The backward jump modification of the continuous-time random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a high-frequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bid-ask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market high-frequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le Chatelier-Braun principle of contrariness.

Transparent biological tissues can be precisely dissected with ultrafast lasers using optical breakdown in the tight focal zone. Typically, tissues are cut by sequential application of pulses, each of which produces a single cavitation bubble. We investigate the hydrodynamic interactions between simultaneous cavitation bubbles originating from multiple laser foci. Simultaneous expansion and collapse of cavitation bubbles can enhance the cutting efficiency, by increasing the resulting deformations in tissue, and the associated rupture zone. An analytical model of the flow induced by the bubbles is presented and experimentally verified. The threshold strain of the material rupture is measured in a model tissue. Using the computational model and the experimental value of the threshold strain one can compute the shape of the rupture zone in tissue resulting from application of multiple bubbles. With the threshold strain of 0.7 two simultaneous bubbles produce a continuous cut when applied at the distance 1.35 times greater than that required in sequential approach. Simultaneous focusing of the laser in multiple spots along the line of intended cut can extend this ratio to 1.7. Counterpropagating jets forming during collapse of two bubbles in materials with low viscosity can further extend the cutting zone—up to approximately a factor of 1.5.

We study the Lagrangian mechanism of the fluctuation dynamo at zero Prandtl number and infinite magnetic Reynolds number, in the Kazantsev-Kraichnan model of white-noise advection. With a rough velocity field corresponding to a turbulent inertial range, flux freezing holds only in a stochastic sense. We show that field lines arriving to the same point which were initially separated by many resistive lengths are important to the dynamo. Magnetic vectors of the seed field that point parallel to the initial separation vector arrive anticorrelated and produce an “antidynamo” effect. We also study the problem of “magnetic induction” of a spatially uniform seed field. We find no essential distinction between this process and fluctuation dynamo, both producing the same growth rates and small-scale magnetic correlations. In the regime of very rough velocity fields where fluctuation dynamo fails, we obtain the induced magnetic energy spectra. We use these results to evaluate theories proposed for magnetic spectra in laboratory experiments of turbulent induction.

We investigate the possibility of exploiting the speed and low noise features of Josephson junctions for detecting sinusoidal signals masked by Gaussian noise. We show that the escape time from the static locked state of a Josephson junction is very sensitive to a small periodic signal embedded in the noise, and therefore the analysis of the escape times can be employed to reveal the presence of the sinusoidal component. We propose and characterize two detection strategies: in the first, the initial phase is supposedly unknown (incoherent strategy), while in the second, the signal phase remains unknown but is fixed (coherent strategy). Our proposals are both suboptimal, with the linear filter being the optimal detection strategy, but they present some remarkable features, such as resonant activation, that make detection through Josephson junctions appealing in some special cases.

We propose a modified version of the Tomlinson model for static friction between two chains of beads. We introduce disorder in terms of vacancies in the chain, and distribute the remaining beads in a scale invariant way. For this we utilize a generalized random Cantor set. We relate the static friction force to the overlap distribution of the chains, and discuss how the distribution of the static friction force depends on the distribution of the remaining beads. For the random Cantor set we find a scaled distribution which is independent on the generation of the set.

We study optical, structural, and surface anchoring properties of thermotropic nematic bent-core material A131. The focus is on the features associated with orientational order as the material has been reported to exhibit not only the usual uniaxial nematic but also the biaxial nematic phase. We demonstrate that A131 experiences a surface anchoring transition from a perpendicular to tilted alignment when the temperature decreases. The features of the tilted state are consistent with surface-induced birefringence associated with smectic layering near the surface and a molecular tilt that changes along the normal to the substrates. The surface-induced birefringence is reduced to zero by a modest electric field that establishes a uniform uniaxial nematic state. Both refractive and absorptive optical properties of A131 are consistent with the uniaxial order. We found no evidence of the “polycrystalline” biaxial behavior in the cells placed in crossed electric and magnetic fields. We observe stable topological point defects (boojums and hedgehogs) and nonsingular “escaped” disclinations pertinent only to the uniaxial order. Finally, freely suspended films of A131 show uniaxial nematic and smectic textures; a decrease in the film thickness expands the temperature range of stability of smectic textures, supporting the idea of surface-induced smectic layering. Our conclusion is that A131 features only a uniaxial nematic phase and that the apparent biaxiality is caused by subtle surface effects rather than by the bulk biaxial phase.

