2,329 research outputs found
Hybrid Control of a Bioreactor with Quantized Measurements: Extended Version
We consider the problem of global stabilization of an unstable bioreactor
model (e.g. for anaerobic digestion), when the measurements are discrete and in
finite number ("quantized"), with control of the dilution rate. The model is a
differential system with two variables, and the output is the biomass growth.
The measurements define regions in the state space, and they can be perfect or
uncertain (i.e. without or with overlaps). We show that, under appropriate
assumptions, a quantized control may lead to global stabilization: trajectories
have to follow some transitions between the regions, until the final region
where they converge toward the reference equilibrium. On the boundary between
regions, the solutions are defined as a Filippov differential inclusion. If the
assumptions are not fulfilled, sliding modes may appear, and the transition
graphs are not deterministic
Modelling of vorticity, sound and their interaction in two-dimensional superfluids
Vorticity in two-dimensional superfluids is subject to intense research
efforts due to its role in quantum turbulence, dissipation and the BKT phase
transition. Interaction of sound and vortices is of broad importance in
Bose-Einstein condensates and superfluid helium [1-4]. However, both the
modelling of the vortex flow field and of its interaction with sound are
complicated hydrodynamic problems, with analytic solutions only available in
special cases. In this work, we develop methods to compute both the vortex and
sound flow fields in an arbitrary two-dimensional domain. Further, we analyse
the dispersive interaction of vortices with sound modes in a two-dimensional
superfluid and develop a model that quantifies this interaction for any vortex
distribution on any two-dimensional bounded domain, possibly non-simply
connected, exploiting analogies with fluid dynamics of an ideal gas and
electrostatics. As an example application we use this technique to propose an
experiment that should be able to unambiguously detect single circulation
quanta in a helium thin film.Comment: 23 pages, 8 figure
Quantum Phase Slips: from condensed matter to ultracold quantum gases
Quantum phase slips are the primary excitations in one-dimensional
superfluids and superconductors at low temperatures. They have been well
characterized in most condensed-matter systems, and signatures of their
existence has been recently observed in superfluids based on quantum gases too.
In this review we briefly summarize the main results obtained on the
investigation of phase slips from superconductors to quantum gases. In
particular we focus our attention on recent experimental results of the
dissipation in one-dimensional Bose superfluids flowing along a shallow
periodic potential, which show signatures of quantum phase slips.Comment: 10 pages, 6 figure
Lazy global feedbacks for quantized nonlinear event systems
We consider nonlinear event systems with quantized state information and
design a globally stabilizing controller from which only the minimal required
number of control value changes along the feedback trajectory to a given
initial condition is transmitted to the plant. In addition, we present a
non-optimal heuristic approach which might reduce the number of control value
changes and requires a lower computational effort. The constructions are
illustrated by two numerical examples
Nondemolition Principle of Quantum Measurement Theory
We give an explicit axiomatic formulation of the quantum measurement theory
which is free of the projection postulate. It is based on the generalized
nondemolition principle applicable also to the unsharp, continuous-spectrum and
continuous-in-time observations. The "collapsed state-vector" after the
"objectification" is simply treated as a random vector of the a posteriori
state given by the quantum filtering, i.e., the conditioning of the a priori
induced state on the corresponding reduced algebra. The nonlinear
phenomenological equation of "continuous spontaneous localization" has been
derived from the Schroedinger equation as a case of the quantum filtering
equation for the diffusive nondemolition measurement. The quantum theory of
measurement and filtering suggests also another type of the stochastic equation
for the dynamical theory of continuous reduction, corresponding to the counting
nondemolition measurement, which is more relevant for the quantum experiments.Comment: 23 pages. See also related papers at
http://www.maths.nott.ac.uk/personal/vpb/research/mes_fou.html and
http://www.maths.nott.ac.uk/personal/vpb/research/cau_idy.htm
Magnon-polarons in cubic collinear Antiferromagnets
We present a theoretical study of excitations formed by hybridization between
magnons and phonons - magnon-polarons - in antiferromagnets. We first outline a
general approach to determining which magnon and phonon modes can and cannot
hybridize in a system thereby addressing the qualitative questions concerning
magnon-polaron formation. As a specific and experimentally relevant case, we
study Nickel Oxide quantitatively and find perfect agreement with the
qualitative analysis, thereby highlighting the strength of the former. We find
that there are two distinct features of antiferromagnetic magnon-polarons which
differ from the ferromagnetic ones. First, hybridization between magnons and
the longitudinal phonon modes is expected in many cubic antiferromagnetic
structures. Second, we find that the very existence of certain hybridizations
can be controlled via an external magnetic field, an effect which comes in
addition to the ability to move the magnon modes relative to the phonons modes.Comment: arXiv admin note: text overlap with arXiv:1808.0901
Dynamical Equilibration Across a Quenched Phase Transition in a Trapped Quantum Gas
The formation of an equilibrium quantum state from an uncorrelated thermal
one through the dynamical crossing of a phase transition is a central question
of non-equilibrium many-body physics. During such crossing, the system breaks
its symmetry by establishing numerous uncorrelated regions separated by
spontaneously-generated defects, whose emergence obeys a universal scaling law
with the quench duration. Much less is known about the ensuing re-equilibrating
or "coarse-graining" stage, which is governed by the evolution and interactions
of such defects under system-specific and external constraints. In this work we
perform a detailed numerical characterization of the entire non-equilibrium
process, addressing subtle issues in condensate growth dynamics and
demonstrating the quench-induced decoupling of number and coherence growth
during the re-equilibration process. Our unique visualizations not only
reproduce experimental measurements in the relevant regimes, but also provide
valuable information in currently experimentally-inaccessible regimes.Comment: Supplementary Movie Previes: SM-Movie-1: https://youtu.be/3q7-CvuBylg
SM-Movie-2: https://youtu.be/-Gymaiv9rC0 SM-Movie-3:
https://youtu.be/w-O2SPiw3nE SM-Movie-4: https://youtu.be/P4xGyr4dwK
Dynamical thermalization and vortex formation in stirred 2D Bose-Einstein condensates
We present a quantum mechanical treatment of the mechanical stirring of
Bose-Einstein condensates using classical field techniques. In our approach the
condensate and excited modes are described using a Hamiltonian classical field
method in which the atom number and (rotating frame) energy are strictly
conserved. We simulate a T = 0 quasi-2D condensate perturbed by a rotating
anisotropic trapping potential. Vacuum fluctuations in the initial state
provide an irreducible mechanism for breaking the initial symmetries of the
condensate and seeding the subsequent dynamical instability. Highly turbulent
motion develops and we quantify the emergence of a rotating thermal component
that provides the dissipation necessary for the nucleation and motional-damping
of vortices in the condensate. Vortex lattice formation is not observed, rather
the vortices assemble into a spatially disordered vortex liquid state. We
discuss methods we have developed to identify the condensate in the presence of
an irregular distribution of vortices, determine the thermodynamic parameters
of the thermal component, and extract damping rates from the classical field
trajectories.Comment: 22 pages, 15 figures. v2: Minor refinements made at suggestion of
referee. Discussion of other treatments revised. To appear in Phys. Rev.
Complex aspects of gravity
This paper presents reflections on the validity of a series of mathematical
methods and technical assumptions that are encrusted in macrophysics (related
to gravitational interaction), that seem to have little or no physical
significance. It is interesting to inquire what a change can occur if one
removes some of the traditional assumptions.Comment: 10 page
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