We present a kinetic theory of two-dimensional decaying turbulence in the context of two-body and three-body vortex merging processes. By introducing the equations of motion for two or three vortices in the effective noise due to all the other vortices, we demonstrate analytically that a two-body mechanism becomes inefficient at low vortex density $n\ll 1$. When the more efficient three-body vortex mergings are considered (involving vortices of different signs), we show that $n\sim t^{-\xi }$, with $\xi =1$. We generalize this argument to three-dimensional geostrophic turbulence, finding $\xi =5/4$, in excellent agreement with direct Navier-Stokes simulations [McWilliams et al., J. Fluid Mech. 401, 1 (1999)].

A nonlinear stability theory is adopted to study centrifugal thermal convection in a magnetic-fluid-saturated and differentially heated porous layer placed in a zero-gravity environment. The axis of rotation of the layer is placed within its boundaries that leads to an alternating direction of the centrifugal body force. An analysis through the variational principles is made to find the unconditional and sharp nonlinear limits. The compound matrix method is employed to solve the eigenvalue problems of the nonlinear and corresponding linear theories. The importance of nonlinear theory is established by demonstrating the failure of the linear theory in capturing the physics of the onset of convection.

Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A wavelet-based scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity.

Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries and imposed axial magnetic and electric fields. The thus injected magnetic helicity in the system can be redistributed by magnetic helicity fluxes down the gradient of the local current helicity of the small-scale magnetic field. A weak reversal of the axial magnetic field is found to be a consequence of the magnetic helicity flux in the system. Such fluxes are known to alleviate so-called catastrophic quenching of the $\alpha$ effect in astrophysical applications. A stronger field reversal can be obtained if there is also a significant kinetic $\alpha$ effect. Application to the reversed field pinch in plasma confinement devices is discussed.

The Jarzynski-relation-based free-energy calculation is limited by the very slow convergence of the estimate when dissipation is high. We present two novel perturbation protocols able to significantly improve the quality of the potential of mean force (PMF) calculation by reducing the estimate’s bias without increasing the number of samples. The protocols are directly applicable with both numerical simulations and real-life experiments. The improvement is achieved through the intentional but controlled widening of the distribution of the external work used to perturb a given system. Our protocols can achieve the same accuracy in PMF estimation as the normal constant velocity pulling with less than 10% of the required samples.

A detailed description of the time-step-targeting time evolution method within the density-matrix renormalization-group algorithm is presented. The focus of this publication is on the implementation of the algorithm and its generic application. The case of one-site excitations within a Hubbard model is analyzed as a test for the algorithm, using open chains and two-leg ladder geometries. The accuracy of the procedure in the case of the recently discussed holon-doublon photo excitations of Mott insulators is also analyzed. Performance and parallelization issues are discussed. In addition, the full open-source code is provided as supplementary material.

A simple expression is derived, enabling the calculation of the entropy difference between two microcanonical equilibrium states at different energies in atomistic computer simulations. This expression only requires potential energy samples from molecular dynamics or Monte Carlo simulations at the relevant energies. This presents an alternative to switching methods such as thermodynamic integration or nonequilibrium work relations, as well as flat-histogram random walks, all of which involve sampling in between the relevant states. The method is especially suited for small (nanoscopic) systems such as clusters and proteins, and is applicable to first-principles data directly.

We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained differ from others intuitively proposed and that oscillatory behavior is not possible in this system. We discuss the calculation of correlation functions in stochastic systems with delay, stressing the differences with Markovian processes. The exact results allow us to clarify the interplay between stochasticity and delay.

Creation of electrons or excitons by external fields in a system with initially statistically independent unrelaxed vibrational modes leads to an initial condition term. The contribution of this term in the time convolution generalized master-equation approach is studied in the second order of the perturbation theory in path-integral formalism. The developed approach, applied for the analysis of dynamics in the photosynthetic reaction center, exhibits the key role of the initial condition terms at the primary stage of electron transfer.

