified voter model with locally conserved magnetization and investigate its phase ordering dynamics in two dimensions in numerical simulations. Imposing a local constraint on the dynamics has the surprising effect of speeding up the phase ordering process. The system is shown to exhibit a scaling regime characterized by algebraic domain growth, at odds with the logarithmic coarsening of the standard voter model. A phenomenological approach based on cluster diffusion and similar to Smoluchowski ripening correctly predicts the observed scaling regime. Our analysis exposes unexpected complexity in the phase ordering dynamics without thermodynamic potential.

The cargo motion in living cells transported by two species of motor protein with different intrinsic directionalities is discussed in this study. Similarly to single motor movement, the cargo steps forward and backward along a microtubule stochastically. Recent experiments found that cargo transportation by two motor species has a memory; it does not change its direction as frequently as expected, which means that its forward and backward step rates depend on its previous motion trajectory. By assuming that the cargo has only the least possible memory, i.e., its step direction depends only on the direction of its last step, two cases of cargo motion are analyzed in detail in this study: (I) cargo motion under constant external load, and (II) cargo motion in one fixed optical trap. Due to the existence of memory, in the first case, the cargo can keep moving in the same direction for a long distance. In the second case, the cargo will oscillate in the trap. The oscillation period decreases and the oscillation amplitude increases with increasing forward step rate of the motor, but both of them decrease with increasing trap stiffness. The most likely location of the cargo, where the probability of finding the oscillating cargo is maximum, may be the same as or may be different from the trap center, which depends on the step rates of the two motor species. Meanwhile, if the motors are robust, i.e., their forward to backward step rate ratios are high, there may be two such most likely locations, located one on each side of the trap center. The probability of finding the cargo in a given location, the probability of the cargo being in forward or backward motion, and various mean first passage times of the cargo to a given location or a given state are also analyzed.

We study coupled logistic maps on a one-dimensional lattice. We coarse grain the system by labeling the local state $+$ if the value of the variable is above the fixed point and $-$ if the value is below the (nonzero) fixed point, $x^{☆}=1-1/\mu$. We find that the system exhibits a transition from a global state, in which moving defects occur, to a global state, which is frozen in time (modulo-2). All such states display nonzero value of persistence. Besides, we also observe a state which displays long-range antiferromagnetic order. Onset of such a state is accompanied with a power-law behavior of persistence $P\left(t\right)$ as a function of time at the critical line. Usually, persistence transitions show nonuniversal exponent. However, here persistence exponent for synchronous dynamics is 3/8 over the entire lower critical curve. This exponent is the same as one observed for asynchronous Glauber dynamics simulation of zero-temperature Ising model in one dimension. The expected value for synchronous dynamics is 3/4. We present a plausible argument for this scaling.

The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the quasiharmonic to the relaxational regime occurs via chaotic canard explosions, where large-amplitude relaxation spikes are separated by an irregular number of subthreshold oscillations. We also show that this regime coexists with other periodic attractors, on which the trajectories evolve on a substantially faster time scale. The experimental results are reproduced and analyzed by means of a detailed physical model of our system.

This work is a continuation of our efforts to quantify the irregular scalar stress signals from the Ananthakrishna model for the Portevin–Le Chatelier instability observed under constant strain rate deformation conditions. Stress related to the spatial average of the dislocation activity is a dynamical variable that also determines the time evolution of dislocation densities. We carry out detailed investigations on the nature of spatiotemporal patterns of the model realized in the form of different types of dislocation bands seen in the entire instability domain and establish their connection to the nature of stress serrations. We then characterize the spatiotemporal dynamics of the model equations by computing the Lyapunov dimension as a function of the drive parameter. The latter scales with the system size only for low strain rates, where isolated dislocation bands are seen, and at high strain rates, where fully propagating bands are seen. At intermediate applied strain rates corresponding to the partially propagating bands, the Lyapunov dimension exhibits two distinct slopes, one for small system sizes and another for large. This feature is rationalized by demonstrating that the spatiotemporal patterns for small system sizes are altered from the partially propagating band types to isolated burst type. This in turn allows us to reconfirm that low-dimensional chaos is projected from the stress signals as long as there is a one-to-one correspondence between the bursts of dislocation bands and the stress drops. We then show that the stress signals in the regime of partially to fully propagative bands have features of extensive chaos by calculating the correlation dimension density. We also show that the correlation dimension density also depends on the system size. A number of issues related to the system size dependence of the Lyapunov dimension density and the correlation dimension density are discussed.

We introduce a mean-field approximation based on the reconciliation of maximum entropy and linear response for correlations in the cluster variation method. Within a general formalism that includes previous mean-field methods, we derive formulas improving on, e.g., the Bethe approximation and the Sessak-Monasson result at high temperature. Applying the method to direct and inverse Ising problems, we find improvements over standard implementations.

The dynamics of a spin in the presence of a deterministic and a fluctuating magnetic field is solved for analytically to obtain the averaged value of the spin as a function of time for various kinds of fluctuations (noise). Specifically, analytic results are obtained for the time dependence of the expectation value of the spin, averaged over fluctuations, for Gaussian white noise, Gaussian colored noise, and non-Gaussian telegraph noise. Fluctuations cause the decay of the average spin vector (decoherence). For noise with a finite temporal correlation time, a deterministic component of the field can suppress the decoherence of the spin component along the field. Hence, decoherence can be manipulated by controlling the deterministic magnetic field. A simple universal physical picture emerges which explains the mechanism for the suppression of decay.

Molecular dynamics simulations are performed to investigate heterogeneous dynamics in amorphous glassy materials under oscillatory shear strain. We consider three-dimensional binary Lennard-Jones mixture well below the glass transition temperature. The structural relaxation and dynamical heterogeneity are quantified by means of the self-overlap order parameter and the dynamic susceptibility. We found that at sufficiently small strain amplitudes, the mean square displacement exhibits a broad subdiffusive plateau and the system undergoes nearly reversible deformation over about ${10}^4$ cycles. Upon increasing strain amplitude, the transition to the diffusive regime occurs at shorter time intervals and the relaxation process involves intermittent bursts of large particle displacements. The detailed analysis of particle hopping dynamics and the dynamic susceptibility indicates that mobile particles aggregate into clusters whose sizes increase at larger strain amplitudes. Finally, the correlation between particle mobilities in consecutive time intervals demonstrates that dynamic facilitation becomes increasingly pronounced at larger strain amplitudes.

Using high-speed digital holographic microscopy and microfluidics, we discover that, when encountering fluid flow shear above a threshold, unicellular green alga Dunaliella primolecta migrates unambiguously in the cross-stream direction that is normal to the plane of shear and coincides with the local fluid flow vorticity. The flow shear drives motile microalgae to collectively migrate in a thin two-dimensional horizontal plane and consequently alters the spatial distribution of microalgal cells within a given suspension. This shear-induced algal migration differs substantially from periodic rotational motion of passive ellipsoids, known as Jeffery orbits, as well as gyrotaxis by bottom-heavy swimming microalgae in a shear flow due to the subtle interplay between torques generated by gravity and viscous shear. Our findings could facilitate mechanistic solutions for modeling planktonic thin layers and sustainable cultivation of microalgae for human nutrition and bioenergy feedstock.