20,921 research outputs found
Symmetry for the duration of entropy-consuming intervals
We introduce the violation fraction as the cumulative fraction of
time that a mesoscopic system spends consuming entropy at a single trajectory
in phase space. We show that the fluctuations of this quantity are described in
terms of a symmetry relation reminiscent of fluctuation theorems, which involve
a function, , which can be interpreted as an entropy associated to the
fluctuations of the violation fraction.
The function , when evaluated for arbitrary stochastic realizations of
the violation fraction, is odd upon the symmetry transformations which are
relevant for the associated stochastic entropy production. This fact leads to a
detailed fluctuation theorem for the probability density function of .
We study the steady-state limit of this symmetry in the paradigmatic case of
a colloidal particle dragged by optical tweezers through an aqueous solution.
Finally, we briefly discuss on possible applications of our results for the
estimation of free-energy differences from single molecule experiments.Comment: 11 pages, 4 figures. Last revised. Version accepted for publication
in Phys. Rev.
Duration of local violations of the second law of thermodynamics along single trajectories in phase space
We define the {\it violation fraction} as the cumulative fraction of
time that the entropy change is negative during single realizations of
processes in phase space. This quantity depends both on the number of degrees
of freedom and the duration of the time interval . In the
large- and large- limit we show that, for ergodic and microreversible
systems, the mean value of scales as
. The
exponent is positive and generally depends on the protocol for the
external driving forces, being for a constant drive. As an example,
we study a nontrivial model where the fluctuations of the entropy production
are non-Gaussian: an elastic line driven at a constant rate by an anharmonic
trap. In this case we show that the scaling of with
and agrees with our result. Finally, we discuss how this scaling law may
break down in the vicinity of a continuous phase transition.Comment: 8 pages, 2 figures, Final version, as accepted for publication in
Phys. Rev.
A characterization of some families of Cohen--Macaulay, Gorenstein and/or Buchsbaum rings
We provide algorithmic methods to check the Cohen--Macaulayness,
Buchsbaumness and/or Gorensteiness of some families of semigroup rings that are
constructed from the dilation of bounded convex polyhedrons of .
Some families of semigroup rings are given satifying these properties
Detection of Communities within the Multibody System Dynamics Network and Analysis of Their Relations
Multibody system dynamics is already a well developed branch of theoretical, computational and applied mechanics. Thousands of documents can be found in any of the well-known scientific databases. In this work it is demonstrated that multibody system dynamics is built of many thematic communities. Using the Elsevierâs abstract and citation database SCOPUS, a massive amount of data is collected and analyzed with the use of the open source visualization tool Gephi. The information is represented as a large set of nodes with connections to study their graphical distribution and explore geometry and symmetries. A randomized radial symmetry is found in the graphical representation of the collected information. Furthermore, the concept of modularity is used to demonstrate that community structures are present in the field of multibody system dynamics. In particular, twenty-four different thematic communities have been identified. The scientific production of each community is analyzed, which allows to predict its growing rate in the next years. The journals and conference proceedings mainly used by the authors belonging to the community as well as the cooperation between them by country are also analyzed
Does the Chinese banking system benefit from foreign investors?
We find empirical evidence that the Chinese banking system has benefited from the entry of foreign investors through higher profitability and increased efficiency of the banking system. Foreign participation, which consists of a minority stake in a Chinese bank (in contrast to the typical pattern in emerging countries), appears to be most effective when the foreign bank acts as a strategic investor. Purely financial investors contribute little, if anything, to bank performance.China; banking system; foreign participation
The convex hull of a finite set
We study -separately convex hulls of finite
sets of points in , as introduced in
\cite{KirchheimMullerSverak2003}. When is considered as a
certain subset of matrices, this notion of convexity corresponds
to rank-one convex convexity . If is identified instead
with a subset of matrices, it actually agrees with the quasiconvex
hull, due to a recent result \cite{HarrisKirchheimLin18}.
We introduce " complexes", which generalize constructions. For a
finite set , a " -complex" is a complex whose extremal points
belong to . The "-complex convex hull of ", , is the union
of all -complexes. We prove that is contained in the
convex hull .
We also consider outer approximations to convexity based in the
locality theorem \cite[4.7]{Kirchheim2003}. Starting with a crude outer
approximation we iteratively chop off "-prisms". For the examples in
\cite{KirchheimMullerSverak2003}, and many others, this procedure reaches a
" -complex" in a finite number of steps, and thus computes the
convex hull.
We show examples of finite sets for which this procedure does not reach the
convex hull in finite time, but we show that a sequence of outer
approximations built with -prisms converges to a -complex. We
conclude that is always a " -complex", which has interesting
consequences
DebatesâStochastic subsurface hydrology from theory to practice: why stochastic modeling has not yet permeated into practitioners?
This is the peer reviewed version of the following article: [Sanchez-Vila, X., and D. FernĂ ndez-Garcia (2016), DebatesâStochastic subsurface hydrology from theory to practice: Why stochastic modeling has not yet permeated into practitioners?, Water Resour. Res., 52, 9246â9258, doi:10.1002/2016WR019302], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/2016WR019302/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingWe address modern topics of stochastic hydrogeology from their potential relevance to real modeling efforts at the field scale. While the topics of stochastic hydrogeology and numerical modeling have become routine in hydrogeological studies, nondeterministic models have not yet permeated into practitioners. We point out a number of limitations of stochastic modeling when applied to real applications and comment on the reasons why stochastic models fail to become an attractive alternative for practitioners. We specifically separate issues corresponding to flow, conservative transport, and reactive transport. The different topics addressed are emphasis on process modeling, need for upscaling parameters and governing equations, relevance of properly accounting for detailed geological architecture in hydrogeological modeling, and specific challenges of reactive transport. We end up by concluding that the main responsible for nondeterministic models having not yet permeated in industry can be fully attributed to researchers in stochastic hydrogeology.Peer ReviewedPostprint (author's final draft
Designing optimal controls by parameter optimization for a stance-control knee-ankle-foot orthosis
Inverse dynamics simulation is often used in robotic and mechatronic systems to track a
desired trajectory by feed-forward control. Musculoskeletal multibody systems are highly
overactuated and show a switching number of closed kinematical loops. The method
of inverse dynamics is also successfully applied to overactuated systems by parameter
optimization for two- and three-dimensional models of the human musculoskeletal system.
The presented simulation approach is fully based on optimizationPostprint (published version
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