Path integrals similar to those describing stiff polymers arise in the Helfrich model for membranes. We show how these types of path integrals can be evaluated and apply our results to study the thermodynamics of a minority stripe phase in a bulk membrane. The fluctuation induced contribution to the line tension between the stripe and the bulk phase is computed. Also the effective interaction between the interfaces of the two phases can be computed. Explict forms are given for this Casmir-like interaction in the tensionless case where the two phases have differing bending rigidities.

We have studied the polarization relaxation process after removing an applied electric field in the columnar hexagonal phase of $N,N^{\prime }$-bis(3,4,5-trihexadecyloxyphenyl)urea by means of second-harmonic generation (SHG), switching current, and texture observation. Transient SHG and current associated by sudden field change show polarization switching associated with a molecular reorientation of about a few ms depending on the field strength. Furthermore, the texture observation reveals a column undulation process during $10\mathrm{s}\text{to}1\min$. The size of the polar domains was estimated to be $160\text{molecules}$ by analyzing the field dependence of the SHG signal intensity on the basis of an Ising model.

We studied the structure of the $B_x$ phase formed from the short terminal homolog, 1,3-(4-bromobenzene) bis[4-(4-$n$-butoxyphenylliminomethyl)benzoate] (4Br-P-4-O-PIMB), by focusing a microbeam of x ray on the well-developed fan-shaped texture. From the highly oriented x-ray patterns detected at the two states of DC-ON and DC-OFF, the $B_x$ structure was definitely illustrated. It is a kind of frustrated one similar to the $B_1$ phase: the molecules lie perpendicularly to the layer, and the frustration takes place perpendicularly to the bent direction. Unlike in the $B_1$ phase, however, the size of the resulting antidomain is not definite, but fluctuates from position to position as observed in the $B_6$ phase.

We present a model for innovation, evolution, and opinion dynamics whose spreading is dictated by a unanimity rule. The underlying structure is a directed network, the state of a node is either activated or inactivated. An inactivated node will change only if all of its incoming links come from nodes that are activated, while an activated node will remain activated forever. It is shown that a transition takes place depending on the initial condition of the problem. In particular, a critical number of initially activated nodes is necessary for the whole system to get activated in the long-time limit. The influence of the degree distribution of the nodes is naturally taken into account. For simple network topologies we solve the model analytically; the cases of random and small world are studied in detail. Applications for food-chain dynamics and viral marketing are discussed.

We have investigated the bioconvection of Paramecium tetraurelia in high-density suspensions made by centrifugal concentration. When a suspension is kept at rest in a Hele-Shaw cell, a crowded front of paramecia is formed in the vicinity of the bottom and it propagates gradually toward the water-air interface. Fluid convection occurs under this front, and it is driven persistently by the upward swimming of paramecia. The roll structures of the bioconvection become turbulent with an increase in the depth of the suspension; they also change rapidly as the density of paramecia increases. Our experimental results suggest that lack of oxygen in the suspension causes the active individual motions of paramecia to induce the formation of this front.

The intermittency characteristics of the longitudinal $\left(u\right)$ and transverse $\left(v\right)$ velocity and temperature $\left(\theta \right)$ at similar Taylor microscale Reynolds numbers have been compared in a turbulent round jet. We examine the scaling exponents ${\zeta }_{\alpha }\left(n\right)$ ($\alpha =u$, $v$, and $\theta$) of structure functions ${⟨\left(\delta \alpha \right)⟩}^n$, the intermittency exponents ${\mu }_{\alpha }$ based on individual and mixed sixth-order structure functions, the scaling exponents ${\tau }^{\alpha }\left(n\right)$ of the locally averaged energy and temperature dissipation rates approximated by ${(\partial \alpha ∕\partial x)}^2$, the flatness factors of the derivatives $\partial \alpha ∕\partial x$, and the probability density functions (PDFs) of $\partial \alpha ∕\partial x$, the increment $\delta \alpha$ and ${(\partial \alpha ∕\partial x)}^2$. It is found that $v$ and $\theta$ are similar in terms of their intermittency characteristics. They are more intermittent than $u$. The scaling exponent ${\zeta }_v\left(n\right)$ is marginally larger than ${\zeta }_{\theta }\left(n\right)$. The intermittency exponent ${\mu }_{\theta }$ is smaller than ${\mu }_v$ based on the estimate of mixed sixth-order structure functions, while ${\mu }_{\theta }$ is nearly equal to ${\mu }_v$ based on the estimate of individual sixth-order structure functions. The temperature dissipation rate is more intermittent than the turbulent energy dissipation rate, as indicated by ${\tau }^{\alpha }\left(n\right)$. The flatness factor of $\partial \theta ∕\partial x$ is marginally larger than that of $\partial v∕\partial x$. The PDFs of $\partial \theta ∕\partial x$, $\delta \theta$, and ${(\partial \theta ∕\partial x)}^2$ show the strongest departure from the Gaussian distribution.

