1,720,961 research outputs found
On the creation of quantized vortex lines in rotating He II
No full textIn this paper we present some hydrodynamical consequences of a previously proposed stochastic model for superfluid4He. We discuss in particular the possibility of time-dependent evolutions which, starting from a rotational initial state, lead to asymptotic stationary solutions where the vorticity is concentrated in singular regions. An example of such asymptotic stationary solutions is the quantized vortex line solution. We also recall the concept of quantum critical slipping velocity and investigate some possible consequences on the spin-up problem and on the creation of systems of vortex lines
Lagrangian variational principle in stochastic mechanics: gauge structure and stability
No full textThe Lagrangian variational principle with the classical action leads, in stochastic mechanics, to Madelung’s fluid equations, if only irrotational velocity fields are allowed, while new dynamical equations arise if rotational velocity fields are also taken into account. The new equations are shown to be equivalent to the (gauge invariant) system of a Schrödinger equation involving a four‐vector potential (A,Φ) and the coupled evolution equation (of magnetohydrodynamical type) for the vector field A. A general energy theorem can be proved and the stability properties of irrotational and rotational solutions investigated
Stochastic mechanics and superfluidity in He4: rotation paradox and transition to turbulence
No full textSelf-consistent hydrodynamical model for He II near absolute zero in the framework of stochastic mechanics
No full textWorking in the framework of stochastic mechanics we propose a simple model, based on the hard-sphere gas approximation, for He II at T=0. The model seems to describe correctly the peculiar hydrodynamical behavior of He II near absolute zero and also provides good estimates for the critical velocities and the kinematic viscosity
Stochastic Quantization for a System of N Identical Interacting Bose Particles
No full textWe apply stochastic quantization to a system of N interacting identical bosons in an external potential Φ, by means of a general stationary-action principle. The collective motion is described in terms of a Markovian diffusion on , with joint density and entangled current velocity field , in principle of non-gradient form, related to one another by the continuity equation. Dynamical equations relax to those of canonical quantization, in some analogy with Parisi–Wu stochastic quantization. Thanks to the identity of particles, the one-particle marginal densities ρ, in the physical space , are all the same and it is possible to give, under mild conditions, a natural definition of the single-particle current velocity, which is related to ρ by the continuity equation in . The motion of single particles in the physical space comes to be described in terms of a non-Markovian three-dimensional diffusion with common density ρ and, at least at dynamical equilibrium, common current velocity v. The three-dimensional drift is perturbed by zero-mean terms depending on the whole configuration of the N-boson interacting system. Finally, we discuss in detail under which conditions the one-particle dynamical equations, which in their general form allow rotational perturbations, can be particularized, up to a change of variables, to the Gross–Pitaevskii equations
Stochastic quantization for a system of N identical Bose particles
No full textWe apply Stochastic Quantization to a system of N interacting identical Bosons in an external potential Phi, by means of a general stationary-action principle. The collective motion is described in terms of a Markovian diffusion on R^(3N), with joint density Rho and entangled current velocity field V, in principle of non-gradient form, related one to the other by the continuity equation. Dynamical equations relax to those of canonical quantization, in some analogy with Parisi-Wu stochastic quantization. Thanks to the identity of particles, the one-particle marginal densities rho, in the physical space R^3, are all the same and it is possible to give, under mild conditions, a natural definition of the single-particle current velocity, which is related to rho by the continuity equation in R^3. The motion of single particles in the physical space comes to be described in terms of a non-Markovian three-dimensional diffusion with common density rho and, at least at dynamical equilibrium, common current velocity v. The three-dimensional drift is perturbed by zero-mean terms depending on the whole configuration of the N-bosons interacting system. Finally we discuss in detail under which conditions the one-particle dynamical equations, which in their general form allow rotational perturbations, can be particularized, up to a change of variables, to Gross-Pitaevskii equations
Addendum to "A stochastic algorithm to compute optimal probabilities in the chaos game": a new convergence criterium
No full textWe propose a new convergence criterion for the stochastic algorithm for the optimization of probabilities (SAOP) described in an earlier paper. The criterion is based on the dissection principle for irreducible finite Markov chain
Cubic nonlinear Schrödinger equation with vorticity
No full textIn this paper, we introduce a new class of nonlinear Schrödinger equations (NLSEs), with an electromagnetic potential (A Φ), both depending on the wavefunction ψ. The scalar potential π depends on |ψ| 2, whereas the vector potential A satisfies the equation of magnetohydrodynamics with coefficient depending on ψ. In Madelung variables, the velocity field comes to be not irrotational in general and we prove that the vorticity induces dissipation, until the dynamical equilibrium is reached. The expression of the rate of dissipation is common to all NLSEs in the class. We show that they are a particular case of the one-particle dynamics out of dynamical equilibrium for a system of N identical interacting Bose particles, as recently described within stochastic quantization by Lagrangian variational principle. The cubic case is discussed in particular. Results of numerical experiments for rotational excitations of the ground state in a finite two-dimensional trap with harmonic potential are reported. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft
Proliferation and Death in a Binary Environment : a Stochastic Model of Cellular Ecosystems
No full textThe activation, growth and death of animal cells are accompanied by changes in the chemical composition of the surrounding environment. Cells and their microscopic environment constitute therefore a cellular ecosystem whose
time-evolution determines processes of interest for either biology (e.g. animal development) and medicine (e.g. tumor spreading, immune response). In this paper, we consider a general stochastic model of the interplay between cells and environmental cellular niches. Niches may be either favourable or unfavourable in sustaining cell activation, growth and death, the state of the niches depending on the state of the cells. Under the hypothesis of random coupling between the state of the environmental niche and the state of the cell, the rescaled model reduces to a set of four non-linear differential equations. The biological meaning of the model is studied and illustrated by fitting experimental data on the growth of multicellular tumor spheroids. A detailed analysis of the stochastic model, of its deterministic
limit, and of normal fluctuations is provided
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