We compare photoinduced reorientation of homeotropic and planar aligned nematic liquid crystal 4-pentyl-4-cyanobiphenyl (5CB) doped with trace amounts of azo-dye disperse orange 3 (DO3) by studying the optical nonlinearities of the sample. Theoretical and experimental analyses confirm the proposal that the trans and cis isomers can be treated as independent contributors to the enhancement factor. Dynamic measurements indicate three contributions to photoinduced optical nonlinearities, two of which are isotropic and a third corresponding director reorientation. We also measure a large negative enhancement factor for the trans isomer and a positive enhancement factor for the cis isomer, consistent with previous measurements. The latter indicates that the mean field for the cis isomer is very small. Planar aligned samples demonstrate zenithal gliding whereas homeotropic samples do not. In addition, steady-state and dynamic measurements indicate loss of liquid crystal order associated with absorption as well as possible out-of-plane reorientation.

We introduce a scheme to obtain key logic-gate structures, using synchronization of nonlinear systems. We demonstrate the idea explicitly by numerics and experiments on nonlinear circuits. A significant feature of this scheme is that a single nonlinear drive-response circuit can be used to flexibly yield the different logic gates, and switch logic behavior by small changes in the parameter of the response system; so the response system can act as a “logic output controller.” Thus this scheme may help to construct dynamic general-purpose computational hardware with reconfigurable abilities.

We propose a basic mechanism for isochronal synchrony and communication with mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators, mutually coupled with a propagation delay, synchronize isochronally when both are symmetrically driven by a third Ikeda oscillator. This synchronous operation, unstable in the two delay-coupled oscillators alone, facilitates simultaneous, bidirectional communication of messages with chaotic carrier wave forms. This approach to combine both bidirectional and unidirectional coupling represents an application of generalized synchronization using a mediating drive signal for a spatially distributed and internally synchronized multicomponent system.

Linear stability analysis of a fully developed two-dimensional periodic steady flow in a spatially modulated symmetric channel is investigated numerically. Both walls are sinusoidally modulated. The modulation amplitude is assumed to be small. The base steady flow is calculated using a regular perturbation expansion of the flow field coupled to a variable-step finite-difference scheme. The disturbance flow equations are derived within the framework of Floquet theory and solved using a two-point boundary value method. The implemented procedure is simple, direct, and very efficient. The accuracy of this method is established. The influence of geometric parameters on the threshold for the onset of instability is systematically investigated. It is established that the critical Reynolds number for the onset of hydrodynamic instability decreases as the wall modulation amplitude or wave number increases. Modulated channel flow is characterized by the formation of a recirculation region or vortices beneath the modulation crest as the Reynolds number exceeds a certain critical threshold. The relation between the thresholds for the onset of instability and vortex flow is examined over a wide range of geometric parameters. Vortex flow effects on the conditions for the onset of instability are systematically investigated. The parameter regime of stable vortex flow is established. It is found that the parameter regime of stable vortex flow increases significantly with the wall modulation wave number for small wave numbers. This increase become less pronounced as the wave number is further increased.

We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: ${\partial }_x\tilde{G}\left(H_x\right)$. We find that the stability of steady states depends on $dv∕dq$, the derivative of the interface velocity on the wave vector $q$ of the steady state. If the standard nonlinearity vanishes, coarsening is possible, in principle, only if $\tilde{G}$ is an odd function of $H_x$. In this case, the equation falls in the category of the generalized Cahn-Hilliard equation, whose dynamical behavior was recently studied by the same authors. Alternatively, if $\tilde{G}$ is an even function of $H_x$, we show that steady-state solutions are not permissible.

Three fluid-borne colloidal spheres circulating around a ringlike optical vortex trap have been predicted to undergo periodic collective motion due to their hydrodynamic coupling. In fact, the quenched disorder in an experimentally projected optical vortex drives a transition to a dynamical state characterized by power-law divergence of phase-space trajectories and collective fluctuations characterized by noninteger exponents. The observed relationship between scaling in the microscopic trajectories and macroscopic collective fluctuations is consistent with predictions for the onset of weak chaos within the experimentally accessible time window.

