The reflection and transmission spectra from right-handed cholesteric liquid crystals are computed in the visible region for a linearly, circularly, or elliptically polarized incident plane wave at oblique incidence. The liquid crystal cell is sandwiched between dielectric layers of certain thickness and refractive index. The underlined formulation is based on a modal analysis of the governing field expressions in the dielectric and liquid-crystal regions. A representative matrix system is obtained after enforcing the continuity of the tangential electric and magnetic fields at the material interfaces. Solution of the governing matrix system results in the reflectance and transmittance for a given wavelength. Numerical results for both normal and oblique incidence were obtained and compared with data published in the literature. The underlined formulation is effective, accurate, robust, versatile, and computationally efficient.

We develop a tricomponent (ternary) hydrodynamic model for multiphase flows of biomass and solvent mixtures, which we employ to simulate biofilm. In this model, the three predominant effective components in biofilms, which are the extracellular polymeric substance (EPS) network, the bacteria, and the effective solvent (consisting of the solvent and nutrient, etc.), are modeled explicitly. The tricomponent fluid mixture is assumed incompressible as a whole, while intercomponent mixing, dissipation, and conversion are allowed among the effective components. Bacterial growth and EPS production due to the growing bacterial population are modeled in the biomass transport equations. Bacterial decay due to starvation and natural causes is accounted for in the bacterial population dynamics to capture the possible bacterial population reduction due to the depletion of the nutrient. In the growth regime for biofilms, the mixture behaves like a multiphase viscous fluid, in which the molecular relaxation is negligible in the corresponding time scale. In this regime, the dynamics of biofilm growth in the solvent (water) are simulated using a two-dimensional finite difference solver that we developed, in which the distribution and evolution of the EPS and bacterial volume fractions are investigated. The hydrodynamic interaction between the biomass and the solvent flow field is also simulated in a shear cell environment, demonstrating the spatially and temporally heterogeneous distribution of the EPS and bacteria under shear. This model together with the numerical codes developed provides a predictive tool for studying biomass-flow interaction and other important biochemical interactions in the biofilm and solvent fluid mixture.

We extend the continuum theory of random intermittent search processes to the case of $N$ independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi-infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to $n$ successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as $1/N$, we show that there exists a well-defined mean-field limit $N\to \infty$, in which the stochastic model reduces to a deterministic system of linear reaction-hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time-dependent rate of filling $\lambda \left(t\right)$ depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with $n$ particles in terms of the waiting time density $f_n\left(t\right)$. The latter is determined by the integrated Poisson rate $\mu \left(t\right)={\int }_0^t\lambda \left(s\right)ds$, which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection-diffusion equation using a quasisteady-state analysis. We compare our analytical results for the mean-field model with Monte Carlo simulations for finite $N$. We thus determine how the mean first passage time (MFPT) for filling the target depends on $N$ and $n$.

Nanoconfined water and surface-structured water impacts a broad range of fields. For water confined between hydrophilic surfaces, measurements and simulations have shown conflicting results ranging from “liquidlike” to “solidlike” behavior, from bulklike water viscosity to viscosity orders of magnitude higher. Here, we investigate how a homogeneous fluid behaves under nanoconfinement using its bulk response function: The Green's function of water extracted from a library of $S(q,\omega )$ inelastic x-ray scattering data is used to make femtosecond movies of nanoconfined water. Between two confining surfaces, the structure undergoes drastic changes as a function of surface separation. For surface separations of $\approx$9 Å, although the surface-associated hydration layers are highly deformed, they are separated by a layer of bulklike water. For separations of $\approx$6 Å, the two surface-associated hydration layers are forced to reconstruct into a single layer that modulates between localized “frozen’ and delocalized “melted” structures due to interference of density fields. These results potentially reconcile recent conflicting experiments. Importantly, we find a different delocalized wetting regime for nanoconfined water between surfaces with high spatial frequency charge densities, where water is organized into delocalized hydration layers instead of localized hydration shells, and are strongly resistant to `freezing' down to molecular distances ($<$6 Å).

Using dissipative particle dynamics simulations we give numerical evidence of the formation of “striped” (or $AB$ alternating) diamond and gyroid network structures and other hierarchical morphologies in $A_m$$B_m$$C_n$ ($2m+n$)-miktoarm star terpolymers where the main variable is the ratio $x=n/m$ with $m,n$ being the number of equal length polymer arms of $A$ and $B$ and $C$, respectively. The formed networks are purely a result of the star topology, as clearly shown by direct comparison with parallel $ABC$ miktoarm star terpolymer simulations with matching overall composition. Progressively changing $x$, the system adopts the following phase sequence: three-colored lamellae, $C$ spheres embedded in $AB$ lamellae, $C$ spheres decorating $AB$ lamellae, three-colored [6.6.6] tiling, $AB$ striped diamond network, $AB$ striped gyroid network, $AB$ striped hexagonally arranged cylinders, and finally $AB$ striped globular aggregates. The striped gyroid is particularly interesting as it constitutes an inherently chiral structure made from achiral building blocks.

Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles. Here we formulate two computer simulation methods: (1) a kinetic Monte Carlo (KMC) and (2) a cellular particle dynamics (CPD) method, which are capable of describing and predicting the shape evolution in time of three-dimensional multicellular systems during their biomechanical relaxation. Our work is motivated by the need of developing quantitative methods for optimizing postprinting structure formation in bioprinting-assisted tissue engineering. The KMC and CPD model parameters are determined and calibrated by using an original computational-theoretical-experimental framework applied to the fusion of two spherical cell aggregates. The two methods are used to predict the (1) formation of a toroidal structure through fusion of spherical aggregates and (2) cell sorting within an aggregate formed by two types of cells with different adhesivities.

We investigate the properties of the semiclassical short periodic orbit approach for the study of open quantum maps that was recently introduced [Novaes, Pedrosa, Wisniacki, Carlo, and Keating, Phys. Rev. E 80, 035202(R) (2009)]. We provide solid numerical evidence, for the paradigmatic systems of the open baker and cat maps, that by using this approach the dimensionality of the eigenvalue problem is reduced according to the fractal Weyl law. The method also reproduces the projectors $|{\psi }_n^R\rangle \langle {\psi }_n^L|$, which involves the right and left states associated with a given eigenvalue and is supported on the classical phase-space repeller.

After suggesting criteria to recognize a new system and a new attractor—and to make a distinction between them—the paper details the topological analysis of the “cord” attractor. This attractor, which resembles a cord between two leaves, is produced by a three-dimensional system that is obtained after a modification of the Lorenz-84 model for the global atmospheric circulation [L. A. Aguirre and C. Letellier, Phys. Rev. E 83, 066209 (2011)]. The nontrivial topology of the attractor is described in terms of a template that corresponds to a reverse horseshoe, that is, to a spiral Rössler attractor with negative and positive global $\pi$ twists. Due to its particular structure and to the fact that such a system has two variables from which the dynamics is poorly observable, this attractor qualifies as a challenging benchmark in nonlinear dynamics.

Calculating the frequency-dependent dielectric function for strongly coupled plasmas, the relations within kinetic theory and linear response theory are derived and discussed in comparison. In this context, we give a proof that the Kohler variational principle can be extended to arbitrary frequencies. It is shown to be a special case of the Zubarev method for the construction of a nonequilibrium statistical operator from the principle of the extremum of entropy production. Within kinetic theory, the commonly used energy-dependent relaxation time approach is strictly valid only for the Lorentz plasma in the static case. It is compared with the result from linear response theory that includes electron-electron interactions and applies for arbitrary frequencies, including bremsstrahlung emission. It is shown how a general approach to linear response encompasses the different approximations and opens options for systematic improvements.

How long will a fluid membrane vesicle stressed with a steady ramp of micropipette last before rupture? Or conversely, how high should the surface tension be to rupture such a membrane? To answer these challenging questions we developed a theoretical framework that allows for the description and reproduction of dynamic tension spectroscopy (DTS) observations. The kinetics of the membrane rupture under ramps of surface tension is described as a succession of an initial pore formation followed by the Brownian process of the pore radius crossing the time-dependent energy barrier. We present the formalism and a derive (formal) analytical expression of the survival probability describing the fate of the membrane under DTS conditions. Using numerical simulations for the membrane prepared in an initial state with a given distribution of times for pore nucleation, we study the membrane lifetime (or inverse of rupture rate) and distribution of membrane surface tension at rupture as a function of membrane characteristics like pore nucleation rate, the energy barrier to failure, and tension loading rate. It is found that simulations reproduce the main features of DTS experiments, particularly the pore nucleation and pore-size diffusion-controlled limits of membrane rupture dynamics. This approach can be adapted and applied to processes of permeation and pore opening in membranes (electroporation, membrane disruption by antimicrobial peptides, vesicle fusion).

Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion from a relatively small number of components. Here we propose that the modular building blocks are made of the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. We find that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop-specific parameters, and we compute their statistical distribution in the Protein Data Bank (PDB). We explicitly construct a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop. The ensuing profiles cover practically all those proteins in PDB that have a resolution which is better than 2.0 Å, with a precision such that the average root-mean-square distance between the loop and its soliton is less than the experimental $B$-factor fluctuation distance. We also present two examples that describe how the loop library can be employed both to model and to analyze folded proteins.

We have done a finite-size scaling study of a continuous phase transition altered by the quenched bond disorder, investigating systems at quasicritical temperatures of each disorder realization by using the equilibriumlike invaded cluster algorithm. Our results indicate that in order to access the thermal critical exponent $y_{\tau }$, it is necessary to average the free energy at quasicritical temperatures of each disorder configuration. Despite the thermal fluctuations on the scale of the system at the transition point, we find that spatial inhomogeneities form in the system and become more pronounced as the size of the system increases. This leads to different exponents describing rescaling of the fluctuations of observables in disorder and thermodynamic ensembles.

