1,378 research outputs found
Problems on electrorheological fluid flows
We develop a model of an electrorheological fluid such that the fluid is
considered as an anisotropic one with the viscosity depending on the second
invariant of the rate of strain tensor, on the module of the vector of electric
field strength, and on the angle between the vectors of velocity and electric
field. We study general problems on the flow of such fluids at nonhomogeneous
mixed boundary conditions, wherein values of velocities and surface forces are
given on different parts of the boundary. We consider the cases where the
viscosity function is continuous and singular, equal to infinity, when the
second invariant of the rate of strain tensor is equal to zero. In the second
case the problem is reduced to a variational inequality. By using the methods
of a fixed point, monotonicity, and compactness, we prove existence results for
the problems under consideration. Some efficient methods for numerical solution
of the problems are examined.Comment: Presented to the journal "Discrete and Continuous Dynamical Systems,
Series
Indirect coupling between spins in semiconductor quantum dots
The optically induced indirect exchange interaction between spins in two
quantum dots is investigated theoretically. We present a microscopic
formulation of the interaction between the localized spin and the itinerant
carriers including the effects of correlation, using a set of canonical
transformations. Correlation effects are found to be of comparable magnitude as
the direct exchange. We give quantitative results for realistic quantum dot
geometries and find the largest couplings for one dimensional systems.Comment: 4 pages, 3 figure
q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant
In this paper we construct a q-analogue of the Legendre transformation, where
q is a matrix of formal variables defining the phase space braidings between
the coordinates and momenta (the extensive and intensive thermodynamic
observables). Our approach is based on an analogy between the semiclassical
wave functions in quantum mechanics and the quasithermodynamic partition
functions in statistical physics. The basic idea is to go from the
q-Hamilton-Jacobi equation in mechanics to the q-Legendre transformation in
thermodynamics. It is shown, that this requires a non-commutative analogue of
the Planck-Boltzmann constants (hbar and k_B) to be introduced back into the
classical formulae. Being applied to statistical physics, this naturally leads
to an idea to go further and to replace the Boltzmann constant with an infinite
collection of generators of the so-called epoch\'e (bracketing) algebra. The
latter is an infinite dimensional noncommutative algebra recently introduced in
our previous work, which can be perceived as an infinite sequence of
"deformations of deformations" of the Weyl algebra. The generators mentioned
are naturally indexed by planar binary leaf-labelled trees in such a way, that
the trees with a single leaf correspond to the observables of the limiting
thermodynamic system
Minimal half-spaces and external representation of tropical polyhedra
We give a characterization of the minimal tropical half-spaces containing a
given tropical polyhedron, from which we derive a counter example showing that
the number of such minimal half-spaces can be infinite, contradicting some
statements which appeared in the tropical literature, and disproving a
conjecture of F. Block and J. Yu. We also establish an analogue of the
Minkowski-Weyl theorem, showing that a tropical polyhedron can be equivalently
represented internally (in terms of extreme points and rays) or externally (in
terms of half-spaces containing it). A canonical external representation of a
polyhedron turns out to be provided by the extreme elements of its tropical
polar. We characterize these extreme elements, showing in particular that they
are determined by support vectors.Comment: 19 pages, 4 figures, example added with a new figure, figures
improved, references update
Present and Future Experiments with Stored Exotic Nuclei at Relativistic Energies
Recent progress is presented from experiments on masses and lifetimes of bare
and few-electron exotic nuclei at GSI.Comment: Proceedings of International Conference on "Frontiers in Nuclear
Structure, Astrophysics and Reactions", Kos, Greece, September 12-17, 200
Influence of the atomic-wall collision elasticity on the coherent population trapping resonance shape
We studied theoretically a coherent population trapping resonance formation
in cylindrical cell without buffer gas irradiated by a narrow laser beam. We
take into account non-zero probabilities of elastic ("specular") and inelastic
("sticking") collision between the atom and the cell wall. We have developed a
theoretical model based on averaging over the random Ramsey pulse sequences of
times that atom spent in and out of the beam. It is shown that the shape of
coherent population trapping resonance line depends on the probability of
elastic collision.Comment: 18 pages, 5 figure
Computing the vertices of tropical polyhedra using directed hypergraphs
We establish a characterization of the vertices of a tropical polyhedron
defined as the intersection of finitely many half-spaces. We show that a point
is a vertex if, and only if, a directed hypergraph, constructed from the
subdifferentials of the active constraints at this point, admits a unique
strongly connected component that is maximal with respect to the reachability
relation (all the other strongly connected components have access to it). This
property can be checked in almost linear-time. This allows us to develop a
tropical analogue of the classical double description method, which computes a
minimal internal representation (in terms of vertices) of a polyhedron defined
externally (by half-spaces or hyperplanes). We provide theoretical worst case
complexity bounds and report extensive experimental tests performed using the
library TPLib, showing that this method outperforms the other existing
approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section
5 (using directed hypergraphs), detailed appendix; v3: major revision of the
article (adding tropical hyperplanes, alternative method by arrangements,
etc); v4: minor revisio
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