The regulatory system of the transcription factor NF-$\kappa$B plays a great role in many cell functions, including inflammatory response. Interestingly, the NF-$\kappa$B system is known to up-regulate production of its own triggering signal—namely, inflammatory cytokines such as TNF, IL-1, and IL-6. In this paper we investigate a previously presented model of the NF-$\kappa$B, which includes both spatial effects and the positive feedback from cytokines. The model exhibits the properties of an excitable medium and has the ability to propagate waves of high cytokine concentration. These waves represent an optimal way of sending an inflammatory signal through the tissue as they create a chemotactic signal able to recruit neutrophils to the site of infection. The simple model displays three qualitatively different states; low stimuli leads to no or very little response. Intermediate stimuli leads to reoccurring waves of high cytokine concentration. Finally, high stimuli leads to a sustained high cytokine concentration, a scenario which is toxic for the tissue cells and corresponds to chronic inflammation. Due to the few variables of the simple model, we are able to perform a phase-space analysis leading to a detailed understanding of the functional form of the model and its limitations. The spatial effects of the model contribute to the robustness of the cytokine wave formation and propagation.

We consider the problem of searching for a node on a labeled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of random graph are proposed with properties particularly amenable to this kind of algorithm. We derive equations for the probability that the search is successful and also study the number of hops required, finding both numerical and analytic evidence of a transition as the number of links is varied.

A secure steganographic communication algorithm based on patterns evolving in a Beddington-de Angelis-type predator-prey model with self- and cross-diffusion is proposed in this paper. Small perturbations of initial states of the system around the state of equilibrium result in the evolution of self-organizing patterns. Small differences between initial perturbations result in slight differences also in the evolving patterns. It is shown that the generation of interpretable target patterns cannot be considered as a secure mean of communication because contours of the secret image can be retrieved from the cover image using statistical techniques if only it represents small perturbations of the initial states of the system. An alternative approach when the cover image represents the self-organizing pattern that has evolved from initial states perturbed using the dot-skeleton representation of the secret image can be considered as a safe visual communication technique protecting both the secret image and communicating parties.

Fish usually bend their bodies into a ‘‘C’’ shape and then beat their tails one or more times to escape from predators (in nature) or stimuli (in experiments). The maneuvering behavior, i.e., the C-shape bending and the return flapping, is called C-start. In this paper, the escaping performance of fishlike C-start motions has been numerically investigated for a flow physics study by the use of a two-dimensional deformable foil bending and stretching quickly. The C-start motions, performed in the quiescent water and based on prescribed deforming modes, are predicted by a numerical method coupling the two-dimensional incompressible Navier-Stokes equations and the deforming body dynamic equations. It has been found earlier that a typical C-start motion consists of (1) a main C-shape bending and (2) a rearward travelling curvature wave which was seldom mentioned in previous studies. In order to reveal the flow control mechanism of the traveling curvature wave in a fish's C-start motion, two kinds of C-start flows with different deforming modes, namely the integrated mode (IM, a C-shape bending plus a travelling curvature wave) and the basic mode (BM, a C-shape bending only) are analyzed and compared in detail. According to the numerical results, it shows that if proper values of the travelling curvature wave parameters are chosen, the foil's escaping maneuverability presented in the IM is much better than that in the BM, i.e. the turn angle and the speed of the center of mass at the end of a C-start in the IM is almost twice as large as those in the BM. Further study shows that the travelling curvature wave not only can enhance the thrust and the centripetal force but also increase the propulsive efficiency. These results suggest that an efficient travelling curvature wave is of great significance in the flow control of a C-start motion. Finally, a parametric study finds that the phase difference between the C-shape bending and the travelling curvature wave (i.e., the initial phase angle in the travelling curvature wave of the deforming model) is a key parameter in the flow control. To achieve the desirable turn angle, escaping speed, and propulsive efficiency in the C-start motions, the initial phase angles must be ranged within specific magnitudes. It is found that for optimum values of the initial phase angle, the foil's flexible deforming process is qualitatively consistent with that of a fish body in nature. The results obtained in this study provide a new physical insight into the understanding of swimming mechanisms of fish's C-start maneuvers.

