Nonlinear electrophoresis of dielectric and metal spheres in a nematic liquid crystal

Electrophoresis is a motion of charged dispersed particles relative to a fluid in a uniform electric field. The effect is widely used to separate macromolecules, to assemble colloidal structures, to transport particles in nano- and micro-fluidic devices and displays. Typically, the fluid is isotropic (for example, water) and the electrophoretic velocity is linearly proportional to the electric field. In linear electrophoresis, only a direct current (DC) field can drive the particles. An alternate current (AC) field is more desirable because it allows one to overcome problems such as electrolysis and absence of steady flows. Here we show that when the electrophoresis is performed in a nematic fluid, the effect becomes strongly non-linear with a velocity component that is quadratic in the applied voltage and has a direction that generally differs from the direction of linear velocity. The new phenomenon is caused by distortions of the LC orientation around the particle that break the fore-aft (or left-right) symmetry. The effect allows one to transport both charged and neutral particles, even when the particles themselves are perfectly symmetric (spherical), thus enabling new approaches in display technologies, colloidal assembly, separation, microfluidic and micromotor applications.Comment: 15 pages, 4 figure

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe

Compressed resolvents and reduction of spectral problems on star graphs

In this paper a two-step reduction method for spectral problems on a star graph with n+1 edges e₀, e₁, .... , eₙ and a self-adjoint matching condition at the central vertex v is established. The first step is a reduction to the problem on the single edge e₀ but with an energy depending boundary condition at v. In the second step, by means of an abstract inverse result for Q-functions, a reduction to a problem on a path graph with two edges e₀, ẽ₁ joined by continuity and Kirchhoff conditions is given. All results are proved for symmetric linear relations in an orthogonal sum of Hilbert spaces. This ensures wide applicability to various different realizations, in particular, to canonical systems and Krein strings which include, as special cases, Dirac systems and Stieltjes strings. Employing two other key inverse results by de Branges and Krein, we answer e.g. the following question: If all differential operators are of one type, when can the reduced system be chosen to consist of two differential operators of the same type