672 research outputs found
Hamiltonian Formalism in Quantum Mechanics
Heisenberg motion equations in Quantum mechanics can be put into the Hamilton
form. The difference between the commutator and its principal part, the Poisson
bracket, can be accounted for exactly. Canonical transformations in Quantum
mechanics are not, or at least not what they appear to be; their properties are
formulated in a series of Conjectures
Nonlinear porous medium flow with fractional potential pressure
We study a porous medium equation, with nonlocal diffusion effects given by
an inverse fractional Laplacian operator. We pose the problem in n-dimensional
space for all t>0 with bounded and compactly supported initial data, and prove
existence of a weak and bounded solution that propagates with finite speed, a
property that is nor shared by other fractional diffusion models.Comment: 32 pages, Late
Natural equilibrium states for multimodal maps
This paper is devoted to the study of the thermodynamic formalism for a class
of real multimodal maps. This class contains, but it is larger than,
Collet-Eckmann. For a map in this class, we prove existence and uniqueness of
equilibrium states for the geometric potentials , for the largest
possible interval of parameters . We also study the regularity and convexity
properties of the pressure function, completely characterising the first order
phase transitions. Results concerning the existence of absolutely continuous
invariant measures with respect to the Lebesgue measure are also obtained
Linear Paul trap design for an optical clock with Coulomb crystals
We report on the design of a segmented linear Paul trap for optical clock
applications using trapped ion Coulomb crystals. For an optical clock with an
improved short-term stability and a fractional frequency uncertainty of 10^-18,
we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the
systematic frequency shifts of such a frequency standard. In particular, we
elaborate on high precision calculations of the electric radiofrequency field
of the ion trap using the finite element method. These calculations are used to
find a scalable design with minimized excess micromotion of the ions at a level
at which the corresponding second- order Doppler shift contributes less than
10^-18 to the relative uncertainty of the frequency standard
On the Lebesgue measure of Li-Yorke pairs for interval maps
We investigate the prevalence of Li-Yorke pairs for and
multimodal maps with non-flat critical points. We show that every
measurable scrambled set has zero Lebesgue measure and that all strongly
wandering sets have zero Lebesgue measure, as does the set of pairs of
asymptotic (but not asymptotically periodic) points.
If is topologically mixing and has no Cantor attractor, then typical
(w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally
admits an absolutely continuous invariant probability measure (acip), then
typical pairs have a dense orbit for . These results make use of
so-called nice neighborhoods of the critical set of general multimodal maps,
and hence uniformly expanding Markov induced maps, the existence of either is
proved in this paper as well.
For the setting where has a Cantor attractor, we present a trichotomy
explaining when the set of Li-Yorke pairs and distal pairs have positive
two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure
Come back Marshall, all is forgiven? : Complexity, evolution, mathematics and Marshallian exceptionalism
Marshall was the great synthesiser of neoclassical economics. Yet with his qualified assumption of self-interest, his emphasis on variation in economic evolution and his cautious attitude to the use of mathematics, Marshall differs fundamentally from other leading neoclassical contemporaries. Metaphors inspire more specific analogies and ontological assumptions, and Marshall used the guiding metaphor of Spencerian evolution. But unfortunately, the further development of a Marshallian evolutionary approach was undermined in part by theoretical problems within Spencer's theory. Yet some things can be salvaged from the Marshallian evolutionary vision. They may even be placed in a more viable Darwinian framework.Peer reviewedFinal Accepted Versio
Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method
We complete classical investigations concerning the dynamical stability of an
infinite homogeneous gaseous medium described by the Euler-Poisson system or an
infinite homogeneous stellar system described by the Vlasov-Poisson system
(Jeans problem). To determine the stability of an infinite homogeneous stellar
system with respect to a perturbation of wavenumber k, we apply the Nyquist
method. We first consider the case of single-humped distributions and show
that, for infinite homogeneous systems, the onset of instability is the same in
a stellar system and in the corresponding barotropic gas, contrary to the case
of inhomogeneous systems. We show that this result is true for any symmetric
single-humped velocity distribution, not only for the Maxwellian. If we
specialize on isothermal and polytropic distributions, analytical expressions
for the growth rate, damping rate and pulsation period of the perturbation can
be given. Then, we consider the Vlasov stability of symmetric and asymmetric
double-humped distributions (two-stream stellar systems) and determine the
stability diagrams depending on the degree of asymmetry. We compare these
results with the Euler stability of two self-gravitating gaseous streams.
Finally, we determine the corresponding stability diagrams in the case of
plasmas and compare the results with self-gravitating systems
The design and evaluation of travelling gun irrigation systems: enrolador software
Technical Paperinfo:eu-repo/semantics/publishedVersio
Recent experimental results in sub- and near-barrier heavy ion fusion reactions
Recent advances obtained in the field of near and sub-barrier heavy-ion
fusion reactions are reviewed. Emphasis is given to the results obtained in the
last decade, and focus will be mainly on the experimental work performed
concerning the influence of transfer channels on fusion cross sections and the
hindrance phenomenon far below the barrier. Indeed, early data of sub-barrier
fusion taught us that cross sections may strongly depend on the low-energy
collective modes of the colliding nuclei, and, possibly, on couplings to
transfer channels. The coupled-channels (CC) model has been quite successful in
the interpretation of the experimental evidences. Fusion barrier distributions
often yield the fingerprint of the relevant coupled channels. Recent results
obtained by using radioactive beams are reported. At deep sub-barrier energies,
the slope of the excitation function in a semi-logarithmic plot keeps
increasing in many cases and standard CC calculations over-predict the cross
sections. This was named a hindrance phenomenon, and its physical origin is
still a matter of debate. Recent theoretical developments suggest that this
effect, at least partially, may be a consequence of the Pauli exclusion
principle. The hindrance may have far-reaching consequences in astrophysics
where fusion of light systems determines stellar evolution during the carbon
and oxygen burning stages, and yields important information for exotic
reactions that take place in the inner crust of accreting neutron stars.Comment: 40 pages, 63 figures, review paper accepted for EPJ
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
- âŠ