We present a dynamical spectral model for large-eddy simulation of the incompressible magnetohydrodynamic (MHD) equations based on the eddy damped quasinormal Markovian approximation. This model extends classical spectral large-eddy simulations for the Navier-Stokes equations to incorporate general (non-Kolmogorovian) spectra as well as eddy noise. We derive the model for MHD flows and show that the introduction of an eddy damping time for the dynamics of spectral tensors, in the absence of equipartition between the velocity and magnetic fields, leads to better agreement with direct numerical simulations, an important point for dynamo computations.

An accurate shell model of spherical Coulomb crystals is presented. Employing intrashell angular particle positions that correspond to the global energy minima of the pertinent Thomson problems, it yields rigorous upper bounds to the exact energies that are accurate to within 0.03%, which constitutes an improvement of two orders of magnitude over its predecessors based upon continuous intrashell distributions. In addition, the present model faithfully reproduces mean crystal radii and shell occupancies without recourse to any empirical parameters. Thanks to its simple form and the well-known asymptotics of the Thomson problem at the bulk limit, it affords analytical formulas for energies and mean crystal radii of very large spherical Coulomb crystals. Moreover, it rigorously accounts for certain features of the less accurate models published previously.

An efficient method is proposed for numerical solutions of nonlinear Schrödinger equations on an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation, absorbing boundary conditions are designed to truncate the unbounded domain, which are in nonlinear form and can perfectly absorb waves outgoing from the boundaries of the truncated computational domain. The stability of the induced initial boundary value problem defined on the computational domain is examined by a normal mode analysis. Numerical examples are given to illustrate the stable and tractable advantages of the method.

Established expressions for entropy production in irreversible processes are generalized to include friction explicitly, as a source of irreversibility in the interaction between a system and its surroundings. The net amount of heat delivered to the system does not come now only from the reservoir, but may have an additional component coming from the work done against friction forces and dissipated as heat. To avoid ambiguities in interpreting the different contributions to entropy increase, the latter is also written in terms of the heat directly exchanged between the system and surroundings and of the fraction of frictional work that is lost in the system.

We introduce a bond-diluted Ising model with temperature-dependent concentration of bonds, which is intended to simulate the excitations of bond degrees of freedom as in covalently bonded network liquids arising from the thermal electronic transitions between bonding and antibonding electronic states. The critical behavior of this simplified model system, called the thermalized-bond Ising model, is investigated in terms of the Monte Carlo simulation results of finite-size regular Ising systems, as input for the method of chemical potentials that is generally used to obtain the thermodynamic properties of annealed impurity models. A finite-size scaling analysis of the susceptibility and the fourth-order cumulant results in a reliable estimation of the renormalized critical exponents. The exponents are found to be consistent with the phenomenological renormalization relations, due to Fisher, despite the temperature-dependent bond dilution.

The statistics of a subcritical spatially homogeneous $XY$ spin system driven by dichotomous Markov noise as an external field is investigated, particularly focusing on the switching process of the sign of the order parameter parallel to the external field. The switching process is classified in two types, which are called the Bloch-type switching and the Ising-type switching, according to whether or not the order parameter perpendicular to the external field takes finite value at the switching. The phase diagram for the onset of the switching process with respect to the amplitude of the external field and the anisotropy parameter of the system is constructed. It is revealed that the power spectral density $I\left(\omega \right)$ for the time series of the order parameter in the case of the Bloch-type switching is proportional to ${\omega }^{-3∕2}$ in an intermediate region of $\omega$. Furthermore, the scaling function of $I\left(\omega \right)$ near the onset point of the Bloch-type switching is derived.

When a stochastic system evolves from its unstable state the phenomenon of transient multimodality may appear, namely for a period of time, probability distribution develops a larger number of maxima than it possesses in the initial and in the stationary states. We investigate the influence of potential fluctuations generated by a Gaussian white noise on this effect. Some general conditions which suffice for the occurrence of noise induced transient multimodality are presented. The opposite phenomenon, namely the noise suppression of transient multimodality, is shown as well.

We have calculated the Tsallis entropy and Fisher information matrix (entropy) of spatially correlated nonextensive systems, by using an analytic non-Gaussian distribution obtained by the maximum entropy method. The effects of the correlated variability on the Fisher information matrix are shown to be different from those on the Tsallis entropy. The Fisher information is increased (decreased) by a positive (negative) correlation, whereas the Tsallis entropy is decreased with increasing absolute magnitude of the correlation, independently of its sign. This fact arises from the difference in their characteristics. It implies from the Cramér-Rao inequality that the accuracy of an unbiased estimate of fluctuation is improved by a negative correlation. A critical comparison is made between the present study and previous ones employing the Gaussian approximation for the correlated variability due to multiplicative noise.

It is well established that at ambient and supercooled conditions water can be described as a percolating network of H bonds. This work is aimed at identifying, by neutron diffraction experiments combined with computer simulations, a percolation line in supercritical water, where the extension of the H-bond network is in question. It is found that in real supercritical water liquidlike states are observed at or above the percolation threshold, while below this threshold gaslike water forms small, sheetlike configurations. Inspection of the three-dimensional arrangement of water molecules suggests that crossing of this percolation line is accompanied by a change of symmetry in the first neighboring shell of molecules from trigonal below the line to tetrahedral above.