We consider a plate made from an isotropic but brittle elastic material, which is used to span a rigid aperture, across which a small pressure difference is applied. The problem we address is to find the structure which uses the least amount of material without breaking. Under a simple set of physical approximations and for a certain region of the pressure-brittleness parameter space, we find that a fractal structure in which the plate consists of thicker spars supporting thinner spars in an hierarchical arrangement gives a design of high mechanical efficiency.

We demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure, which manifests itself in the spatial phase distribution of the oscillators. The phase model is described by a nonlinear Fokker-Planck equation, which can be reduced to the complex Ginzburg-Landau equation near the Hopf bifurcation point of the uniform solution. By numerical simulations, we show that the hole structure clearly appears in the space-dependent order parameter, which corresponds to the Nozaki-Bekki hole solution of the complex Ginzburg-Landau equation.

We investigated the carrier transport phenomena in model liquid crystalline systems, which were constructed on the basis of the Gay-Berne potential and Monte Carlo calculation. The carrier transport was analyzed under the condition that the molecular arrangement in the system was fixed and thermally activated carriers were transported by hopping in the system. The carrier transport simulation was performed by Monte Carlo method using Miller-Abrahams hopping ratio. By these calculations, we reproduced the experimental results of the electronic conduction in nematic liquid crystals.

In random walks, the path representation of the Green’s function is an infinite sum over the length of path probability density functions (PDFs). Recently, a closed-form expression for the Green’s function of an arbitrarily inhomogeneous semi-Markovian random walk in a one-dimensional (1D) chain of $L$ states was obtained by utilizing path-PDFs calculations. Here we derive and solve, in Laplace space, the recursion relation for the $n$ order path PDF for the same system. The recursion relation relates the $n$ order path PDF to $L∕2$ (round towards zero for an odd $L$) shorter path PDFs and has $n$ independent coefficients that obey a universal formula. The $z$ transform of the recursion relation straightforwardly gives the generating function for path PDFs, from which we recover the Green’s function of the random walk, but, moreover, derive an explicit expression for any path PDF of the random walk. These expressions give the most detailed description of arbitrarily inhomogeneous semi-Markovian random walks in 1D.

We report here measurements of rheological properties of the human airway smooth muscle cell using forced nanoscale motions of Arg-Gly-Asp RGD-coated microbeads tightly bound to the cytoskeleton. With changes of forcing amplitude, the storage modulus showed small but systematic nonlinearities, especially after treatment with a contractile agonist. In a dose-dependent manner, a large oscillatory shear applied from a few seconds up to $400\mathrm{s}$ caused the cytoskeleton matrix to soften, a behavior comparable to physical rejuvenation observed in certain inert soft materials; the stiffness remained constant for as long as the large oscillatory shear was maintained, but suddenly fell with shear cessation. Stiffness then followed a slow scale-free recovery, a phenomenon comparable to physical aging. However, acetylated low-density lipoprotein acLDL-coated microbeads, which connect mainly to scavenger receptors, did not show similar out-of-equilibrium behaviors. Taken together, these data demonstrate in the cytoskeleton of the living cell behaviors with all the same signatures as that of soft inert condensed systems. This unexpected intersection of condensed matter physics and cytoskeletal biology suggests that trapping, intermittency, and approach to kinetic arrest represent central mesoscale features linking underlying molecular events to integrative cellular functions.

We investigate the spatiotemporal dynamics in a two-dimensional array of excitable elements subjected to independent external noise, where elements are prepared by localizing the Belousov-Zhabotinsky reaction in a gel matrix. We experimentally demonstrate that the coherence of noise-induced firings is improved with increasing the array size, i.e., the occurrence of array-enhanced coherence resonance. Furthermore, it is found that synchronization among oscillators which are barely coupled can be achieved via coherence resonance. Experimental observations are approximately reproduced in a numerical simulation with a forced Oregonator reaction-diffusion model.

