scholarly journals Optimal transport with discrete long-range mean-field interactions

2020 ◽  
Vol 10 (02) ◽  
pp. 2050011
Author(s):  
Jiakun Liu ◽  
Grégoire Loeper
Keyword(s):  
Force Field ◽  
Long Range ◽  
Interaction Potential ◽  
Velocity Potential ◽  
Optimal Transport ◽  
Mean Field ◽  
External Force Field ◽  
Intermediate Time ◽  
Optimal Transport Map ◽  
Intermediate Density

We study an optimal transport problem where, at some intermediate time, the mass is either accelerated by an external force field or self-interacting. We obtain the regularity of the velocity potential, intermediate density, and optimal transport map, under the conditions on the interaction potential that are related to the so-called Ma–Trudinger–Wang condition from optimal transport [X.-N. Ma, N. S. Trudinger and X.-J. Wang, Regularity of potential functions of the optimal transportation problems, Arch. Ration. Mech. Anal. 177 (2005) 151–183.].

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

Semi-automated Optimization of the CHARMM36 Lipid Force Field to Include Explicit Treatment of Long-Range Dispersion

2021 ◽  
Vol 17 (3) ◽  
pp. 1562-1580 ◽  
Author(s):  
Yalun Yu ◽  
Andreas Krämer ◽  
Richard M. Venable ◽  
Andrew C. Simmonett ◽  
Alexander D. MacKerell ◽  
...  
Keyword(s):  
Force Field ◽  
Long Range ◽  
Automated Optimization

Bismuthene from sonoelectrochemistry as a superior anode for potassium-ion batteries

2020 ◽  
Vol 8 (1) ◽  
pp. 453-460 ◽  
Author(s):  
Chao Shen ◽  
Tianle Cheng ◽  
Chunyan Liu ◽  
Lu Huang ◽  
Mengyang Cao ◽  
...  
Keyword(s):  
Force Field ◽  
External Force ◽  
Potassium Ion ◽  
Cycle Life ◽  
High Rate ◽  
Rate Performance ◽  
Electrochemical Exfoliation ◽  
Long Cycle Life ◽  
External Force Field ◽  
High Rate Performance

An external force field-assisted electrochemical exfoliation method was adopted to produce few-layered bismuthene nanosheets (FBNs). These FBNs exhibited a high rate performance and ultra-long cycle life for KIBs anode.

scholarly journals Power-law bounds for critical long-range percolation below the upper-critical dimension

2021 ◽  
Author(s):  
Tom Hutchcroft
Keyword(s):  
Long Range ◽  
Power Law ◽  
Upper Bound ◽  
Mean Field ◽  
Maximum Size ◽  
Finite Graph ◽  
Critical Dimension ◽  
Point Function ◽  
Upper Critical Dimension ◽  
Infinite Cluster

AbstractWe study long-range Bernoulli percolation on $${\mathbb {Z}}^d$$ Z d in which each two vertices x and y are connected by an edge with probability $$1-\exp (-\beta \Vert x-y\Vert ^{-d-\alpha })$$ 1 - exp ( - β ‖ x - y ‖ - d - α ) . It is a theorem of Noam Berger (Commun. Math. Phys., 2002) that if $$0<\alpha <d$$ 0 < α < d then there is no infinite cluster at the critical parameter $$\beta _c$$ β c . We give a new, quantitative proof of this theorem establishing the power-law upper bound $$\begin{aligned} {\mathbf {P}}_{\beta _c}\bigl (|K|\ge n\bigr ) \le C n^{-(d-\alpha )/(2d+\alpha )} \end{aligned}$$ P β c ( | K | ≥ n ) ≤ C n - ( d - α ) / ( 2 d + α ) for every $$n\ge 1$$ n ≥ 1 , where K is the cluster of the origin. We believe that this is the first rigorous power-law upper bound for a Bernoulli percolation model that is neither planar nor expected to exhibit mean-field critical behaviour. As part of the proof, we establish a universal inequality implying that the maximum size of a cluster in percolation on any finite graph is of the same order as its mean with high probability. We apply this inequality to derive a new rigorous hyperscaling inequality $$(2-\eta )(\delta +1)\le d(\delta -1)$$ ( 2 - η ) ( δ + 1 ) ≤ d ( δ - 1 ) relating the cluster-volume exponent $$\delta $$ δ and two-point function exponent $$\eta $$ η .

ABSENCE OF PHASE TRANSITIONS ON TREE STRUCTURES

1993 ◽  
Vol 07 (29n30) ◽  
pp. 1947-1950 ◽  
Author(s):  
RAFFAELLA BURIONI ◽  
DAVIDE CASSI
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Linear Chain ◽  
Mean Field ◽  
Range Order ◽  
The Other ◽  
Long Range Order ◽  
Field Phase ◽  
Tree Structures ◽  
Bethe Lattices

We rigorously prove that the correlation functions of any statistical model having a compact transitive symmetry group and nearest-neighbor interactions on any tree structure are equal to the corresponding ones on a linear chain. The exponential decay of the latter implies the absence of long-range order on any tree. On the other hand, for trees with exponential growth such as Bethe lattices, one can show the existence of a particular kind of mean field phase transition without long-range order.

scholarly journals Pollution Transfer as Optimal Mass Transport Problem

2016 ◽  
Vol 8 (6) ◽  
pp. 58
Author(s):  
L. Ndiaye ◽  
Mb. Ndiaye ◽  
A. Sy ◽  
D. Seck
Keyword(s):  
Porous Media ◽  
Optimal Transport ◽  
Existence Of Solution ◽  
Nonlinear Pde ◽  
Mathematical Framework ◽  
Sufficient Condition ◽  
Mass Transportation ◽  
Optimal Mass Transport ◽  
Transportation Theory ◽  
Optimal Transport Map

In this paper, we use mass transportation theory to study pollution  transfer in  porous media.  We show   the existence of a $L^2-$regular vector field defined by a $W^{1, 1}-$ optimal transport map. A sufficient condition for solvability of our model, is given by   a (non homogeneous) transport equation with  a  source defined by a measure. The mathematical framework used, allows us to  show in some specifical cases, existence of solution for  a nonlinear PDE deriving from the modelling. And we end by numerical simulations.

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