In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash equilibria correspond to stable fixed points that are always evolutionarily stable. However, in finite populations stochastic effects can drive the system away from strict Nash equilibria, which gives rise to a new concept for evolutionary stability. The conventional and the new stability concepts may apparently contradict each other leading to conflicting predictions in large yet finite populations. We show that the two concepts can be derived from the frequency dependent Moran process in different limits. Our results help to determine the appropriate stability concept in large finite populations. The general validity of our findings is demonstrated showing that the same results are valid employing vastly different co-evolutionary processes.

The model of DNA charge inversion by Nguyen and Shklovskii [T. T. Nguyen and B. I. Shklovskii, Phys. Rev. Lett. 89, 018101 (2002)] is extended. A single double-helix strand of DNA is represented by a lattice of negative charges at the positions of the protruding oxygens of the phosphates along the DNA backbone, and the adsorbed polyelectrolyte molecules are represented by charged dimers. A lattice-gas model is used in which dimers adsorbing either parallel or perpendicular to the lattice are treated as separate species, and the model allows for vacancies between adsorbed species. The mean field theory used is formulated as a saddle-point approximation of the exact functional integral representation of the grand canonical partition function, opening the way for the inclusion of the effects of charge fluctuation corrections.

We consider a driven Brownian particle, subject to both conservative and nonconservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski, and Gallavotti-Cohen in different special cases.

Energetic proton acceleration from concave targets, the front of which were irradiated with $40\mathrm{fs}$ laser pulses with an intensity of ${10}^{20}\mathrm{W}∕{\mathrm{cm}}^2$, has been studied as a function of the depth of the concave shape. Three kinds of targets, a triangular concave target, a circular concave target and a parabolic concave target are considered. When the depth of the concave shape was varied, the peak proton energy showed a maximum. The underlying mechanism for the existence of a maximum peak proton energy is presented by tracing the proton trajectory. It is concluded that a parabolic concave target is the best, among the targets considered, for accelerating a proton beam, since a proton beam from a parabolic concave target goes through the strongest electric field.

We are concerned with improving the forecast capabilities of the global approach to time series. We assume that the normal techniques of global mapping are applied, the noise reduction is performed, etc. Then, using the mathematical foundations behind such approaches, we propose a method that, without a great computational cost, greatly increases the accuracy of the corresponding forecasting.

New tools for automatically finding data clusters that share statistical properties in a heterogeneous data set are imperative in pattern recognition research. Here we introduce a deterministic procedure as a tool for pattern recognition in a hierarchical way. The algorithm finds attractors of mutually close points based on the neighborhood ranking. A memory parameter $\mu$ acts as a hierarchy parameter, in which the clusters are identified. The final result of the method is a general tree that represents the nesting structure of the data in an invariant way by scale transformation.

We develop and test the last-passage diffusion algorithm, a charge-based Monte Carlo algorithm, for the mutual capacitance of a system of conductors. The first-passage algorithm is highly efficient because it is charge based and incorporates importance sampling; it averages over the properties of Brownian paths that initiate outside the conductor and terminate on its surface. However, this algorithm does not seem to generalize to mutual capacitance problems. The last-passage algorithm, in a sense, is the time reversal of the first-passage algorithm; it involves averages over particles that initiate on an absorbing surface, leave that surface, and diffuse away to infinity. To validate this algorithm, we calculate the mutual capacitance matrix of the circular-disk parallel-plate capacitor and compare with the known numerical results. Good agreement is obtained.

Lévy flights are known to be optimal search strategies in the particular case of revisitable targets. In the relevant situation of nonrevisitable targets, we propose an alternative model of two-dimensional (2D) search processes, which explicitly relies on the widely observed intermittent behavior of foraging animals. We show analytically that intermittent strategies can minimize the search time, and therefore do constitute real optimal strategies. We study two representative modes of target detection and determine which features of the search time are robust and do not depend on the specific characteristics of detection mechanisms. In particular, both modes lead to a global minimum of the search time as a function of the typical times spent in each state, for the same optimal duration of the ballistic phase. This last quantity could be a universal feature of 2D intermittent search strategies.

The escape of Brownian motion through a narrow absorbing window in an otherwise reflecting boundary of a domain is a rare event. In the presence of a deep potential well, there are two long time scales, the mean escape time from the well and the mean time to reach the absorbing window. We derive a generalized Kramers formula for the mean escape time through the narrow window.

The capillary flow alignment of the thermotropic liquid crystal $4\text{−}n\text{−}\mathrm{octyl}\text{−}{4}^{\prime }\text{−}\mathrm{cyanobiphenyl}$ in the nematic and smectic phases is investigated using time-resolved synchrotron small-angle x-ray scattering. Samples were cooled from the isotropic phase to erase prior orientation. Upon cooling through the nematic phase under Poiseuille flow in a circular capillary, a transition from the alignment of mesogens along the flow direction to the alignment of layers along the flow direction (mesogens perpendicular to flow) appears to occur continuously at the cooling rate applied. The transition is centered on a temperature at which the Leslie viscosity coefficient ${\alpha }_3$ changes sign. The configuration with layers aligned along the flow direction is also observed in the smectic phase. The transition in the nematic phase on cooling has previously been ascribed to an aligning-nonaligning or tumbling transition. At high flow rates there is evidence for tumbling around an average alignment of layers along the flow direction. At lower flow rates this orientation is more clearly defined. The layer alignment is ascribed to surface-induced ordering propagating into the bulk of the capillary, an observation supported by the parallel alignment of layers observed for a static sample at low temperatures in the nematic phase.