This paper develops the theoretical foundations for the ability of a control field to cooperate with noise in the manipulation of quantum dynamics. The noise enters as run-to-run variations in the control amplitudes, phases, and frequencies with the observation being an ensemble average over many runs as is commonly done in the laboratory. Weak field perturbation theory is developed to show that noise in the amplitude and frequency components of the control field can enhance the process of population transfer in a multilevel ladder system. The analytical results in this paper support the point that under suitable conditions an optimal field can cooperate with noise to improve the control outcome.

In this study, the relaxation dynamics of iron-group dihalides by making use of spin-$1∕2$ metamagnetic Ising model has been formulated by the method of thermodynamics of irreversible processes. Using a molecular field approximation for the magnetic Gibbs energy, the magnetic Gibbs energy production in the irreversible process is calculated and time derivatives of the order parameters are treated as fluxes conjugate to their appropriate generalized forces in the sense of Onsager’s theory of irreversible thermodynamics. Two relaxation times are calculated and their temperature variances are examined. Moreover, the phase transition behaviors of the relaxation times are also obtained anaytically via the critical exponents.

The simplest bounded potential is that of penetrable spheres, which takes a positive finite value $ϵ$ if the two spheres are overlapped, being zero otherwise. In this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of $T^{*}\equiv k_{B}T∕ϵ$ (where $k_B$ is the Boltzmann constant and $T$ is the temperature) for penetrable sphere fluids. The expressions are exact, except for the function represented by an elementary diagram inside the core, which is approximated by a polynomial form in excellent agreement with accurate results obtained by Monte Carlo integration. Comparison with the hypernetted-chain (HNC) and Percus-Yevick (PY) theories shows that the latter is better than the former for $T^{*}\lesssim 1$ only. However, even at zero temperature (hard sphere limit), the PY solution is not accurate inside the overlapping region, where no practical cancellation of the neglected diagrams takes place. The exact fourth virial coefficient is positive for $T^{*}\lesssim 0.73$, reaches a minimum negative value at $T^{*}\approx 1.1$, and then goes to zero from below as $1∕T^{*4}$ for high temperatures. These features are captured qualitatively, but not quantitatively, by the HNC and PY predictions. In addition, in both theories the compressibility route is the best one for $T^{*}\lesssim 0.7$, while the virial route is preferable if $T^{*}\gtrsim 0.7$.

Using synchrotron x-ray diffraction, we have determined the ensemble-averaged density profile of colloidal fluids within confining channels of different widths. We observe an oscillatory ordering-disordering behavior of the colloidal particles as a function of the channel width, while the colloidal solution remains in the liquid state. This phenomenon has been suggested by surface force studies of hard-sphere fluids and also theoretically predicted, but here we see it by direct measurements of the structure for comparable systems.

A detailed x-ray scattering and high-resolution ac calorimetric study has been carried out near the smectic-$A$ to chiral smectic-$C$ phase transition of liquid-crystal compounds 4-(2-methyl butyl) phenyl 4-$n$-octylbiphenyl-4-carboxylate (CE8) and $p$-($n$-decyloxy) benzylidene-$p$-amino-(2-methylbutyl) cinnamate (DOBAMBC) confined in hydrophilic and hydrophobic aerosil nanoparticle networks. The character of the transition, which is mean field near a tricritical point in bulk, is changed dramatically with an increase of aerosil-induced disorder. X-ray measurements revealed pretransitional behavior and compression of the smectic layers, phenomena that are strongly pronounced in high aerosil concentrations. A theoretical model that takes into account the interplay of relevant mechanisms is proposed to explain the observed phenomena. The effect of chirality on the interaction of liquid crystals with aerosils is discussed.

