We analyze theoretically the effects of curvature on the diffusion in a fluid membrane, within the Saffman-Delbrück hydrodynamic model. We calculate the effect of curvature on the intrinsic fluidity of a membrane through changes in its thickness, for both static or fluctuating curvature. We treat both thermal curvature fluctuations, and fluctuations due to active processes. Such curvature fluctuations increase the average membrane thickness and diminish the projected area, thereby decreasing the diffusion coefficient. This calculation allows us to predict the effect of shear flow on the membrane diffusion, and to compare to observations on living cells.

We observed $-4.9\mathrm{nsec}$ negative group delay in the optical wave-packet propagation through a fiber taper coupled with a single Mie sphere. The observed fast light under the Mie scattering process agrees excellently with the anomalous dispersion calculated on the basis of a directional coupling theory on the undercoupling condition, which also predicts a positive group delay on the overcoupling condition.

A general semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial state, and does not require that the initial state be localized in position or momentum. This general dephasing representation is special in that, counterintuitively, all of fidelity decay is due to dephasing and none is due to the decay of classical overlaps. Surprising accuracy of the approximation is justified by invoking the shadowing theorem: twice—both for physical perturbations and for numerical errors. Beyond justifying the approximation, the shadowing theorem makes the dephasing representation practical: without shadowing it would be impossible to find numerically the precise trajectories needed in a semiclassical approximation. It is shown how the general expression reduces to the previously known special forms for localized states. The superiority of the general over the specialized forms is explained and supported by numerical tests for wave packets, nonlocal pure states, and for simple and random mixed states. The tests are done in nonuniversal regimes in mixed phase space where detailed features of fidelity are important. Although semiclassically motivated, the present approach is valid for abstract systems with a finite Hilbert basis provided that the discrete Wigner transform is used. This makes the method applicable, via a phase-space approach, to problems of quantum computation.

We report experimental observations of enhanced stability of quasipatterns and superlattice patterns in a vertically oscillated, deep viscous fluid layer with the addition of a third driving frequency. With two-frequency driving in the ratios 4:5 and 6:7, 12-fold quasipatterns and type-I superlattice patterns appear, respectively, as a secondary instability for a range of relative phases and amplitudes. Addition of a small third-frequency component at twice the difference frequency, i.e., 4:5:2 and 6:7:2, shifts the region of stability for these patterns closer to onset. For a range of parameter values the stabilized patterns become the primary instability. The degree of stabilization is sensitive to the amplitude and relative phase of the third-frequency term in qualitative agreement with a recent symmetry based analysis of resonant three-wave interactions.

This paper reports on measurements of the ion energy distribution (IED) at the cathode of an argon dc microdischarge using energy-resolved molecular beam mass spectrometry. The measurements are conducted at a fixed pressure-electrode separation product $\left(pd\right)$ of $1\mathrm{cm}\text{Torr}$ with a maximum discharge pressure of $20\text{Torr}$. The measured IED is compared to the theory of Davis and Vanderslice [W. D. Davis and T. A. Vanderslice, Phys. Rev. 131, 219 (1963)]. A higher pressure in a case of almost constant normalized current densities by pressure $(J{p}^{-2}=0.080\pm 0.006\mathrm{mA}̸{\mathrm{cm}}^{-2}{\text{Torr}}^{-2})$ yields a lower ratio of the ion mean free path to the sheath thickness. The results in almost constant $J{p}^{-2}$ case then indicate that a scaling law of $J{p}^{-2}$ is no longer applicable for IED of microdischarge. Expected background gaseous temperatures from IEDs with the collisional Child law have reasonable increasing with increased current density $\left(J\right)$ in both cases of almost constant $J{p}^{-2}$ and a constant pressure of $10\text{Torr}$. Supported by temperature measurement by laser absorption spectroscopy, it is demonstrated that the expanded theory might be applicable also to microdischarges $(\mathrm{Ar}\sim 20\text{Torr})$ with temperature adjusting.