The swimming behavior of self-propelled microorganisms is studied by particle-based mesoscale simulations. The simulation technique includes both hydrodynamics and thermal fluctuations that are both essential for the dynamics of microswimmers. The swimmers are modeled as squirmers, i.e., spherical objects with a prescribed tangential surface velocity, where the focus of thrust generation can be tuned from pushers to pullers. For passive squirmers (colloids), we show that the velocity autocorrelation function agrees quantitatively with the Boussinesq approximation. Single active squirmers show a persistent random-walk behavior, determined by forward motion, lateral diffusion, and orientational fluctuations, in agreement with theoretical predictions. For pairs of squirmers, which are initially swimming in parallel, we find an attraction for pushers and a repulsion for pullers, as expected. The hydrodynamic force between squirmer pairs is calculated as a function of the center-to-center distances $d_{cm}$ and is found to be consistent with a logarithmic distance dependence for $d_{cm}$ less than about two sphere diameters; here, the force is considerably stronger than expected from the far-field expansion. The dependence of the force strength on the asymmetry of the polar surface velocity is obtained. During the collision process, thermal fluctuations turn out to be very important and to strongly affect the postcollision velocity directions of both squirmers.

A generic model of complex formation in small volumes was studied under the assumption of perfect mixing. Particles A react in clusters, and each reaction converts $k$ A particles into a P particle. The back reaction is also allowed. The equilibrium state of the model is solved exactly. Fluctuations in product particle number are reduced by increasing the degree of cooperativity $k$. Three qualitatively distinct reactant fluctuation characteristics emerge.

We address the slow generation of crack networks as a problem of pattern formation. Issues of pattern selection and the associated statistical properties were considered by means of a detailed theoretical analysis and simulations of a discrete spring-block model. Developed after observations in desiccation experiments, the model describes the nucleation and propagation of cracks in a layer in contact with a frictional substrate. Competition between stress concentration at crack tips and pinning effect by friction leads to a cellular pattern. We characterized the events prior to cracking by a growth of correlation in the stress field, and those during cracking by progressive damages manifested in the number of broken bonds and energy releases. Qualitatively distinct regimes were shown to correspond to different stages of development. A host of scaling behaviors in measurable quantities were derived and verified. In particular, consistent with experiments, fragment area was found to be quadratic in the layer thickness and be smaller with increasing friction, which explains why morphologically similar patterns may occur over a diverse length scales.

Inviscid swirling flows are modeled, for analytical studies, using axisymmetric azimuthal, $V\left(r\right)$, and axial, $W\left(r\right)$, velocity profiles ($r$ is the distance from the axis). The asymptotic analysis procedure (large wave numbers, $k$ axial and $m$ azimuthal) developed by Leibovich and Stewartson [J. Fluid Mech. 126, 335 (1983)], and used by many authors, breaks down if $k{W}^{\prime }\left(r\right)+m{\Omega }^{\prime }\left(r\right)\ne 0,\forall r$ or if $k{W}^{\prime }\left(r\right)+m{\Omega }^{\prime }\left(r\right)=0,\forall r$, $\Omega =V/r$. This latter case occurs if $W$ is constant with $m=0$, if $\Omega$ is constant with $k=0$, or if both $W$ and $\Omega$ are constant with arbitrary wave-number vector. These particular cases are considered by Leblanc and LeDuc [J. Fluid Mech. 537, 433 (2005)]. Thus, the case where $W$ and $\Omega$ both vary and the Leibovich and Stewartson asymptotics breaks down remains. It is addressed in the present paper for weak variations of axial and azimuthal velocities. The asymptotic results are checked using numerically computed growth rates of the linearized Euler equations for a family of variable-density Batchelor-like vortices as base flows. Good agreement is found even for low values of $m$ and $k$.

The nonlinear evolution of an interface subject to a parallel shear flow is studied by the vortex sheet model. We perform long-time computations for the vortex sheet in density-stratified fluids by using the point vortex method and investigate late-time dynamics of the Kelvin-Helmholtz instability. We apply an adaptive point insertion procedure and a high-order shock-capturing scheme to the vortex method to handle the nonuniform distribution of point vortices and enhance the resolution. Our adaptive vortex method successfully simulates chaotically distorted interfaces of the Kelvin-Helmholtz instability with fine resolutions. The numerical results show that the Kelvin-Helmholtz instability evolves a secondary instability at a late time, distorting the internal rollup, and eventually develops to a disordered structure.

We propose a simple classical concept of nanodevices working in an absolute negative mobility (ANM) regime: the minimal spatial asymmetry required for ANM to occur is embedded in the geometry of the transported particle, rather than in the channel design. This allows for a tremendous simplification of device engineering, thus paving the way toward practical implementations of ANM. Operating conditions and performance of our model device are investigated, both numerically and analytically.

We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results aim at aiding the proper extraction of information in data-driven analysis.

