For a large class of nonlinear stochastic processes with pure multiplicative fluctuations the corresponding time-dependent Fokker-Planck-equation is solved exactly by analytic methods. A universal eigenvalue spectrum and set eigenfunctions are obtained in closed form. The consists discrete as well continuous part. To emphasize significance model proposed for description more-general authors investigate its stability respect to inclusion weak additive fluctuations. discussion differences...

We discuss the interaction of localized solutions as they arise for subcritical bifurcation to traveling waves. find that a large parameter range can interact so emerge after collision with size and shape unchanged compared well before collision. The mechanism this behavior, which is unusual strongly dissipative system, qualitatively different from associated solitons completely integrable systems. In accord we other values counterpropagating annihilate.

We discuss time-dependent spatially localized solutions of the quintic complex Ginzburg-Landau equation applicable near a weakly inverted bifurcation to traveling waves. find that there are---in addition stationary pulses reported previously---stable are periodic, quasiperiodic, or even chaotic in time. An intuitive picture for stability these is presented and novelty phenomena comparison arising exactly integrable systems emphasized.

It is shown that for systems developing stationary periodic patterns there exists at most one stable wavelength state if a supercritical region connected to subcritical by the imposition of slow spatial variation external parameters. In nonpotential selected depends on particular combination parameters vary but not (slow) rate variation. Suitable parameter variations force system into dynamic state.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSymmetry and defects in the CM phase of polymeric liquid crystalsHelmut R. Brand, P. E. Cladis, Harald PleinerCite this: Macromolecules 1992, 25, 26, 7223–7226Publication Date (Print):December 1, 1992Publication History Published online1 May 2002Published inissue 1 December 1992https://pubs.acs.org/doi/10.1021/ma00052a025https://doi.org/10.1021/ma00052a025research-articleACS PublicationsRequest reuse permissionsArticle...

An amplitude equation is derived for thermal convection in a binary fluid mixture porous medium and bulk, the vicinity of intersection point lines stationary oscillatory instabilities. Slow spatial modulations are included near this codimension-2 bifurcation. The experimental realizability mixtures discussed with use data specific systems such as alcohol-water normal-fluid $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures. Analogies drawn to other physical which easily accessible experiment,...

Abstract The influence of the spacer length was investigated for correlation between network anisotropy and order parameter mesogenic units. Stress‐optical measurements show that a closer coupling moieties to polymer backbone results in an increased interaction mechanical field groups. phase transformation temperature T NI stress σ is represented using both, our experimental derivation from Landau‐de Gennes (LDG) formulation. From results, it possible, first time, estimate cross‐coupling...

The nonlinear hydrodynamic equations for biaxial discotics with two broken translational symmetries (which have been identified experimentally very recently) are presented and the structure of excitations is considered. For rotational symmetries, owing to existence preferred axes, gradient free energy, representing a generalization Frank energy nematic liquid crystals, given derived. As striking result set three commutator-type relations reflecting anholomomity variables characterizing found...

Measurements of the correlation function below electrohydrodynamic instability in a thin layer nematic liquid crystal reveal fluctuating convection patches. Their amplitude A\ifmmode\bar\else\textasciimacron\fi{}, length \ensuremath{\xi}, and time \ensuremath{\tau} can be desribed by stochastic mean-field model. The agrees with expected fluctuations due to thermal noise.

Abstract The mechanical response of a smectic A liquid single crystal elastomer (LSCE) to stress applied perpendicular and parallel the layers is described. We find that static modulus two orders magnitude larger than layer direction, where latter completely due crosslinking. Macroscopically width LSCE does not shrink when while length film increases by factor 2 thus demonstrating in‐plane fluidity layering.

Abstract We describe the preparation and characterization of uniaxial magnetic gels. Fibril formation embedded particles generates easily detectable optical anisotropies. A finite magnetization is frozen‐in leads to a ferromagnetic‐like response in small homogeneous external fields. present, for first time, frequency dependent measurements shear modulus G ′. Despite their anisotropy, gels are mechanically isotropic. The time‐dependent ′ ferrogel parallel orientation field 200 mT. magnified image

We study the influence of noise on spatially localized, temporally regular states (stationary, one frequency, two frequencies) in regime anomalous dispersion for cubic-quintic complex Ginzburg-Landau equation as a function bifurcation parameter. find that fairly small strength $\ensuremath{\eta}$ is sufficient to reach chaotic state with exploding dissipative solitons. That means can induce explosions over large range values parameter $\ensuremath{\mu}$. Three different routes chaos solitons...

We present the derivation of macroscopic equations for uniaxial ferrogels. In addition to usual hydrodynamic variables gels we introduce magnetization and relative rotations between network as variables. The introduced here a system with magnetic degrees freedom are analog by de Gennes in nematic elastomers director respect elastomeric network. These give rise large number static well dynamic effects due their coupling magnetization, strain field, density linear momentum. A few them...

Abstract We present the results of our investigations on electrooptic properties smectic O and O* phases m7tac (1-methylheptyl terephthalylidene-bis-4-aminocinnamate). At low voltages, we observed striking electrochromic effects and, in at high a field induced phase transition. Freely suspended thick films are weakly biaxial. A framework is proposed to account for observations.

We experimentally investigate, in detail, electromechanical effects liquid-crystal elastomers (LCEs) previously swollen with low-molecular-weight liquid crystals (LMWLCs). Both polydomain (POLY) and monodomain (MONO) LCEs were studied. used a well known LMWLC, 4-n-pentyl-4-cyanobiphenyl (5CB) as solvent. After swelling POLY MONO (LSCE) 5CB, shape changes measured by recording the displacement of edge LCE at different voltages, V, temperature. With 100 microm distance between electrodes,...