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

We report a thorough characterization of the glassy dynamics of benzophenone by broadband dielectric spectroscopy. We detect a well-pronounced $\beta$ relaxation peak developing into an excess wing with increasing temperature. A previous analysis of results from Optical-Kerr-effect measurements of this material within the mode-coupling theory revealed a high-frequency Cole-Cole peak. We address the question if this phenomenon also may explain the Johari-Goldstein $\beta$ relaxation, a so-far unexplained spectral feature inherent to glass-forming matter, mainly observed in dielectric spectra. Our results demonstrate that according to the present status of theory, both spectral features seem not to be directly related.

An autocatalytic reacting system with particles interacting at a finite distance is studied. We investigate the effects of the discrete-particle character of the model on properties like reaction rate, quenching phenomenon, and front propagation, focusing on differences with respect to the continuous case. We introduce a renormalized reaction rate depending both on the interaction radius and the particle density, and we relate it to macroscopic observables (e.g., front speed and front thickness) of the system.

We investigate the low-temperature relaxation dynamics toward a nonequilibrium steady state in a tilted asymmetric periodic potential based on the WKB analysis and the numerical diagonalization of the Fokker-Planck operator. Due to the tilting, the Fokker-Planck operator, and thus the Schrödinger operator associated with it, are non-Hermitian. Therefore, we evaluate the decay rate based on the WKB analysis both for real- and complex-valued eigenvalues. In the tilting range where the double-humped barrier exists, the decay rate is shown to obey a law which is a subtle nonequilibrium extension of the so-called Kramers escape rate. The decay rate for the single-humped barrier case is analyzed as well. The large tilting regime where the barriers no longer exist is also investigated.

The results of parallel kinetic Monte Carlo (KMC) simulations of island coarsening based on a bond-counting model are presented. Our simulations were carried out both as a test of and as an application of the recently developed semirigorous synchronous sublattice (SL) algorithm. By carrying out simulations over long times and for large system sizes the asymptotic coarsening behavior and scaled island-size distribution (ISD) were determined. Our results indicate that while cluster diffusion and coalescence play a role at early and intermediate times, at late times the coarsening proceeds via Ostwald ripening. In addition, we find that the asymptotic scaled ISD is significantly narrower and more sharply peaked than the mean-field theory prediction. The dependence of the scaled ISD on coverage is also studied. Our results demonstrate that parallel KMC simulations can be used to effectively extend the time scale over which realistic coarsening simulations can be carried out. In particular, for simulations of the late stages of coarsening with system size $L=1600$ and eight processors, a parallel efficiency larger than 80% was obtained. These results suggest that the SL algorithm is likely to be useful in the future in parallel KMC simulations of more complicated models of coarsening.

The nonlinear dynamics of a biological double membrane that consists of two coupled lipid bilayers, typical of some intracellular organelles such as mitochondria or nuclei, is studied. A phenomenological free-energy functional is formulated in which the curvatures of the two parts of the double membrane and the distance between them are coupled to the lipid chemical composition. The derived nonlinear evolution equations for the double-membrane dynamics are studied analytically and numerically. A linear stability analysis is performed, and the domains of parameters are found in which the double membrane is stable. For the parameter values corresponding to an unstable membrane, numerical simulations are performed that reveal various types of complex dynamics, including the formation of stationary, spatially periodic patterns.

Synchronization of chaotic units coupled by their time-delayed variables is investigated analytically. A type of cooperative behavior is found: Sublattice synchronization. Although the units of one sublattice are not directly coupled to each other, they completely synchronize without time delay. The chaotic trajectories of different sublattices are only weakly correlated but not related by generalized synchronization. Nevertheless, the trajectory of one sublattice is predictable from the complete trajectory of the other one. The spectra of Lyapunov exponents are calculated analytically in the limit of infinite delay times, and phase diagrams are derived for different topologies.

We show the existence of strange nonchaotic repellers—that is, systems with transient dynamics whose nonattracting invariant set is fractal, but whose maximum Lyapunov coefficient is zero. We introduce the concept using a simple one-dimensional map and argue that strange nonchaotic repellers are a general phenomenon, occurring in bifurcation points of transient chaotic systems. All strange nonchaotic systems studied to date have been attractors; here, it is revealed that strange nonchaotic sets are also present in transient systems.