This paper deals with the stability and the dynamics of a harmonically excited elastic perfectly plastic asymmetrical oscillator. The hysteretical system is written as a nonsmooth, forced autonomous system. The dimension of the phase space can be reduced using adapted variables. It is shown that asymmetry of boundary conditions (forcing term) and material asymmetry lead to an equivalent system for this simple structural case. The forced vibration of such an oscillator is treated by a numerical approach by using time locating techniques. Stability of the limit cycles is analytically investigated with a perturbation approach. The boundary between elastoplastic shakedown and dynamic ratcheting is given in closed form. It is shown that the divergence rate is strongly correlated to the internal asymmetry of the oscillator.

We investigate the evolution of localized blobs of swirling or buoyant fluid in an infinite, inviscid, electrically conducting fluid. We consider the three cases of a strong imposed magnetic field, a weak imposed magnetic field, and no magnetic field. For a swirling blob in the absence of a magnetic field, we find, in line with others, that the blob bursts radially outward under the action of the centrifugal force, forming a thin annular vortex sheet. A simple model of this process predicts that the vortex sheet thins exponentially fast and that it moves radially outward with constant velocity. These predictions are verified by high-resolution numerical simulations. When an intense magnetic field is applied, this phenomenon is suppressed, with the energy and angular momentum of the blob now diffusing axially along the magnetic field lines, converting the blob into a columnar structure. For modest or weak magnetic fields, there are elements of both types of behavior, with the radial bursting dominating over axial diffusion for weak fields. However, even when the magnetic field is very weak, the flow structure is quite distinct to that of the nonmagnetic case. In particular, a small but finite magnetic field places a lower bound on the thickness of the annular vortex sheet and produces an annulus of counter-rotating fluid that surrounds the vortex core. The behavior of the buoyant blob is similar. In the absence of a magnetic field, it rapidly develops the mushroomlike shape of a thermal, with a thin vortex sheet at the top and sides of the mushroom. Again, a simple model of this process predicts that the vortex sheet at the top of the thermal thins exponentially fast and rises with constant velocity. These predictions are consistent with earlier numerical simulations. Curiously, however, it is shown that the net vertical momentum associated with the blob increases linearly in time, despite the fact that the vertical velocity at the front of the thermal is constant. As with the swirling blob, an imposed magnetic field inhibits the formation of a vortex sheet. A strong magnetic field completely suppresses the phenomenon, replacing it with an axial diffusion of momentum, while a weak magnetic field allows the sheet to form, but places a lower bound on its thickness. The magnetic field does not, however, change the net vertical momentum of the blob, which always increases linearly with time.

As classical imaging fails with diffusive media, one way to image a multiple-scattering medium is to achieve local measurements of the dynamic transport properties of a wave undergoing diffusion. This paper presents a method to obtain local measurements of the diffusion constant $D$ in a multiple-scattering medium. The experimental setup consists in an array of programmable transducers placed in front of the multiple-scattering medium to be imaged. By achieving Gaussian beamforming both at emission and reception, an array of virtual sources and receivers located in the near field is constructed. The time evolution of the incoherent component of the intensity backscattered on this virtual array is shown to represent directly the growth of the diffusive halo as $\sqrt{Dt}$. A matrix treatment is proposed to separate the incoherent intensity from the coherent backscattering peak. Once the incoherent contribution is isolated, a local measurement of the diffusion constant is possible. The technique is applied to image the long-scale variations of $D$ in a random-scattering sample made of two parts with a different concentration of cylindrical scatterers. This experimental result is obtained with ultrasonic waves around $3\mathrm{MHz}$. It illustrates the possibility of imaging diffusive media from local measurements of the diffusion constant, based on coherent Gaussian beamforming and a matrix “antisymmetrization,” which creates a virtual antireciprocity.

An investigation of the spatiotemporal stability of hollow jets in unbounded coflowing liquids, using a general dispersion relation previously derived, shows them to be absolutely unstable for all physical values of the Reynolds and Weber numbers. The roots of the symmetry breakdown with respect to the liquid jet case, and the validity of asymptotic models are here studied in detail. Asymptotic analyses for low and high Reynolds numbers are provided, showing that old and well-established limiting dispersion relations [J. W. S. Rayleigh, The Theory of Sound (Dover, New York, 1945); S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961)] should be used with caution. In the creeping flow limit, the analysis shows that, if the hollow jet is filled with any finite density and viscosity fluid, a steady jet could be made arbitrarily small (compatible with the continuum hypothesis) if the coflowing liquid moves faster than a critical velocity.