Molecular-dynamics simulations are used to study the effective interactions in charged stabilized colloidal suspensions. We focus on highly charged macroions in the limit of low salt concentrations. Within this regime, nonlinear corrections to Debye-Hückel (DH) theory have to be considered. For non-bulk-like systems, such as isolated pairs or triples of macroions, we show that nonlinear effects can become relevant, which cannot be described by the charge renormalization concept [S. Alexander et al., J. Chem. Phys. 80, 5776 (1984)]. For an isolated pair of macroions, we find an almost perfect qualitative agreement between our simulation data and DH theory. However, on a quantitative level, neither DH theory nor the charge renormalization concept can be confirmed in detail. This seems mainly to be related to the fact that for small ion concentrations, microionic layers can strongly overlap, whereas, simultaneously, excluded volume effects are less important. In the case of isolated triples, where we compare between coaxial and triangular geometries, we find attractive corrections to pairwise additivity in the limit of small macroion separations and salt concentrations. These triplet interactions arise if all three microionic layers around the macroions exhibit a significant overlap. In contrast to the case of two isolated colloids, the charge distribution around a macroion in a triple is found to be anisotropic.

The diffusivity of spherical colloidal particles close to a planar hard wall is studied by dynamic light scattering with evanescent illumination. A novel setup allows us to independently vary the scattering vector components parallel $Q_{\Vert }$ and normal $Q_{\perp }$ to the wall. An expression for the initial decay rate $\Gamma$ of the time autocorrelation functions is derived as a function of both $Q_{\Vert }$ and $Q_{\perp }$, as well as the penetration depth of the evanescent wave, where hydrodynamic interactions of particles with the wall are included. This makes it possible to study the viscous wall drag effect quantitatively for particles as small as $85\mathrm{nm}$ in radius.

Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapor interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by nonlinear quasistatic simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a nonuniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find that data collapse onto a master curve for both buckling pressure and deformation mode, thus allowing us to predict when the deformed shape is a dimple, Mexican hat, and so on. This master curve is parameterized by a dimensionless measure of the nonuniformity of the shell. We also speculate on how overlapping time scales for gelation and deformation may alter our findings.

The structure of a molecular liquid, in both the nematic liquid crystalline and isotropic phases, around a cylindrical macroparticle, is studied using density functional theory. In the nematic phase the structure of the fluid is highly anisotropic with respect to the director, in agreement with results from simulation and phenomenological theories. On going into the isotropic phase the structure becomes rotationally invariant around the macroparticle with an oriented layer at the surface.

We studied the low-energy excitations in the meV region as well as the picosecond fast process in polystyrene thin supported films using inelastic and quasielastic neutron scattering in a temperature range from $11\text{to}430\mathrm{K}$, covering the bulk glass transition temperature $T_{\mathrm{g}}$. It was found that the mean square displacement $⟨u^2⟩$ decreased with the film thickness below and above the glass transition temperature $T_{\mathrm{g}}$, suggesting that the hardening occurs with decreasing the film thickness. Corresponding to the decrease in $⟨u^2⟩$, it was also found that the density of phonon states $G\left(\omega \right)$ decreased with film thickness. This decrease occurs mainly in the Debye mode while the contribution of the boson peak mode also decreases with the film thickness without changing the boson peak energy. As for the fast process, which appeared above at about $150\mathrm{K}$ as a quasielastic scattering, the fraction $A_{\mathit{\text{fast}}}\left(Q\right)$ decreased with the film thickness in a similar manner with the boson peak without changing the relaxation rate, suggesting a common origin for the boson peak and the fast process. These observations showing the hardening were well explained by assuming a hard dense layer at the interface, where the numbers of the boson peak mode as well as the fast process are less than the bulk state.

Proteins can locate their specific targets on DNA up to two orders of magnitude faster than the Smoluchowski three-dimensional diffusion rate. This happens due to nonspecific adsorption of proteins to DNA and subsequent one-dimensional sliding along DNA. We call such a one-dimensional route towards the target an “antenna.” We studied the role of the dispersion of nonspecific binding energies within the antenna due to a quasirandom sequence of natural DNA. A random energy profile for sliding proteins slows the searching rate for the target. We show that this slowdown is different for macroscopic and mesoscopic antennas.

The recent applications of nanosecond, megavolt-per-meter electric field pulses to biological systems show striking cellular and subcellular electric field induced effects and revive the interest in the biophysical mechanism of electroporation. We first show that the absolute rate theory, with experimentally based parameter input, is consistent with membrane pore creation on a nanosecond time scale. Secondly we use a Smoluchowski equation-based model to formulate a self-consistent theoretical approach. The analysis is carried out for a planar cell membrane patch exposed to a $10\mathrm{ns}$ trapezoidal pulse with $1.5\mathrm{ns}$ rise and fall times. Results demonstrate reversible supraelectroporation behavior in terms of transmembrane voltage, pore density, membrane conductance, fractional aqueous area, pore distribution, and average pore radius. We further motivate and justify the use of Krassowska’s asymptotic electroporation model for analyzing nanosecond pulses, showing that pore creation dominates the electrical response and that pore expansion is a negligible effect on this time scale.

There are systematic discrepancies unexplained so far between theory and experiment for opacities of mid- and high-$Z$ plasmas. To address this issue, we investigated the radiative opacity of gold plasmas by using a detailed level-accounting (DLA) method, in which various physical effects can be taken into account. In this work, we studied in detail the effects of core-valence electron correlation and linewidth on the opacity of gold plasmas. Our DLA results correctly explain the relative intensity of the two strong absorption peaks located near the photon energies of 70 and $80\mathrm{eV}$, which was experimentally observed by Eidmann et al. [Europhys. Lett. 44, 459 (1998)]. Meanwhile, the DLA results showed that effects of saturation for the strong individual lines are evident in the transmission spectrum.