We analyze the explicit contribution of fluid inertia and fluid unsteadiness to the force acting on a solid sphere moving in a vertical solid-body rotation flow, in the limit of small Reynolds and Taylor numbers. This problem can be thought of as a test case where the flow induced by the particle is both unsteady (in the laboratory frame) and convected by the unperturbed flow. Many authors assume that the contributions of these two effects can be approximately superposed, and postulate that the particle motion equation is composed of the classical Boussinesq-Basset-Oseen equation (obtained by neglecting the fluid inertia) plus an additive lift force. In the present paper the simplicity of the unperturbed flow enables one to calculate analytically the explicit contribution of each term appearing in the perturbed flow equation (by using matched asymptotic expansions). Our results show how the convective terms and the unsteady term do contribute to the particle drag and lift coefficients in a very complex and nonadditive manner.

We perform systematic molecular dynamics simulations of water confined between two nanoscale plates at $T=300\mathrm{K}$. We investigate the effect of pressure $(-0.15\mathrm{GPa}⩽P⩽0.2\mathrm{GPa})$ and plate separation $(0.4\mathrm{nm}⩽d⩽1.6\mathrm{nm})$ on the phase behavior of water when the plates are either hydrophobic or hydrophilic. When water is confined between hydrophobic plates, capillary evaporation occurs between the plates at low enough $P$. The threshold value of $d$ at which this transition occurs decreases with $P$ (e.g., $1.6\mathrm{nm}$ at $P\approx -0.05\mathrm{GPa}$, $0.5\mathrm{nm}$ at $P\approx 0.1\mathrm{GPa}$), until, at high $P$, no capillary evaporation occurs. For $d\approx 0.6\mathrm{nm}$ and $P⩾0.1\mathrm{GPa}$, the system crystallizes into a bilayer ice. A $P$-$d$ phase diagram showing the vapor, liquid, and bilayer ice phases is proposed. When water is confined by hydrophilic (hydroxylated silica) plates, it remains in the liquid phase at all $P$ and $d$ studied. Interestingly, we observe for this case that even at the $P$ at which bulk water cavitates, the confined water remains in the liquid state. We also study systematically the state of hydration at different $P$ for both kinds of plates. For the range of conditions studied here, we find that in the presence of hydrophobic plates the effect of $P$ is to enhance water structure and to push water molecules toward the plates. The average orientation of water molecules next to the hydrophobic plates does not change upon pressurization. In contrast, in the presence of hydrophilic plates, water structure is insensitive to $P$. Hence, our results suggest that upon pressurization, hydrophobic plates behave as “soft” surfaces (in the sense of accommodating pressure-dependent changes in water structure) while hydrophilic walls behave as “hard” surfaces.

We present a simple physical model to estimate the blocked pore probability of an ion channel that can be blocked by a highly charged drug in solution. The model is inspired by recent experimental work on the blocking of the ${\mathrm{PA}}_{63}$ channel, involved in the anthrax toxin infection, by a highly charged drug [Karginov et al. PNAS 102, 15075 (2005)]. The drug binding to the pore is highly specific but the strong dependence of blocking on the applied voltage and electrolyte concentration suggests that long range electrostatic interactions are important. Since basic electrostatic concepts rather than detailed molecular models are considered, the microscopic details of the channel blocking are ignored, although the model captures most of the qualitative characteristics of the problem.

Membrane inclusions such as membrane-embedded peptides or proteins exhibit a curvature-dependent interaction with the surrounding lipid matrix due to the mismatch between their intrinsic curvature and the local membrane curvature. This interaction causes an inhomogeneous lateral distribution of the inclusions and a corresponding adjustment of the vesicle shape. We have studied theoretically the axisymmetric equilibrium shapes of lipid vesicles with mobile inclusions, taking into account that the membrane free energy includes the elastic energy of the lipid bilayer and a contribution due to an inclusion-membrane interaction. Equations describing the shape are derived by minimizing the total free energy at fixed membrane area, enclosed volume, and number of inclusions and are then solved numerically. It is shown that vesicle shape may assume a symmetry that differs from that of the vesicle with no inclusions. If the inclusion-membrane interaction exceeds a certain value, there is no axisymmetric solution of the equations with a continuous and derivable lateral density of inclusions over the whole area of the vesicle. When approaching the critical vesicle shape, the shapes obtained differ qualitatively from those described by the area difference elasticity model of the elastic properties of lipid membranes. In general, vesicle shapes adjust to the presence of inclusions by increasing regions with favorable curvature and decreasing regions of unfavorable curvature in a way such that the lateral distribution of inclusions becomes inhomogeneous.