The shapes of flat pebbles may be characterized in terms of the statistical distribution of curvatures measured along their contours. We illustrate this method for clay pebbles eroded in a controlled laboratory apparatus, and also for naturally occurring rip-up clasts formed and eroded in the Mont St.-Michel bay. We find that the curvature distribution allows finer discrimination than traditional measures of aspect ratios. Furthermore, it connects to the microscopic action of erosion processes that are typically faster at protruding regions of high curvature. We discuss in detail how the curvature may be reliably deduced from digital photographs.

The electrostrictive effects in anisotropic tissue, such as muscle, are interesting and qualitatively different than in an isotropic material. A striking feature in anisotropic tissue is the presence of a charge distribution, which is absent in isotropic tissue. This charge interacts with the electric field to give rise to body forces that deform the tissue. We develop an electromechanical model to investigate how anisotropic tissue deforms due to an electric field, and find analytical solutions for the pressure and displacement. The distribution of the pressure and displacement are complex and dependent on the boundary conditions. The effects of electrostriction are small, but comparable in size to pressures and displacements in other imaging modalities that utilize similar mechanical effects.

The clustered occurrence of earthquakes is viewed as an intermittent phenomenon, interpreting the clusters of events as chaotic bursts combined to the Poissonian occurrence of background seismicity. In particular, we suggest that it can be interpreted as an example of on-off intermittency. This kind of intermittency is parameter driven and exhibits certain universal statistical properties. The study of a Californian catalogue allows to interpret earthquake occurrence as an on-off intermittent phenomenon. Our results suggest the existence of a branching mechanism in earthquake occurrence well explained by epidemic type models.

In this study an experimental investigation of baroclinic waves in air in a differentially heated rotating annulus is presented. Air has a Prandtl number of 0.707, which falls within a previously unexplored region of parameter space for baroclinic instability. The flow regimes encountered include steady waves, periodic amplitude vacillations, modulated amplitude vacillations, and either monochromatic or mixed wave number weak waves, the latter being characterized by having amplitudes less than 5% of the applied temperature contrast. The distribution of these flow regimes in parameter space are presented in a regime diagram. It was found that the progression of transitions between different regimes is, as predicted by recent numerical modeling results, in the opposite sense to that usually found in experiments with high Prandtl number liquids. No hysteresis in the flow type, with respect to variations in the rotation rate, was found in this investigation.

To analyze the motion of gravity current, a common approach is to solve the hyperbolic shallow water equations (SWE) together with the boundary conditions at both the current source at far upstream (i.e., the constrained condition) and the current front at downstream margin (i.e., the front condition). The use of the front condition is aimed to take the resistance from the ambient fluid into account, because the ambient resistance is absent in the SWE. In the present study, we rederive the SWE by taking the ambient resistance into account and end up with the so-called modified shallow water equation (MSWE). In the MSWE the ambient resistance is given by a nonlinear term, so that the use of the front condition becomes unnecessary. These highly nonlinear equations are approximated by the perturbation expansion to the leading order, and the resultant singular perturbation equations are solved analytically by the inner-outer expansion approach. Results show that for constant-flux and constant-volume gravity currents, their outer solutions are exactly the same as the solutions obtained by solving the SWE with the front condition. The inner solutions give both the profile and the velocity of the current head and lead to the recovery of the front condition in a more general form. The combination of inner and outer solutions gives a composite solution for the whole current, which was called by Benjamin [J. Fluid Mech. 31, 209 (1968)] a “formidably complicated” task. To take the turbulent drag on the current into account, we introduce the semiempirical Chezy drag term into the MSWE and results agreed with experimental data very well. The MSWE can be extended for three-dimensional gravity currents, while the resultant equations become so complicated that analytical solutions might not be available.