One example of a random change of time that transforms a generalized diffusion process into an ordinary one

We propose a random change of time for a class of generalized diffusion processes such that the corresponding stochastic differential equation (with generalized coefficients) is transformed into an ordinary one (its coefficients are some non-generalized functions). It turns out that the latter stochastic differential equation has no property of the (weak) uniqueness of a solution

One class of multidimensional stochastic differential equations having no property of weak uniqueness of a solution

A class of stochastic differential equations in a multidimensional Euclidean space such that the property of a solution to be unique (in a weak sense) fails for it is considered. We present the correct formulation of the corresponding martingale problem and prove the uniqueness of its solution

A uniqueness theorem for the martingale problem describing a diffusion in media with membranes

We formulate a martingale problem that describes a diffusion process in a multidimensional Euclidean space with a membrane located on a given mooth surface and having the properties of skewing and delaying. The theorem on the existence of no more than one solution to the problem is proved

Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve

We investigate pathwise uniqueness for the squared Bessel and Cox-Ingersoll-Ross processes with additional reflection term that is multiplied by some real number strictly between minus one and one. The reflection term is the symmetric local time of the corresponding processes at a deterministic time dependent curve.Comment: Structured introduction and modified Section

Optical and X-ray scattering studies of the electric field-induced orientational order in colloidal suspensions of pigment nanorods

© 2018 Elsevier B.V. Under pulsed or a.c. electric fields, colloidal suspensions of nanorods can show strong electro-optic effects, such as the Kerr effect, with fast response times (a few ms), which makes them good candidates for some commercial applications. For this purpose, suspensions of Pigment red 176 nanorods in dodecane were recently developed and their physical properties have been studied. We report here on the investigation of the orientational order induced by electric fields in isotropic suspensions of pigment nanorods by three different techniques: transient electric birefringence, transient electric dichroism, and in-situ small-angle X-ray scattering under electric field (“Electro-SAXS”). We show that, in spite of the apolar character of the solvent, the Maxwell-Wagner-O'Konski mechanism (i.e. the polarization of the counter-ion cloud around each particle) is responsible for the field-induced alignment of the nanorods. Although the particles are only weakly charged and the dielectric constant of dodecane is low, the pigment nanorods effectively behave as metallic particles in an insulating matrix and reach strong values (S ~0.5) of the induced nematic order parameter at moderate field amplitudes (~1 V/μm). This study confirms the feasibility of using suspensions of Pigment red 176 nanorods in dodecane for electro-optic applications