Recently, the existence and properties of unbounded cavity modes, resulting in extensive plastic deformation failure of two-dimensional sheets of amorphous media, were discussed in the context of the athermal shear-transformation-zones (STZ) theory. These modes pertain to perfect circular symmetry of the cavity and the stress conditions. In this paper we study the shape stability of the expanding circular cavity against perturbations, in both the unbounded and the bounded growth regimes (for the latter the unperturbed theory predicts no catastrophic failure). Since the unperturbed reference state is time dependent, the linear stability theory cannot be cast into standard time-independent eigenvalue analysis. The main results of our study are as follows: (i) sufficiently small perturbations are stable; (ii) larger perturbations within the formal linear decomposition may lead to an instability; this dependence on the magnitude of the perturbations in the linear analysis is a result of the nonstationarity of the growth; and (iii) the stability of the circular cavity is particularly sensitive to perturbations in the effective disorder temperature; in this context we highlight the role of the rate sensitivity of the limiting value of this effective temperature. Finally we point to the consequences of the form of the stress dependence of the rate of STZ transitions. The present analysis indicates the importance of nonlinear effects that were not taken into account yet. Furthermore, the analysis suggests that details of the constitutive relations appearing in the theory can be constrained by the modes of macroscopic failure in these amorphous systems.

The nonlocal complex Ginzburg-Landau equation (NCGLE) has been recently derived as a general model for electrochemical systems close to a supercritical Hopf bifurcation [V. Garcia-Morales and K. Krischer, Phys. Rev. Lett. 100, 054101 (2008)]. We carry out the stability analysis of plane waves for arbitrary Fourier numbers providing the generalized Eckhaus criterion for stability to long-wavelength fluctuations in the NCGLE. We also show that coherent structures (standing waves, heteroclinic orbits) arise in the NCGLE at intermediate coupling ranges from states which are turbulent under local coupling. These results are substantiated through simulations of the full NCGLE and bifurcation analysis of the truncated NCGLE which preserves the symmetry of the observed patterns. We briefly discuss the effect of the nonlocal coupling on other localized structures (Bekki-Nozaki holes) found in the NCGLE.

We explore numerically the flow induced in a spherical shell by differentially rotating the inner and outer spheres. The fluid is also taken to be electrically conducting (in the low magnetic Reynolds number limit), and a magnetic field is imposed parallel to the axis of rotation. If the outer sphere is stationary, the magnetic field induces a Shercliffe layer on the tangent cylinder, the cylinder just touching the inner sphere and parallel to the field. If the magnetic field is absent, but a strong overall rotation is present, Coriolis effects induce a Stewartson layer on the tangent cylinder. The nonaxisymmetric instabilities of both types of layer separately have been studied before; here, we consider the two cases side by side, as well as the mixed case, and investigate how magnetic and rotational effects interact. We find that if the differential rotation and the overall rotation are in the same direction, the overall rotation may have a destabilizing influence, whereas if the differential rotation and the overall rotation are in the opposite direction, the overall rotation always has a stabilizing influence.

The criticality of the $(2+1)$-dimensional $XY$ model is investigated with the numerical diagonalization method. So far, it has been considered that the diagonalization method would not be very suitable for analyzing the criticality in large dimensions $(d⩾3)$; in fact, the tractable system size with the diagonalization method is severely restricted. In this paper, we employ Novotny’s method, which enables us to treat a variety of system sizes $N=6,8,\dots ,20$ ($N$ is the number of spins constituting a cluster). For that purpose, we develop an off-diagonal version of Novotny’s method to adopt the off-diagonal (quantum-mechanical $XY$) interaction. Moreover, in order to improve the finite-size-scaling behavior, we tune the coupling-constant parameters to a scale-invariant point. As a result, we estimate the critical indices as $\nu =0.675\left(20\right)$ and $\gamma ∕\nu =1.97\left(10\right)$.

The Molière theory of multiple Coulomb scattering is improved to take account of ionization loss by applying a differential formulation of the theory. Distributions for the deflection angle $\vec{\theta }$, as well as for any linear combination between $\vec{\theta }$ and the lateral displacement $\vec{r}$, under the ionization process are derived by a series expansion with the same universal functions $f^{\left(n\right)}\left(\vartheta \right)$ of Molière, except that the values for both the expansion parameter $B$ and the scale angle ${\theta }_M$ are corrected from those under the fixed-energy process. We find that Goudsmit-Saunderson angular distribution with ionization is also expressed by the same characteristic parameters $B$ and ${\theta }_M$ derived above by the Molière theory. The transport mechanism of Molière process of multiple Coulomb scattering and the stochastic property of Molière series expansion are also investigated and discussed.

