431 research outputs found
Flow Invariance on Stratified Domains
This paper studies conditions for invariance of dynamical systems on
stratified do- mains as originally introduced by Bressan and Hong. We establish
Hamiltonian conditions for both weak and strong invariance of trajectories on
systems with non-Lipschitz data. This is done via the identification of a new
multifunction, the essential velocity multifunction. Properties of this
multifunction are investigated and used to establish the relevant invariance
criteria
On the Strong Invariance Property for Non-Lipschitz Dynamics
We provide a new sufficient condition for strong invariance for differential
inclusions, under very general conditions on the dynamics, in terms of a
Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the
multifunction, we assume a feedback realization condition that can in
particular be satisfied for measurable dynamics that are neither upper nor
lower semicontinuous.Comment: 15 pages, 0 figures. For this revision, the authors added a remark
about an alternative nonconstructive proof of the main resul
Acoustic Attenuation in High- Superconductors
We analyze the acoustic attenuation rate in high- superconductors, and
find that this method offers an additional way to examine the anisotropy of the
superconducting order parameter in these materials. We argue that it should be
possible to distinguish the electronic contribution to the acoustic
attenuation, which has a strong temperature dependence near , from the
lattice contribution, which does not show a strong temperature dependence near
. We propose that this can be utilized to measure the anisotropy of the
order parameter by measuring the attenuation rate near in different
directions.Comment: 9 pages, latex, 2 postscript figures, in press Physica C, (uuencoded
file consisting of paper and 2 figures, please contact J.C. Swihart
([email protected]) for a printed copy
Thurston's metric on TeichmĂŒller space of semi-translation surfaces
We define two pseudo-metrics L_F and K_F on the TeichmĂŒller space of semi-translation surfaces, which are the symmetric counterparts to the metrics defined by William Thurston. We prove some nice properties of L_F and K_F, most notably that they are complete pseudo-metrics. In the second part of the thesis we define their asymmetric analogues L_F^a and K_F^a and prove that their equality depends on two statements regarding 1-Lipschitz maps between polygons. We are able to prove the first statement, but the second one remains a conjecture: nonetheless, we explain why we believe it is true
Semiconcavity of the value function for a class of differential inclusions
We provide intrinsic sufficient conditions on a multifunction F and
endpoint data phi so that the value function associated to the Mayer problem is semiconcave
Convexity and Duality in Hamilton-Jacobi Theory
Value functions propagated from initial or terminal costs and constraints by way of a differential or more broadly through a Lagrangian that may take on "alpha," are studied in the case where convexity persists in the state argument. Such value functions, themselves taking on "alpha," are shown to satisfy a subgradient form of the Hamilton-Jacobi equation which strongly supports properties of local Lipschitz continuity, semidifferentibility and Clarke regularity. An extended `method of characteristics' is developed which determines them from Hamiltonian dynamics underlying the given Lagrangian. Close relations with a dual value function are revealed
The Mayer and Minimum Time Problems with Stratified State Constraints *
International audienceThis paper studies optimal control problems with state constraints by imposing structural assumptions on the constraint domain coupled with a tangential restriction with the dynamics. These assumptions replace pointing or controllability assumptions that are common in the literature, and provide a framework under which feasible boundary trajectories can be analyzed directly. The value functions associated with the state constrained Mayer and minimal time problems are characterized as solutions to a pair of Hamilton-Jacobi inequalities with appropriate boundary conditions. The novel feature of these inequalities lies in the choice of the Hamiltonian
Jan Ćukasiewicz, Sur la Logique des stoĂŻciens
Jan Ćukasiewicz a Ă©laborĂ© un programme de recherche portant sur lâhistoire de la logique. Ă son avis, la logique mathĂ©matique contemporaine (modern) est en continuitĂ© directe avec la logique formelle du passĂ©. En consĂ©quence, une interprĂ©tation correcte et fidĂšle des idĂ©es anciennes exige une application des outils logiques contemporains. Autrement dit, de bonnes Ă©tudes historiques sur la logique doivent consister Ă examiner la logique dâautrefois Ă travers les lunettes logiques contemporaine..
Ultrasonic Attenuation in Clean d-Wave Superconductors
We calculate the low temperature longitudinal ultrasonic attenuation rate
in clean d-wave superconductors. We consider the contribution of
previously ignored processes involving the excitation of a pair of quasi-holes
or quasi-particles. These processes, which are forbidden by energy conservation
in conventional s-wave superconductors, have a finite phase space in d-wave
superconductors due to the presence of nodes in the gap which give rise to soft
low-energy electronic excitations. We find the contribution to from
these processes to be proportional to in the regime ,(ultra-low temperature regime) and to be proportional to 1/T in
the region , (low temperature regime) where is the ultrasound wave-vector and is the maximum gap amplitude.
We explicitly evaluate these terms, for parameters appropriate to the cuprates,
for along the nodal and the antinodal directions and compare it with
the contribution from processes considered earlier(I.Vekhter et al {\it Phys.
Rev.}{\bf B59}, 7123(1999)). In the ultra-low temperature regime, the processes
considered by us make a contribution which is smaller by about a factor of 10
for along the nodal direction, while along the antinodal direction it
is larger by a factor of 100 or so. In the low temperature regime on the other
hand the contribution made by these terms is small. However taken together with
the original terms we describe a possible way to evaluate the parameter
.Comment: 9 pages, RevTex, accepted for publication in Physica
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