We study the nature of the phase transition in the fully frustrated simple cubic lattice with the $XY$ spin model. This system is the Villain’s model generalized in three dimensions. The ground state is very particular with a 12-fold degeneracy. Previous studies have shown unusual critical properties. With the powerful Wang-Landau flat-histogram Monte Carlo method, we carry out in this work intensive simulations with very large lattice sizes. We show that the phase transition is clearly of first order, putting an end to the uncertainty which has lasted for more than 20 years.

We investigate the capture of particles in soft porous media. Liquid foam constitutes a model system for such a study, allowing the radii of passage in the pore space to be tuned over several orders of magnitude by adjusting the liquid volume fraction. We show how particle capture is determined by the coupling of interstitial liquid flow and network deformation, and present a simple model of the capture process that shows good agreement with our experimental data.

We investigate experimentally and theoretically the dynamics of paramagnetic microrods anchored to a surface and driven by a precessing magnetic field. We identify two distinct regimes, corresponding to extended domains in the $\left(\omega ,{\theta }_{\text{B}}\right)$ plane, where $\omega$ and ${\theta }_{\text{B}}$ are, respectively, the frequency and inclination of the driving field. At low frequencies, the response of the rod is linear whatever is the inclination of the field, and the rod precesses at $\omega$. However, above a characteristic frequency, two qualitatively different behaviors are distinguished, depending on the inclination ${\theta }_{\text{B}}$. For small inclinations of the magnetic field, the response of the filament remains linear at all frequencies. Conversely, when ${\theta }_{\text{B}}$ exceeds a critical value ${\theta }_{{\text{B}}_{\text{c}}}\sim 55°$, the response becomes nonlinear, and the tip of the rod follows a complex trajectory exhibiting three-dimensional back-and-forth patterns. A minimal model, which neglects both the flexibility of the rod and the hydrodynamic interaction with the surface, correctly captures the main features of both regimes. We thus show that the complex trajectory patterns are chiefly due to the geometrical nonlinearities in the magnetic dipolar coupling. The critical angle is itself set by a purely geometrical criterium, arising from the magnetic nature of the rod. The paper is closed by a generalization of our results to the case of soft filaments.

Second-harmonic generation (SHG) is studied in the magnetically aligned nematic phase of a bent-core liquid crystal (BCN) and compared to similar measurements made on a conventional rodlike (calamitic) nematic compound. The second-harmonic (SH) light detected from both materials is predominantly due to scattering and therefore incoherent. Results on the calamitic are consistent with a polarization induced by ordinary director fluctuations in the nematic phase. However, the SH scattering collected in the BCN exhibits a different temperature and angular dependence. We discuss how these differences could arise from the effects of short-range correlated, smectic-C—type molecular clusters, which have been detected in recent studies on various BCN materials.

In many natural synchronization phenomena, communication between individual elements occurs not directly but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in the environment which in turn are sensed and used for population coordination. Extending this motivation to a general nonlinear dynamical system context, this paper analyzes synchronization phenomena in networks where communication and coupling between nodes are mediated by shared dynamical quantities, typically provided by the nodes’ environment. Our model includes the case when the dynamics of the shared variables themselves cannot be neglected or indeed play a central part. Applications to examples from system biology illustrate the approach.

We present theory and experiments for the force-distance curve $F\left(z_0\right)$ of an atomic force microscope (AFM) tip (radius $R$) indenting a supported fluid bilayer (thickness $2d$). For realistic conditions the force is dominated by the area compressibility modulus ${\kappa }_A$ of the bilayer and, to an excellent approximation, given by $F=\pi {\kappa }_{A}R{z}_0^2/{\left(2d-z_0\right)}^2$. The experimental AFM force curves from coexisting liquid ordered and liquid disordered domains in three-component lipid bilayers are well described by our model, which provides ${\kappa }_A$ in agreement with literature values. The liquid ordered phase has a yieldlike response that we model as due to the breaking of hydrogen bonds.

This paper suggests that reaction-diffusion processes, rather than pure topological rules, are responsible for the emergence of heterogeneous structures of complex chemical reaction networks. In such a network, chemical substances react in each node and diffuse between connected nodes. At the same time, each node is able to sense the difference between its own state and the environmental conditions and can rearrange its neighbors via a local rewiring process so as to eliminate the sensed difference. Then, the network, even originally homogeneous, will develop a heterogeneous structure under certain environmental conditions. Such a resultant heterogeneous network may be disassortative, highly clustering, and small world as well. This implies that the reaction-diffusion equilibrium can be statistically controlled by slightly changing the structure of the underlying network. This structure-control mechanism may be especially useful in the situations where some other macroscopic measurements, such as temperature and pressure, are not allowed to be changed through the process.