3,926 research outputs found
Monomer dynamics of a wormlike chain
We derive the stochastic equations of motion for a tracer that is tightly
attached to a semiflexible polymer and confined or agitated by an externally
controlled potential. The generalised Langevin equation, the power spectrum,
and the mean-square displacement for the tracer dynamics are explicitly
constructed from the microscopic equations of motion for a weakly bending
wormlike chain by a systematic coarse-graining procedure. Our accurate
analytical expressions should provide a convenient starting point for further
theoretical developments and for the analysis of various single-molecule
experiments and of protein shape fluctuations.Comment: 6 pages, 4 figure
Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below
We prove existence and uniqueness of optimal maps on spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation. \ua9 2015, Mathematica Josephina, Inc
Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II
Let be a symmetric diffusion operator
with an invariant measure on a complete Riemannian
manifold. In this paper we prove Li-Yau gradient estimates for weighted
elliptic equations on the complete manifold with
and -dimensional Bakry-\'{E}mery Ricci curvature bounded below by some
negative constant. Based on this, we give an upper bound on the first
eigenvalue of the diffusion operator on this kind manifold, and thereby
generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975)
289-297).Comment: Final version. The original proof of Theorem 2.1 using Li-Yau
gradient estimate method has been moved to the appendix. The new proof is
simple and direc
Sub-Gaussian short time asymptotics for measure metric Dirichlet spaces
This paper presents estimates for the distribution of the exit time from
balls and short time asymptotics for measure metric Dirichlet spaces. The
estimates cover the classical Gaussian case, the sub-diffusive case which can
be observed on particular fractals and further less regular cases as well. The
proof is based on a new chaining argument and it is free of volume growth
assumptions
Homotopy on spatial graphs and generalized Sato-Levine invariants
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs
which are generalizations of Milnor's link-homotopy. Fleming and the author
introduced some edge (resp. vertex)-homotopy invariants of spatial graphs by
applying the Sato-Levine invariant for the constituent 2-component
algebraically split links. In this paper, we construct some new edge (resp.
vertex)-homotopy invariants of spatial graphs without any restriction of
linking numbers of the constituent 2-component links by applying the
generalized Sato-Levine invariant.Comment: 16 pages, 13 figure
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
This paper is devoted to a deeper understanding of the heat flow and to the
refinement of calculus tools on metric measure spaces (X,d,m). Our main results
are:
- A general study of the relations between the Hopf-Lax semigroup and
Hamilton-Jacobi equation in metric spaces (X,d).
- The equivalence of the heat flow in L^2(X,m) generated by a suitable
Dirichlet energy and the Wasserstein gradient flow of the relative entropy
functional in the space of probability measures P(X).
- The proof of density in energy of Lipschitz functions in the Sobolev space
W^{1,2}(X,d,m).
- A fine and very general analysis of the differentiability properties of a
large class of Kantorovich potentials, in connection with the optimal transport
problem.
Our results apply in particular to spaces satisfying Ricci curvature bounds
in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the
doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4,
Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop.
4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6
simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients,
still equivalent to all other ones, has been propose
On the isometry group of RCDâ(K,N)-spaces
This is a post-peer-review pre-copyedit version of an article published in Manuscripta Mathematica. The final authentical version is avaible online https://doi.org/10.1007/s00229-018-1010-7We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition,RCDâ(K,N),is a Lie group. We obtain an optimal upper bound on the dimension of this group, and classify the spaces where this maximal dimension is attained.L. Guijarro and J. Santos-RodrĂguez were supported by research grants MTM2014-57769-3-P, and MTM2017-85934-C3-2-P (MINECO) and ICMAT Severo Ochoa Project SEV-2015-0554 (MINECO). J. Santos-RodrĂguez was supported by a PhD scholarship awarded byCONACY
Four-Loop Decoupling Relations for the Strong Coupling
We compute the matching relation for the strong coupling constant within the
framework of QCD up to four-loop order. This allows a consistent five-loop
running (once the function is available to this order) taking into
account threshold effects. As a side product we obtain the effective coupling
of a Higgs boson to gluons with five-loop accuracy.Comment: 11 page
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