38,566 research outputs found
Self-similar solutions for a superdiffusive heat equation with gradient nonlinearity
This paper is devoted to global well-posedness, self-similarity and
symmetries of solutions for a superdiffusive heat equation with superlinear and
gradient nonlinear terms with initial data in new homogeneous Besov-Morrey type
spaces. Unlike the heat equation, we need to develop an appropriate
decomposition of the two-parametric Mittag-Leffler function in order to obtain
Mikhlin-type estimates get our well-posedness theorem. To the best of our
knowledge, the present work is the first one concerned with a well-posedness
theory for a time-fractional partial differential equations of order
with non null initial velocity
Statistics, distillation, and ordering emergence in a two-dimensional stochastic model of particles in counterflowing streams
In this paper, we proposed a stochastic model which describes two species of
particles moving in counterflow. The model generalizes the theoretical
framework describing the transport in random systems since particles can work
as mobile obstacles, whereas particles of one species move in opposite
direction to the particles of the other species, or they can work as fixed
obstacles remaining in their places during the time evolution. We conducted a
detailed study about the statistics concerning the crossing time of particles,
as well as the effects of the lateral transitions on the time required to the
system reaches a state of complete geographic separation of species. The
spatial effects of jamming were also studied by looking into the deformation of
the concentration of particles in the two-dimensional corridor. Finally, we
observed in our study the formation of patterns of lanes which reach the steady
state regardless the initial conditions used for the evolution. A similar
result is also observed in real experiments involving charged colloids motion
and simulations of pedestrian dynamics based on Langevin equations, when
periodic boundary conditions are considered (particles counterflow in a ring
symmetry). The results obtained through Monte Carlo numerical simulations and
numerical integrations are in good agreement with each other. However,
differently from previous studies, the dynamics considered in this work is not
Newton-based, and therefore, even artificial situations of self-propelled
objects should be studied in this first-principle modeling.Comment: 27 pages, 13 figure
Rank-1 Tensor Approximation Methods and Application to Deflation
Because of the attractiveness of the canonical polyadic (CP) tensor
decomposition in various applications, several algorithms have been designed to
compute it, but efficient ones are still lacking. Iterative deflation
algorithms based on successive rank-1 approximations can be used to perform
this task, since the latter are rather easy to compute. We first present an
algebraic rank-1 approximation method that performs better than the standard
higher-order singular value decomposition (HOSVD) for three-way tensors.
Second, we propose a new iterative rank-1 approximation algorithm that improves
any other rank-1 approximation method. Third, we describe a probabilistic
framework allowing to study the convergence of deflation CP decomposition
(DCPD) algorithms based on successive rank-1 approximations. A set of computer
experiments then validates theoretical results and demonstrates the efficiency
of DCPD algorithms compared to other ones
National innovation system, competitiveness and economic growth
Differences in income-elasticities of imports and exports among countries bring about distinct degrees of external constraints to growth. This argument has been pointed out by Prebisch and by authors in the Kaldorian tradition. Prebisch’s explanations for this phenomenon relate to the differences in international insertion between agrarian / peripheral and industrial / central economies. Kaldorian authors, in turn, refer to Prebisch only to explain why such elasticities differ between products and between countries. However, even after undergoing industrialization processes, several economies still face external constraints to growth. The aim of this paper is to explain differences in trade elasticities among industrial economies. Therefore, it intends to demonstrate, by using the Neo-Schumpeterian literature, the causal relations between the development of a National Innovation System, the differences in income-elasticities of imports and exports, the degree of competitiveness and the degree of external vulnerability of an economy.national innovation system, competitiveness, external vulnerability
Towards a Generic Trace for Rule Based Constraint Reasoning
CHR is a very versatile programming language that allows programmers to
declaratively specify constraint solvers. An important part of the development
of such solvers is in their testing and debugging phases. Current CHR
implementations support those phases by offering tracing facilities with
limited information. In this report, we propose a new trace for CHR which
contains enough information to analyze any aspects of \CHRv\ execution at some
useful abstract level, common to several implementations. %a large family of
rule based solvers. This approach is based on the idea of generic trace. Such a
trace is formally defined as an extension of the semantics of
CHR. We show that it can be derived form the SWI Prolog CHR trace
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