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Let S be a monoidal category with equalizers that are preserved by the tensor
product. The notion of categories internal to S is defined, generalizing the notions
of monoid and comonoid in S, and ex...
Scaling Limits for Internal Aggregation Models with Multiple Sources
Scaling Limits Internal Aggregation Models Multiple Sources
2015/8/14
We study the scaling limits of three different aggregation models on Zd: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which parti...
Let each of n particles starting at the origin in Z2 perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set A(n) ...
Let A(t) denote the cluster produced by internal diffusion limited aggregation (internal DLA) with t particles in dimension d ≥ 3. We show that A(t) is approximately spherical, up to an O(√log t) erro...
In previous works, we showed that the internal DLA cluster on Zd with t particles is almost surely spherical up to a maximal error of O(log t) if d = 2 and O(√log t) if d ≥ 3. This paper addresses “av...
Oil and water:a two-type internal aggregation model
Oil and water internal aggregation model
2015/8/14
We introduce a two-type internal DLA model which is an example of a non-unary abelian network. Starting with n “oil” and n “water” particles at the origin, the particles diffuse in Z according to the ...
We study the scaling limits of three different aggregation models on Zd: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which parti...
The ternary commutator obstruction for internal crossed modules
cross-effect commutator internal crossed module semi-abelian category
2011/8/25
Abstract: We study the notion of internal crossed module in terms of cross-effects of the identity functor. These cross-effects give rise to a concept of commutator which allows a description of inter...
Internal Energy And Heat Energy: Distinguish is Essential
Internal Energy Heat Energy Distinguish
2011/7/7
The heat energy and the internal energy have commonly be confused in previous studies. Particularly, in recent years researchers try to establish a general relation between the heat conductivity and t...
Let A(t) denote the cluster produced by internal di usion limited aggregation (internal DLA) with t particles in dimension d 3. We show that A(t) is approximately spherical, up to an O(
p log t) er...
Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon
Asymptotic models generation of internal waves
2011/3/1
This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More gen-
erally, we study the...
We consider internal diffusion limited aggregation in dimension larger or equal to two. This is a random cluster growth model, where random walks start at the origin of the $d$-dimensional lattice, o...
Internal perturbations of homoclinic classes:non-domination, cycles, and self-replication
homoclinic classes non-domination cycles
2010/11/19
Conditions are provided under which lack of domination of a homoclinic class yields robust heterodimensional cycles. Moreover, so-called viral homoclinic classes are studied. Viral classes have the p...
Stability analysis for linear time-delay systems described by fractional parameterized models possessing multiple internal constant discrete delays
Stability analysis linear time-delay systems described fractional parameterized models possessing multiple internal
2010/9/13
This paper discusses linear fractional representations (LFR) of parameter-dependent nonlinear systems with real-rational nonlinearities and point-delayed dynamics. Sufficient conditions for robust glo...
Some Results on the Solutions of Caputo Fractional Linear Time-Invariant Systems of any order with Internal Point Delays
Caputo fractional calculus Riemann- Liouville fractional calculus Positive solutions and systems
2010/12/9
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynami...