Some recent papers were concerned with applicability of the Bayesian (statistical) approach to reconstruction of dynamic systems (DS) from experimental data. A significant merit of the approach is its universality. But, being correct in terms of meeting conditions of the underlying theorem, the Bayesian approach to reconstruction of DS is hard to realize in the most interesting case of noisy chaotic time series (TS). In this work we consider a modification of the Bayesian approach that can be used for reconstruction of DS from noisy TS. We demonstrate efficiency of the modified approach for solution of two types of problems: (1) finding values of parameters of a known DS by noisy TS; (2) classification of modes of behavior of such a DS by short TS with pronounced noise.

We use a one-shot measurement technique to study effects of laser prepulses on the electron laser wakefield acceleration driven by relativistically intense laser pulses ($\lambda =790\mathrm{nm}$, $11\mathrm{TW}$, $37\mathrm{fs}$) in dense helium gas jets. A quasimonoenergetic electron bunch with an energy peak $\sim 11.5\mathrm{MeV}$ [$\Delta E∕E\sim 10\%$ (FWHM)] and with a narrow-cone angle $\left(0.04\pi \mathrm{mm}\mathrm{mrad}\right)$ of ejection is detected at a plasma density of $8\times {10}^{19}{\mathrm{cm}}^{-3}$. A strong correlation between the generation of monoenergetic electrons and optical guiding of the pulse in a thin channel produced by picosecond laser prepulses is observed. This generation mechanism is well corroborated by two-dimensional particle-in-cell simulations.

Two versions of the fundamental measure density functionals together with a new interfacial density profile parametrization were used to study the hard-sphere crystal-melt interface in the framework of the fundamental measure density functional theory. The equilibrium interfacial density profiles and interfacial free energies were found as a result of minimization of grand canonical potential of system with respect to parameters of density profile. We found that the average interfacial free energy is about $0.78$, which is in reasonable agreement with simulation results.

We report on the stress response of gyroidal and lamellar amphiphilic mesophases to steady shear simulated using a bottom-up lattice-Boltzmann model for amphiphilic fluids and sliding periodic (Lees-Edwards) boundary conditions. We study the gyroid per se (above the sponge-gyroid transition, of high crystallinity) and the molten gyroid (within such a transition, of shorter-range order). We find that both mesophases exhibit shear thinning, more pronounced and at lower strain rates for the molten gyroid. At late times after the onset of shear, the skeleton of the crystalline gyroid becomes a structure of interconnected irregular tubes and toroidal rings, mostly oriented along the velocity ramp imposed by the shear, in contradistinction with free-energy Langevin-diffusion studies which yield a much simpler structure of disentangled tubes. We also compare the shear stress and deformation of lamellar mesophases with and without amphiphile when subjected to the same shear flow applied normal to the lamellae. We find that the presence of amphiphile allows (a) the shear stress at late times to be higher than in the case without amphiphile, and (b) the formation of rich patterns on the sheared interface, characterized by alternating regions of high and low curvature.

We study the microstructural glass transition in diblock-copolymer melts using a thermodynamic replica approach. Our approach performs an expansion in terms of the natural smallness parameter—the inverse of the scaled degree of polymerization $\overline{N}$—which allows us to systematically study the approach to mean-field behavior as the degree of polymerization increases. We find that in the limit of infinite chain length, both the onset of glassiness and the vitrification transition (Kauzmann temperature) collapse to the mean-field spinodal, suggesting that the spinodal can be regarded as the mean-field signature for glass transitions in this class of microphase-separating system. We also study the order-disorder transition (ODT) within the same theoretical framework; in particular, we include the leading-order fluctuation corrections due to the cubic interaction in the coarse-grained Hamiltonian, which has been ignored in previous studies of the ODT in block copolymers. We find that the cubic term stabilizes both the ordered (body-centered-cubic) phase and the glassy state relative to the disordered phase. In melts of symmetric copolymers the glass transition always occurs after the order-disorder transition (below the ODT temperature), but for asymmetric copolymers, it is possible for the glass transition to precede the ordering transition.

We study a system of globally coupled FitzHugh-Nagumo equations. Each unit is either excitatory or inhibitory. If the numbers of units of both types are in a specific ratio, we observe the presence of multistable oscillatory states with different excitation or firing rates. In the presence of noise, there is noise-driven switching between these states and the resultant firing pattern is long-range correlated. The choice between higher and lower frequency oscillations depends on the input, which results in increasing adaptability of the system’s output to the periodic input.

We investigate the relationship between the blood flow velocities (BFV) in the middle cerebral arteries and beat-to-beat blood pressure (BP) recorded from a finger in healthy and post-stroke subjects during the quasisteady state after perturbation for four different physiologic conditions: supine rest, head-up tilt, hyperventilation, and $\mathrm{C}{\mathrm{O}}_2$ rebreathing in upright position. To evaluate whether instantaneous BP changes in the steady state are coupled with instantaneous changes in the BFV, we compare dynamical patterns in the instantaneous phases of these signals, obtained from the Hilbert transform, as a function of time. We find that in post-stroke subjects the instantaneous phase increments of BP and BFV exhibit well-pronounced patterns that remain stable in time for all four physiologic conditions, while in healthy subjects these patterns are different, less pronounced, and more variable. We propose an approach based on the cross-correlation of the instantaneous phase increments to quantify the coupling between BP and BFV signals. We find that the maximum correlation strength is different for the two groups and for the different conditions. For healthy subjects the amplitude of the cross-correlation between the instantaneous phase increments of BP and BFV is small and attenuates within 3–5 heartbeats. In contrast, for post-stroke subjects, this amplitude is significantly larger and cross-correlations persist up to 20 heartbeats. Further, we show that the instantaneous phase increments of BP and BFV are cross-correlated even within a single heartbeat cycle. We compare the results of our approach with three complementary methods: direct BP-BFV cross-correlation, transfer function analysis, and phase synchronization analysis. Our findings provide insight into the mechanism of cerebral vascular control in healthy subjects, suggesting that this control mechanism may involve rapid adjustments (within a heartbeat) of the cerebral vessels, so that BFV remains steady in response to changes in peripheral BP.

Quantum effects on multitime distributions and correlation functions of single objects, stemming from both the dynamics and repeated measurements, are calculated for a driven harmonic system using a superoperator generating functional formalism. Marked differences between multipoint observables associated with classical and quantum measurements are identified. The effects of quantum collapse and measurement resolution are discussed.

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact probability distribution function for the particle positions, calculate its moments, and find their corresponding long-time, asymptotic behaviors. The generally anomalous diffusive regimes of the particles are classified, and their dependence on the friction coefficient and the characteristics of the noises is analyzed in detail. The asymptotic predictions are confirmed by exact solutions for two examples.

Drag reduction by bubbles in stationary turbulent flows is sensitive to the compressibility of the bubbles. Without this dynamical effect the bubbles only renormalize the fluid density and viscosity, an effect that by itself can only lead to a small percentage of drag reduction. We show in this paper that the dynamics of bubbles and their effect on the compressibility of the mixture can lead to a much higher drag reduction.

It is demonstrated that metallic horseshoe-shaped (also referred to as u-shaped) nanostructures can exhibit a magnetic resonance in the optical spectral range. This magnetic plasmon resonance is distinct from the purely geometric $LC$ resonance occurring in perfectly conducting split rings because the plasmonic nature of the metal plays the dominant role. Similarly to the electrical surface plasmon resonance, the magnetic plasmon resonance is determined primarily by the metal properties and nanostructure geometry rather than by the ratio of the wavelength and the structure's size. Magnetic plasmon resonance occurs in nanostructures much smaller in size than the optical wavelength. Electromagnetic properties of periodically assembled horseshoe-shaped nanostructures are investigated, and the close proximity of the electrical and magnetic plasmon resonances is exploited in designing a negative index metamaterial. Close to the magnetic plasmon resonance frequency both magnetic permeability $\mu$ and electric permittivity $\epsilon$ can become negative, paving the way for the development of subwavelength negative index materials in the optical range.

The dynamics of the transport of the mean-square diffuse wave amplitude among coupled substructures is examined. Applications include coupled quantum dots, reverberation rooms, and chaotic billiards. A self-consistent theory is found to predict classical diffusive behavior at strong coupling, but to predict localization when coupling times are comparable to or greater than Heisenberg times. Predictions are compared to an exact result, to the Vollhardt-Wolfle self-consistent theory for multiply scattering continua, and to direct numerical simulations.

Current conventions define the deflection angle associated with the classical elastic scattering of particles in terms of the system’s position vector. This is not consistent with the definition of the scattering angle, a function of the momentum vector. A definition of the deflection angle which resolves this inconsistency is introduced and developed for the case of an arbitrary potential in two dimensions. It is shown that the generalized deflection angle reduces to that of Cross [J. Chem. Phys. 49, 609 (1967)] when angular momentum is conserved. An efficient algorithm for the calculation of the generalized deflection angle is given and its utility in the analysis of collision dynamics is demonstrated with a numerical example.

Capillary penetration of a wetting liquid in a microtomographic image of paper board, whose linear dimension was close to the average length of wood fibers, was simulated by the lattice-Boltzmann method. In spite of the size of the system not being large with respect to the size of structural inhomogeneities in the sample, for unidirectional penetration the simulated behavior was described well by that of the Lucas-Washburn equation, while for radial penetration a radial capillary equation described the behavior. In both cases the average penetration depth of the liquid front as a function of time followed a power law over many orders of magnitude. Capillary penetration of small droplets of liquid was also simulated in the same three-dimensional image of paper. In this case the simulation results could be described by a generalized form of the radial-penetration equation.

Chaos thresholds of the $z$-logistic maps $x_{t+1}=1-a\mid x_t{\mid }^z$ $(z>1;t=0,1,2,\dots )$ are numerically analyzed at accumulation points of cycles 2, 3, and 5 (three different cycles 5). We verify that the nonextensive $q$-generalization of a Pesin-like identity is preserved through averaging over the entire phase space. More precisely, we computationally verify ${\lim }_{t\to \infty }⟨S_{q_{sen}^{av}}⟩\left(t\right)∕t={\lim }_{t\to \infty }⟨{\ln }_{q_{sen}^{av}}\xi ⟩\left(t\right)∕t\equiv {\lambda }_{q_{sen}^{av}}^{av}$, where the entropy $S_q\equiv (1-{\sum }_i{p}_i^q)∕(q-1)$ $(S_1=-{\sum }_i{p}_i\ln p_i)$, the sensitivity to the initial conditions $\xi \equiv {\lim }_{\mathrm{\Delta }x\left(0\right)\to 0}\mathrm{\Delta }x\left(t\right)∕\mathrm{\Delta }x\left(0\right)$, and ${\ln }_{q}x\equiv (x^{1-q}-1)∕(1-q)$ $({\ln }_{1}x=\ln x)$. The entropic index $q_{sen}^{av}<1$, and the coefficient ${\lambda }_{q_{sen}^{av}}^{av}>0$ depend on both $z$ and the cycle. We also study the relaxation that occurs if we start with an ensemble of initial conditions homogeneously occupying the entire phase space. The associated Lebesgue measure asymptotically decreases as $1∕t^{1∕(q_{rel}-1)}(q_{rel}>1)$. These results (i) illustrate the connection (conjectured by one of us) between sensitivity and relaxation entropic indices, namely, $q_{rel}-1\simeq A_n(1-q_{sen}^{av}{)}^{{\alpha }_n}$, where the positive numbers $(A_n,{\alpha }_n)$ depend on the cycle; (ii) exhibit an unexpected scaling, namely, $q_{sen}^{av}\left(\mathrm{cycle}n\right)=B_n{q}_{sen}^{av}\left(\mathrm{cycle}2\right)+{ϵ}_n$.

Bifurcation properties, stability behavior, dynamics, and the heat transfer of convection in a horizontal fluid layer that is driven away from thermal equilibrium by imposing a vertical temperature difference are compared with those resulting from imposing a heat current. Similarities and differences are elucidated. In particular various paradigmatic backwards bifurcating convection structures that occur, e.g., in binary fluid mixtures are determined numerically for the two different driving mechanisms. Conditions are given under which current driven convection is stable when temperature driven convection is unstable.

Recent experiments have shown large-scale dynamic coherence in suspensions of the bacterium B. subtilis, characterized by quorum polarity, collective parallel swimming of cells. To probe mechanisms leading to this, we study the response of individual cells to steric stress, and find that they can reverse swimming direction at spatial constrictions without turning the cell body. The consequences of this propensity to flip the flagella are quantified by measurements of the inward and outward swimming velocities, whose asymptotic values far from the constriction show near perfect symmetry, implying that “forwards” and “backwards” are dynamically indistinguishable, as with E. coli.

Structural and thermodynamic properties of spherical particles carrying classical spins are investigated by Monte Carlo simulations. The potential energy is the sum of short range, purely repulsive pair contributions, and spin-spin interactions. These last are of the dipole-dipole form, with however, a crucial change of sign. At low density and high temperature the system is a homogeneous fluid of weakly interacting particles and short range spin correlations. With decreasing temperature particles condense into an equilibrium population of free floating vesicles. The comparison with the electrostatic case, giving rise to predominantly one-dimensional aggregates under similar conditions, is discussed. In both cases condensation is a continuous transformation, provided the isotropic part of the interatomic potential is purely repulsive. At low temperature the model allows us to investigate thermal and mechanical properties of membranes. At intermediate temperatures it provides a simple model to investigate equilibrium polymerization in a system giving rise to predominantly two-dimensional aggregates.

We use molecular dynamics (MD) to simulate an unstable homogeneous mixture of binary fluids (AB), confined in a slit pore of width $D$. The pore walls are assumed to be flat and structureless and attract one component of the mixture (A) with the same strength. The pairwise interactions between the particles are modeled by the Lennard-Jones potential, with symmetric parameters that lead to a miscibility gap in the bulk. In the thin-film geometry, an interesting interplay occurs between surface enrichment and phase separation. We study the evolution of a mixture with equal amounts of A and B, which is rendered unstable by a temperature quench. We find that A-rich surface enrichment layers form quickly during the early stages of the evolution, causing a depletion of A in the inner regions of the film. These surface-directed concentration profiles propagate from the walls towards the center of the film, resulting in a transient layered structure. This layered state breaks up into a columnar state, which is characterized by the lateral coarsening of cylindrical domains. The qualitative features of this process resemble results from previous studies of diffusive Ginzburg-Landau-type models [S. K. Das, S. Puri, J. Horbach, and K. Binder, Phys. Rev. E 72, 061603 (2005)], but quantitative aspects differ markedly. The relation to spinodal decomposition in a strictly two-dimensional geometry is also discussed.

The physical mechanism of liquid crystal (LC) alignment in ferroelectric LC (FLC) droplets dispersed in a photocurable polymer matrix was studied. The orientational ordering of both FLC molecules and the polymer matrix was induced by a rubbed polyimide alignment layer. There existed an optimum FLC droplet size for the production of uniformly oriented molecules and smectic layers for maximum electro-optic modulation. The alignment quality was critically dependent on the droplet size, shape, the helical pitch, and the phase transition sequence of the FLCs. The molecular structure formed inside the FLC droplets resulted from a delicate balance between the elastic energy stored in a restricted geometry and surface interactions at the FLC-polymer interface.