We have studied the electrical conductivity in monolayer films of an ionic disk-shaped liquid-crystal molecule, pyridinium tethered with hexaalkoxytriphenylene (PyTp), and its complex with DNA by current-sensing atomic force microscopy (CS-AFM). The pure PyTp and PyTp-DNA complex monolayer films were first formed at the air-water interface and then transferred onto conducting substrates by the Langmuir-Blodgett (LB) technique to study the nanoscale electron transport through these films. The conductive tip of CS-AFM, the LB film, and the metal substrate form a nanoscopic metal-LB film-metal $\left(M\text{−}\mathrm{LB}\text{−}M\right)$ junction. We have measured the current-voltage $\left(I\text{−}V\right)$ characteristics for the $M\text{−}\mathrm{LB}\text{−}M$ junction using CS-AFM and have analyzed the data quantitatively. We find that the $I\text{−}V$ curves fit well to the Fowler-Nordheim (FN) model, suggesting electron tunneling to be a possible mechanism for electron transport in our system. Further, analysis of the $I\text{−}V$ curves based on the FN model yields the barrier heights of PyTp-DNA complex and pure PyTp films. Electron transport studies of films of ionic disk-shaped liquid-crystal molecules and their complex with DNA are important from the point of view of their applications in organic electronics.

The effect of surfaces on the stability of smectic-$C^{*}$ $\left(\mathrm{Sm}{C}^{*}\right)$ variant phases is investigated. The results obtained using dielectric spectroscopy by varying the cell thickness show that the temperature ranges of $\mathrm{Sm}{C}_{\alpha }^{*}$, $\mathrm{Sm}{C}_A^{*}(1∕2)$, and $\mathrm{Sm}{C}_A^{*}(1∕3)$ phases decrease with decreasing cell thickness, and the $\mathrm{Sm}{C}_A^{*}(1∕3)$ phase is more stable than the $\mathrm{Sm}{C}_A^{*}(1∕2)$ phase. The relative stability of any phase is found to be due to its large polar anchoring strength and low free energy compared to other phases in a cell. Experimental results are found to agree with the theory.

We investigated the structural features of micelles formed by the self-association of the pentablock copolymer poly[$N,N$-(diethyl amino)ethyl methacrylate]-block-poly(ethylene oxide)-block-poly(propylene oxide)-block-poly(ethyleneoxide)-block-poly[$N,N$-(diethylamino)ethyl methacrylate] (PDEAEM-PEO-PPO-PEO-PDEAEM) in aqueous solutions by using small-angle neutron scattering SANS. The pentablock copolymer solutions exhibit micellar and gel phases in response to changes in both the temperature and pH by virtue of (1) the lower critical solution temperature of the PPO blocks and (2) the polyelectrolyte character of the pendant PDEAEM blocks. Two modeling schemes were employed to describe the SANS data of semidilute copolymer solutions at higher temperature as they contain interacting charged micelles at $p\mathrm{H}<7.5$ and interacting neutral micelles at higher pH. We have elucidated the structures of the micelles in terms of size, shape, polydispersity, association number, number density, and surface charge. At low pH the charged spherical micelles are less packed with the copolymers presumably due to the electrostatic repulsion between the charged pendant groups. On the other hand, at higher pH the hydrophobic character of the neutral pendant groups enable them to sequester within the micelle core along with the PPO, thus increasing the number density and the core size of the spherical micelles. At higher copolymer concentration reversible thermoresponsive sol-gel transitions were observed at all pH conditions and the rheological behavior of the gels nicely correlates with different organization of micelles with different shapes.

The $k$-core percolation on the Bethe lattice has been proposed as a simple model of the jamming transition because of its hybrid first-order–second-order nature. We investigate numerically $k$-core percolation on the four-dimensional regular lattice. For $k=4$, the presence of a discontinuous transition is clearly established but its nature is strictly first-order. In particular, the $k$-core density displays no singular behavior before the jump and its correlation length remains finite. For $k=3$, the transition is continuous.

We show that a scaling law exists for the near-resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasiclassical phase-space representation of the quantum system with noise allows a new scaling law to be deduced. The scaling law and associated stability are confirmed by comparison with quantum simulations and experimental data.

We consider a stochastic heat conduction model for solids composed of $N$ interacting atoms. The system is in contact with two heat baths at different temperatures $T_{\mathcal{l}}$ and $T_r$. The bulk dynamics conserves two quantities: the energy and the deformation between atoms. If $T_{\mathcal{l}}\ne T_r$, a heat flux occurs in the system. For large $N$, the system adopts a linear temperature profile between $T_{\mathcal{l}}$ and $T_r$. We establish the hydrodynamic limit for the two conserved quantities. We introduce the fluctuation field of the energy and of the deformation in the nonequilibrium steady state. As $N$ goes to infinity, we show that this field converges to a Gaussian field and we compute the limiting covariance matrix. The main contribution of the paper is the study of large deviations for the temperature profile in the nonequilibrium stationary state. A variational formula for the rate function is derived following the recent macroscopic fluctuation theory of Bertini et al. [J. Stat. Phys. 107, 635 (2002); Math. Phys., Anal. Geom. 6, 231 (2003); J. Stat. Phys. 121, 843 (2005)].