Numerical and experimental data for the heat transfer as a function of the Rossby number $\text{Ro}$ in turbulent rotating Rayleigh-Bénard convection are presented for the Prandtl number $\text{Pr}=4.38$ and the Rayleigh number $\text{Ra}=2.91\times {10}^8$ up to $\text{Ra}=4.52\times {10}^9$. The aspect ratio $\Gamma \equiv D/L$, where $L$ is the height and $D$ the diameter of the cylindrical sample, is varied between $\Gamma =0.5$ and $2.0$. Without rotation, where the aspect ratio influences the global large-scale circulation, we see a small-aspect-ratio dependence in the Nusselt number for $\text{Ra}=2.91\times {10}^8$. However, for stronger rotation, i.e., $1/\text{Ro}\gg 1/{\text{Ro}}_c$, the heat transport becomes independent of the aspect ratio. We interpret this finding as follows: In the rotating regime the heat is mainly transported by vertically aligned vortices. Since the vertically aligned vortices are local, the aspect ratio has a negligible effect on the heat transport in the rotating regime. Indeed, a detailed analysis of vortex statistics shows that the fraction of the horizontal area that is covered by vortices is independent of the aspect ratio when $1/\text{Ro}\gg 1/{\text{Ro}}_c$. In agreement with the results of Weiss et al. [Phys. Rev. Lett. 105, 224501 (2010)], we find a vortex-depleted area close to the sidewall. Here we show that there is also an area with enhanced vortex concentration next to the vortex-depleted edge region and that the absolute widths of both regions are independent of the aspect ratio.

Using different analytical methods (the quasilinear approach, the path-integral technique, and the tau-relaxation approximation) we develop a comprehensive mean-field theory for a pumping effect of the mean magnetic field in homogeneous nonrotating helical turbulence with imposed large-scale shear. The effective pumping velocity is proportional to the product of $\alpha$ effect and large-scale vorticity associated with the shear, and causes a separation of the toroidal and poloidal components of the mean magnetic field along the direction of the mean vorticity. We also perform direct numerical simulations of sheared turbulence in different ranges of hydrodynamic and magnetic Reynolds numbers and use a kinematic test-field method to determine the effective pumping velocity. The results of the numerical simulations are in agreement with the theoretical predictions.

Using molecular-dynamics simulation, we investigate the fragmentation behavior of droplets after collision with a wall. We demonstrate that the ratio of the impact to the cohesive energy $E_{\mathrm{coh}}$ of the droplet is the key quantity characterizing the droplet fragmentation process. To show this both van der Waals–bonded Ar and N${}_2$ droplets and polar H${}_2$O droplets are studied. If the impact energy per molecule $E<\left(0.35\text{--}0.4\right)E_{\mathrm{coh}}$, the droplet is reflected without fragmenting. Beyond that impact energy fragmentation of the droplet abruptly starts. At $E=E_{\mathrm{coh}}$, the fragmentation process already results in a fine dispersal of the droplet into daughter droplets; the maximum fragment contains only less than 4% of the initial droplet mass and around one-third of the droplet has been shattered into isolated molecules. The disintegration process continuously increases with collision energy. These findings are relevant for the process of droplet fragmentation as used in the method of impact desolvation of electrosprayed microdroplets mass spectrometry.

Knudsen force acting on a heated microbeam adjacent to a cold substrate in a rarefied gas is a mechanical force created by unbalanced thermal gradients. The measured force has its direction pointing towards the side with a lower thermal gradient and its magnitude vanishes in both continuum and free-molecule limits. In our previous study, negative Knudsen forces were discovered at the high Knudsen regime before diminishing in the free-molecule limit. Such a phenomenon was, however, neither observed in experiment [A. Passian et al., Phys. Rev. Lett. 90, 124503 (2003)], nor captured in the latest numerical study [J. Nabeth et al., Phys. Rev. E 83, 066306 (2011)]. In this paper, the existence of such a negative Knudsen force is further confirmed using both numerical simulation and theoretical analysis. The asymptotic order of the Knudsen force near the collisionless limit is analyzed and the analytical expression of its leading term is provided, from which approaches for the enhancement of negative Knudsen forces are proposed. The discovered phenomenon could find its applications in novel mechanisms for pressure sensing and actuation.

In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by “nonlinear tweezers,” as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of a nonlinear trap for dragging allows one to pick up and transfer the relevant structures without grabbing surrounding “radiation.” A stability border for the dragged modes is identified by means of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy stationary modes with a divergent norm, which may be dragged by a nonlinear trap moving at a constant acceleration, are briefly considered too.

To determine the universality class of critical phenomena, we propose a method of statistical inference in the scaling analysis of critical phenomena. The method is based on Bayesian statistics, most specifically, the Gaussian process regression. It assumes only the smoothness of a scaling function, and it does not need a form. We demonstrate this method for the finite-size scaling analysis of the Ising models on square and triangular lattices. Near the critical point, the method is comparable in accuracy to the least-square method. In addition, it works well for data to which we cannot apply the least-square method with a polynomial of low degree. By comparing the data on triangular lattices with the scaling function inferred from the data on square lattices, we confirm the universality of the finite-size scaling function of the two-dimensional Ising model.