We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time formulation of the model is expressed in terms of a Fokker-Planck equation. This equation is exactly soluble in the case of a single speaker and can be investigated analytically in the case of multiple speakers who communicate equally with all other speakers and give their utterances equal weight. Whilst the stationary properties of this system have much in common with the single-speaker case, time-dependent properties are richer. In the particular case where linguistic forms can become extinct, we find that the presence of many speakers causes a two-stage relaxation, the first being a common marginal distribution that persists for a long time as a consequence of ultimate extinction being due to rare fluctuations.

A perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions within an $N$-soliton train of the nonlinear Schrödinger equation. Perturbations induced by weak quadratic and periodic external potentials are studied by both analytical and numerical means. It is found that the perturbed CTC adequately models the $N$-soliton train dynamics for both types of potentials. As an application of the developed theory, we consider the dynamics of a train of matter-wave solitons confined to a parabolic trap and optical lattice, as well as tilted periodic potentials. In the last case, we demonstrate that there exist critical values of the strength of the linear potential for which one or more localized states can be extracted from a soliton train. An analytical expression for these critical strengths for expulsion is also derived.

We report in this paper the study of modulated wave trains in the one-dimensional (1D) discrete Ginzburg-Landau model. The full linear stability analysis of the nonlinear plane wave solutions is performed by considering both the wave vector $\left(\mathbf{q}\right)$ of the basic states and the wave vector $\left(\mathbf{Q}\right)$ of the perturbations as free parameters. In particular, it is shown that a threshold exists for the amplitude and above this threshold, the induced modulational instability leads to the formation of ordered and disordered patterns. The theoretical findings have been numerically tested through direct simulations and have been found to be in agreement with the theoretical prediction. We show numerically that modulational instability is also an indicator of the presence of discrete solitons as were early predicted to exist in Ginzburg-Landau lattices.

The phase transitions classes of reaction-diffusion systems with multiparticle reactions are an open challenging problem. Large scale simulations are applied for the $3A\to 4A$, $3A\to 2A$ and the $3A\to 4A$, $3A\to \varnothing$ triplet reaction models with site occupation restriction in one dimension. Static and dynamic mean-field scaling are observed with signs of logarithmic corrections suggesting $d_c=1$ upper critical dimension for this family of models.

We derive a set of identities that relate the higher-order interpoint spacing statistics of the two-dimensional homogeneous Poisson point process to the Wigner surmises for the higher-order spacing distributions of eigenvalues from the three classical random matrix ensembles. We also report a remarkable identity that equates the second-nearest-neighbor spacing statistics of the points of the Poisson process and the nearest-neighbor spacing statistics of complex eigenvalues from Ginibre’s ensemble of $2\times 2$ complex non-Hermitian random matrices.

We consider random diffusive motion of classical particles over the edges of Archimedean lattices. The diffusion coefficient is obtained by using periodic orbit theory. We also study deterministic motion over a honeycomb lattice without the possibility for an immediate return to the preceding node, controlled by a tent map with the golden ratio slope. Numerical analysis is performed to confirm the theoretical results.

We investigate, by numerical simulations, how the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model can induce emergence of scale-free networks and how this emerging structure affects dynamics of the system.

We study a model suspension of sterically stabilized colloidal particles and nonadsorbing ideal polymer coils, both in bulk and adsorbed against a planar hard wall. By integrating out the degrees of freedom of the polymer coils, we derive a formal expression for the effective one-component Hamiltonian of the colloids. We employ an efficient Monte Carlo simulation scheme for this mixture based on the exact effective colloid Hamiltonian; i.e., it incorporates all many-body interactions. The many-body character of the polymer-mediated effective interactions between the colloids yields bulk phase behavior and adsorption phenomena that differ substantially from those found for pairwise simple fluids. We determine the phase behavior for size ratios $q={\sigma }_p∕{\sigma }_c=1$, 0.6, and 0.1, where ${\sigma }_c$ and ${\sigma }_p$ denote the diameters of the colloids and polymer coils, respectively. For $q=1$ and 0.6, we find both a fluid-solid and a stable colloidal gas-liquid transition with an anomalously large bulk liquid regime caused by the many-body interactions. We compare the phase diagrams obtained from simulations with the results of the free-volume approach and with direct simulations of the true binary mixture. Although we did not simulate the polymer coils explicitly, we are able to obtain the three partial structure factors and radial distribution functions. We compare our results with those obtained from density functional theory and the Percus-Yevick approximation. We find good agreement between all results for the structure. We also study the mixture in contact with a single hard wall for $q=1$. Upon approach of the gas-liquid binodal, we find far from the triple point, three layering transitions in the partial wetting regime.

