1,227 research outputs found
Joint distribution of the process and its sojourn time on the positive half-line for pseudo-processes governed by high-order heat equation.
Consider the high-order heat-type equation ∂u/∂t = ±∂Nu/∂xN for an integer N > 2 and introduce the related Markov pseudo-process (X(t))t≥0. In this paper, we study the sojourn time T(t) in the interval [0, +∞) up to a fixed time t for this pseudo-process. We provide explicit expressions for the joint distribution of the couple (T(t),X(t))
Joint distribution of the process and its sojourn time in a half-line for pseudo-processes driven by a high-order heat-type equation.
Let (X(t))t≥0 be the pseudo-process driven by the high-order heat-type equation ∂u = ± ∂Nu , ∂t ∂xN
where N is an integer greater than 2. We consider the sojourn time spent by (X(t))t≥0 in [a,+∞) (a ∈ R), up to a fixed time t > 0: Ta(t) = 0t 1l[a,+∞)(X(s)) ds. The purpose of this paper is to explicit the joint pseudo-distribution of the vector (Ta(t),X(t)) when the pseudo-process starts at a point x ∈ R at time 0. The method consists in solving a boundary value problem satisfied by the Laplace transform of the aforementioned distribution
On the correlation between critical points and critical values for random spherical harmonics
We study the correlation between the total number of critical points of random spherical harmonics and the number of critical points with value in any interval I ⊂ ℝ. We show that the correlation is asymptotically zero, while the partial correlation, after controlling the random L2-norm on the sphere of the eigenfunctions, is asymptotically one. Our findings complement the results obtained by Wigman (2012) and Marinucci and Rossi (2021) on the correlation between nodal and boundary length of random spherical harmonics
An experimental study of the behaviour of two rockfills accounting for the effects of degree of saturation
Rockfill dams have become more and more recognized for their safety, economy and adaptability to widely varying site conditions. As a contribution to the understanding of the main factors affecting the rockfill behaviour, the paper reports and discusses experimental data on several aspects relevant to the interpretation and analysis of their in-situ response. The experimental programme involved three series of oedometric tests on specimens of two different gravels having the same grading, reconstituted at the same initial relative density. Experimental observations on rockfills compressibility are presented and discussed: attention is paid to the role of degree of saturation (Sr) through the analysis of "driest", "fully saturated"conditions, and the transition from one to the other. Grain crushing tests on dry and saturated soil particles are also reported. Grain size distributions of the specimens, both after compaction and after the oedometer tests, are compared in the paper. The results show that the effect of Sr cannot be overlooked in the mechanical characterization of the material, especially in rockfill/stress conditions prone to crushin
Surface tension fluctuations and a new spinodal point in glass-forming liquids
The dramatic slowdown of glass-forming liquids has been variously linked to
increasing dynamic and static correlation lengths. Yet, empirical evidence is
insufficient to decide among competing theories. The random first order theory
(RFOT) links the dynamic slowdown to the growth of amorphous static order,
whose range depends on a balance between configurational entropy and surface
tension. This last quantity is expected to vanish when the temperature
surpasses a spinodal point beyond which there are no metastable states. Here we
measure for the first time the surface tension in a model glass-former, and
find that it vanishes at the energy separating minima from saddles,
demonstrating the existence of a spinodal point for amorphous metastable order.
Moreover, the fluctuations of surface tension become smaller for lower
temperatures, in quantitative agreement with recent theoretical speculation
that spatial correlations in glassy systems relax nonexponentially because of
the narrowing of the surface tension distribution.Comment: 6 pages, 5 figure
A phase-separation perspective on dynamic heterogeneities in glass-forming liquids
We study dynamic heterogeneities in a model glass-former whose overlap with a
reference configuration is constrained to a fixed value. The system
phase-separates into regions of small and large overlap, so that dynamical
correlations remain strong even for asymptotic times. We calculate an
appropriate thermodynamic potential and find evidence of a Maxwell's
construction consistent with a spinodal decomposition of two phases. Our
results suggest that dynamic heterogeneities are the expression of an ephemeral
phase-separating regime ruled by a finite surface tension
Travelling Randomly on the Poincar\'e Half-Plane with a Pythagorean Compass
A random motion on the Poincar\'e half-plane is studied. A particle runs on
the geodesic lines changing direction at Poisson-paced times. The hyperbolic
distance is analyzed, also in the case where returns to the starting point are
admitted. The main results concern the mean hyperbolic distance (and also the
conditional mean distance) in all versions of the motion envisaged. Also an
analogous motion on orthogonal circles of the sphere is examined and the
evolution of the mean distance from the starting point is investigated
Cluster expansion for abstract polymer models. New bounds from an old approach
We revisit the classical approach to cluster expansions, based on tree
graphs, and establish a new convergence condition that improves those by
Kotecky-Preiss and Dobrushin, as we show in some examples. The two ingredients
of our approach are: (i) a careful consideration of the Penrose identity for
truncated functions, and (ii) the use of iterated transformations to bound
tree-graph expansions.Comment: 16 pages. This new version, written en reponse to the suggestions of
the referees, includes more detailed introductory sections, a proof of the
generalized Penrose identity and some additional results that follow from our
treatmen
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