3,049 research outputs found
A Numerical Method to solve Optimal Transport Problems with Coulomb Cost
In this paper, we present a numerical method, based on iterative Bregman
projections, to solve the optimal transport problem with Coulomb cost. This is
related to the strong interaction limit of Density Functional Theory. The first
idea is to introduce an entropic regularization of the Kantorovich formulation
of the Optimal Transport problem. The regularized problem then corresponds to
the projection of a vector on the intersection of the constraints with respect
to the Kullback-Leibler distance. Iterative Bregman projections on each
marginal constraint are explicit which enables us to approximate the optimal
transport plan. We validate the numerical method against analytical test cases
A Statistical Approach to Multifield Inflation: Many-field Perturbations Beyond Slow Roll
We study multifield contributions to the scalar power spectrum in an ensemble
of six-field inflationary models obtained in string theory. We identify
examples in which inflation occurs by chance, near an approximate inflection
point, and we compute the primordial perturbations numerically, both exactly
and using an array of truncated models. The scalar mass spectrum and the number
of fluctuating fields are accurately described by a simple random matrix model.
During the approach to the inflection point, bending trajectories and
violations of slow roll are commonplace, and 'many-field' effects, in which
three or more fields influence the perturbations, are often important. However,
in a large fraction of models consistent with constraints on the tilt the
signatures of multifield evolution occur on unobservably large scales. Our
scenario is a concrete microphysical realization of quasi-single-field
inflation, with scalar masses of order , but the cubic and quartic couplings
are typically too small to produce detectable non-Gaussianity. We argue that
our results are characteristic of a broader class of models arising from
multifield potentials that are natural in the Wilsonian sense.Comment: 39 pages, 17 figures. References added. Matches version published in
JCA
Stable Frank-Kasper phases of self-assembled, soft matter spheres
Single molecular species can self-assemble into Frank Kasper (FK) phases,
finite approximants of dodecagonal quasicrystals, defying intuitive notions
that thermodynamic ground states are maximally symmetric. FK phases are
speculated to emerge as the minimal-distortional packings of space-filling
spherical domains, but a precise quantitation of this distortion and how it
affects assembly thermodynamics remains ambiguous. We use two complementary
approaches to demonstrate that the principles driving FK lattice formation in
diblock copolymers emerge directly from the strong-stretching theory of
spherical domains, in which minimal inter-block area competes with minimal
stretching of space-filling chains. The relative stability of FK lattices is
studied first using a diblock foam model with unconstrained particle volumes
and shapes, which correctly predicts not only the equilibrium {\sigma} lattice,
but also the unequal volumes of the equilibrium domains. We then provide a
molecular interpretation for these results via self-consistent field theory,
illuminating how molecular stiffness regulates the coupling between
intra-domain chain configurations and the asymmetry of local packing. These
findings shed new light on the role of volume exchange on the formation of
distinct FK phases in copolymers, and suggest a paradigm for formation of FK
phases in soft matter systems in which unequal domain volumes are selected by
the thermodynamic competition between distinct measures of shape asymmetry.Comment: 40 pages, 22 figure
The effect of internal and global modes on the radial distribution function of confined semiflexible polymers
The constraints imposed by nano- and microscale confinement on the
conformational degrees of freedom of thermally fluctuating biopolymers are
utilized in contemporary nano-devices to specifically elongate and manipulate
single chains. A thorough theoretical understanding and quantification of the
statistical conformations of confined polymer chains is thus a central concern
in polymer physics. We present an analytical calculation of the radial
distribution function of harmonically confined semiflexible polymers in the
weakly bending limit. Special emphasis has been put on a proper treatment of
global modes, i.e. the possibility of the chain to perform global movements
within the channel. We show that the effect of these global modes significantly
impacts the chain statistics in cases of weak and intermediate confinement.
Comparing our analytical model to numerical data from Monte Carlo simulations
we find excellent agreement over a broad range of parameters.Comment: 6 pages, 3 figures typo corrected, slightly revised line of
reasoning, results unchange
Semiflexible polymers: Dependence on ensemble and boundary orientations
We show that the mechanical properties of a worm-like-chain (WLC) polymer, of
contour length and persistence length \l such that t=L/\l\sim{\cal
O}(1), depend both on the ensemble and the constraint on end-orientations. In
the Helmholtz ensemble, multiple minima in free energy near persists for
all kinds of orientational boundary conditions. The qualitative features of
projected probability distribution of end to end vector depend crucially on the
embedding dimensions. A mapping of the WLC model, to a quantum particle moving
on the surface of an unit sphere, is used to obtain the statistical and
mechanical properties of the polymer under various boundary conditions and
ensembles. The results show excellent agreement with Monte-Carlo simulations.Comment: 15 pages, 15 figures; version accepted for publication in Phys. Rev.
E; one new figure and discussions adde
Monsters, black holes and the statistical mechanics of gravity
We review the construction of monsters in classical general relativity.
Monsters have finite ADM mass and surface area, but potentially unbounded
entropy. From the curved space perspective they are objects with large proper
volume that can be glued on to an asymptotically flat space. At no point is the
curvature or energy density required to be large in Planck units, and quantum
gravitational effects are, in the conventional effective field theory
framework, small everywhere. Since they can have more entropy than a black hole
of equal mass, monsters are problematic for certain interpretations of black
hole entropy and the AdS/CFT duality.
In the second part of the paper we review recent developments in the
foundations of statistical mechanics which make use of properties of
high-dimensional (Hilbert) spaces. These results primarily depend on kinematics
-- essentially, the geometry of Hilbert space -- and are relatively insensitive
to dynamics. We discuss how this approach might be adopted as a basis for the
statistical mechanics of gravity. Interestingly, monsters and other highly
entropic configurations play an important role.Comment: 9 pages, 4 figures, revtex; invited Brief Review to be published in
Modern Physics Letters
Physical origin underlying the entropy loss upon hydrophobic hydration
The hydrophobic effect (HE) is commonly associated with the demixing of oil
and water at ambient conditions and plays the leading role in determining the
structure and stability of biomolecular assembly in aqueous solutions. On the
molecular scale HE has an entropic origin. It is believed that hydrophobic
particles induce order in the surrounding water by reducing the volume of con-
figuration space available for hydrogen bonding. Here we show with computer
simulation results that this traditional picture is not correct. Analyzing
collective fluctuations in water clusters we are able to provide a
fundamentally new picture of HE based on pronounced many-body correlations
affecting the switching of hydrogen bonds between molecules. These correlations
emerge as a non-local compensation of reduced fluctuations of local
electrostatic fields in the presence of an apolar solute
Protein-Mediated DNA Loops: Effects of Protein Bridge Size and Kinks
This paper focuses on the probability that a portion of DNA closes on itself
through thermal fluctuations. We investigate the dependence of this probability
upon the size r of a protein bridge and/or the presence of a kink at half DNA
length. The DNA is modeled by the Worm-Like Chain model, and the probability of
loop formation is calculated in two ways: exact numerical evaluation of the
constrained path integral and the extension of the Shimada and Yamakawa saddle
point approximation. For example, we find that the looping free energy of a 100
base pairs DNA decreases from 24 kT to 13 kT when the loop is closed by a
protein of r = 10 nm length. It further decreases to 5 kT when the loop has a
kink of 120 degrees at half-length.Comment: corrected typos and figures, references updated; 13 pages, 7 figures,
accepted for publication in Phys. Rev.
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