The free energy of nonionic balanced microemulsions based on nonionic surfactants are analyzed using experimental data from (i) phase behavior, (ii) osmotic compressibility of the balanced microemulsion structure, which is obtained from small angle neutron scattering (SANS) experiments, and (iii) data on interfacial tensions obtained by T. Sottmann and R. Strey [J. Chem. Phys. 106 8606 (1997)]. The balanced microemulsion, where the spontaneous curvature vanishes at equal volumes of water and oil, has a finite swelling with the solvent with a minimum surfactant volume fraction, ${\Phi }_{\mathrm{S}}^{*}$. At higher surfactant concentrations the balanced microemulsion phase having the surfactant volume fraction ${\Phi }_{\mathrm{S}1}$ coexists with a lamellar phase of volume fraction ${\Phi }_{\mathrm{S}2}$. Under the constraint of ${\Phi }_{\mathrm{W}}={\Phi }_{\mathrm{O}}$, where ${\Phi }_{\mathrm{W}}$ and ${\Phi }_{\mathrm{O}}$ are the water and oil volume fractions, respectively, the free energy density can be written as an expansion in the surfactant concentration. While the phase equilibria only depend on relative values of the expansion coefficients, absolute values can be obtained from compressibility and interfacial tension data. The osmotic compressibility of the surfactant film was measured by SANS through contrast matching water and oil. The phase behavior of nonionic surfactant-water-oil systems depends strongly on the chain length of the oil, when comparing a homologous series from octane to hexadecane using the same surfactant, here being pentaethylene oxide dodecyl ether $\left({\mathrm{C}}_{12}{\mathrm{E}}_5\right)$. The three concentrations ${\Phi }_{\mathrm{S}}^{*}$, ${\Phi }_{\mathrm{S}1}$, and ${\Phi }_{\mathrm{S}2}$ increase markedly as the chain length of the oil is increased. However, from the analysis of the surface tension data it is concluded that there are no major changes in the bending rigidities as the oil is changed. The data are analyzed within the model free energy densities $G∕V=a_3{\Phi }_{\mathrm{S}}^3+a_5{\Phi }_{\mathrm{S}}^5$ and $G∕V=a{\Phi }_{\mathrm{S}}^3(1+b\ln {\Phi }_{\mathrm{S}})$. We find that within experimental accuracy, the first of these models provides a quantitatively consistent description of the data. For the second model there is a larger discrepancy between observed and calculated values.

A linear chain of cells is considered in which calcium $\left({\mathrm{Ca}}^{2+}\right)$ fluctuations within a cell are described by a simple minimal model. Cells are coupled together by bidirectional paracrine signaling via calcium oscillations. Two typical zones of propagation are observed: a transition zone and a regular zone. The transition zone exhibits the same phenomena that can be observed in single cells, pairs or triplets of cells. Within the regular zone, simple periodic oscillations of calcium propagate and the ${\mathrm{Ca}}^{2+}$ signal is similar from one cell to another (same amplitude and same frequency). But, the signals are separated by a slight phase shift characterizing the propagation of ${\mathrm{Ca}}^{2+}$ waves due to the type of coupling used. We also consider the colonization of the lattice by the abnormal oscillations of sick cells.

We use a path integral representation to solve the Eigen and Crow-Kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions. In the general case, we find that the solution to these molecular evolution models can be written as the optimum of a fitness function, with constraints enforced by Lagrange multipliers and with a term accounting for the entropy of the spreading population in sequence space. The results for the Eigen model are applied to consider virus or cancer proliferation under the control of drugs or the immune system.