The local structure of disordered jammed packings of monodisperse spheres without friction, generated by the Lubachevsky-Stillinger algorithm, is studied for packing fractions above and below $64\%$. The structural similarity of the particle environments to fcc or hcp crystalline packings (local crystallinity) is quantified by order metrics based on rank-four Minkowski tensors. We find a critical packing fraction ${\phi }_{\mathrm{c}}\approx 0.649$, distinctly higher than previously reported values for the contested random close packing limit. At ${\phi }_{\mathrm{c}}$, the probability of finding local crystalline configurations first becomes finite and, for larger packing fractions, increases by several orders of magnitude. This provides quantitative evidence of an abrupt onset of local crystallinity at ${\phi }_{\mathrm{c}}$. We demonstrate that the identification of local crystallinity by the frequently used local bond-orientational order metric $q_6$ produces false positives and thus conceals the abrupt onset of local crystallinity. Since the critical packing fraction is significantly above results from mean-field analysis of the mechanical contacts for frictionless spheres, it is suggested that dynamic arrest due to isostaticity and the alleged geometric phase transition in the Edwards framework may be disconnected phenomena.

The response of ${}^4$He crystals to the rapid reduction of gravity down to practically zero in a superfluid was investigated visually, utilizing the parabolic flight of a jet plane. At a high temperature of 1.6 K, the shape of ${}^4$He crystals in the bcc phase did not change with a reduction of gravity during a parabolic period of 20 s, due to the low crystallization rate. At lower temperatures, such as 0.63 K, where the crystallization rate is sufficiently high, the shape of ${}^4$He crystals in the hcp phase changed significantly, relaxing to a quasiequilibrium shape under zero gravity, where the $c$ facet became enlarged and the $a$ facet emerged on the surface. The crystal did not detach from the sample cell wall at any time because the adhesive force manifested as partial wetting to the wall was sufficiently strong. Some crystals removed from the wall by an acoustic wave pulse were found to float and drift in the superfluid for approximately 4.2 s under zero gravity, although most of them were quickly reattached to the wall.

We show that weak periodic driving can exponentially strongly change the rate of escape from a potential well of a system driven by telegraph noise. The analysis refers to an overdamped system, where escape requires that the noise amplitude $\theta$ exceed a critical value ${\theta }_c$. For $\theta$ close to ${\theta }_c$, the exponent of the escape rate displays a nonanalytic dependence on the amplitude of an additional low-frequency modulation. This leads to giant nonlinearity of the response of a bistable system to periodic modulation. Also studied is the linear response to periodic modulation far from ${\theta }_c$. We analyze the scaling of the logarithm of the escape rate with the distance to the saddle-node and pitchfork bifurcation points. The analytical results are in excellent agreement with numerical simulations.

Flows of dissipative particles driven by the peristaltic motion of a tube are numerically studied. A transition from a slow “unjammed” flow to a fast “jammed” flow is found through the observation of the flow rate at a critical width of the bottleneck of a peristaltic tube. It is also found that the average and fluctuation of the transition time, and the peak value of the second moment of the flow rate exhibit power-law divergence near the critical point and that these variables satisfy scaling relationships near the critical point. The dependence of the critical width and exponents on the peristaltic speed and the density is also discussed.

Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex structures, which are difficult to classify. Topological charge of point defects in nematics has ambiguously defined sign, and its additivity cannot be ensured when defects are observed separately. We demonstrate how the topological charge of complex defect structures can be determined by identifying and counting parts of the texture that satisfy simple geometric rules. We introduce a parameter called the defect rank and show that it corresponds to what is intuitively perceived as a point charge based on the properties of the director field. Finally, we discuss the role of free-energy constraints in the validity of the classification with the defect rank.

Consisting of alternating swelling and nonswelling polymeric layers (SLs and NLs), lamellar gels are one-dimensional photonic crystals with mechanically tunable optical properties. The lamellar structure induces a constraint between the SLs and the NLs, resulting in a highly anisotropic swelling behavior that is coupled with deformation. The coupling gives rise to the mechanochromatic effect, i.e., the color change in the material in response to mechanical deformations. A quantitative understanding of the coupling behavior is the key to many applications. This paper formulates a nonlinear continuum model for lamellar gels by considering the constrained swelling and anisotropic deformation in both layers. A finite-element method is further developed to simulate the mechanochromatic response of a lamellar gel undergoing a nonuniform field.

A theoretical framework is presented, which derives chemical master equations for the number of protein molecules produced in a given time window, It is applied to derive analytical solutions that describe protein production distributions for the random bursting model (with an exponential or geometric burst-size distribution) and the clustering model. This distribution is experimentally observable using recently developed, single-molecule gene expression experiments. Furthermore, intrinsic stochasticity in a gene's expression can be calculated from protein production distributions using a new, time-dependent noise curve analysis. Different models of gene expression are compared with respect to their protein production distributions and intrinsic stochasticity, revealing the effects of molecular memory and burstlike expression on fluctuations in gene expression. It is distinct from and provides major advantages over measurements of steady-state concentrations.

We adapt the method used by Jaynes to derive the equilibria of statistical physics to instead derive equilibria of bounded rational game theory. We analyze the dependence of these equilibria on the parameters of the underlying game, focusing on hysteresis effects. In particular, we show that by gradually imposing individual-specific tax rates on the players of the game, and then gradually removing those taxes, the players move from a poor equilibrium to one that is better for all of them.