10,694 research outputs found
Thermodynamics of Coarse Grained Models of Super-Cooled Liquids
In recent papers, we have argued that kinetically constrained coarse grained
models can be applied to understand dynamic properties of glass forming
materials, and we have used this approach in various applications that appear
to validate this view. In one such paper [J.P. Garrahan and D. Chandler, Proc.
Nat. Acad. Sci. USA 100, 9710 (2003)], among other things we argued that this
approach also explains why the heat capacity discontinuity at the glass
transition is generally larger for fragile materials than for strong materials.
In the preceding article, Biroli, Bouchaud and Tarjus (BB&T) [cond-mat/0412024]
have objected to our explanation on this point, arguing that the class of
models we apply is inconsistent with both the absolute size and temperature
dependence of the experimental specific heat. Their argument, however, neglects
parameters associated with the coarse graining. Accounting for these
parameters, we show here that our treatment of dynamics is not inconsistent
with heat capacity discontinuities.Comment: 5 pages, 2 figures. Revised version to appear in J. Chem. Phy
Pursuit on a Graph Using Partial Information
The optimal control of a "blind" pursuer searching for an evader moving on a
road network and heading at a known speed toward a set of goal vertices is
considered. To aid the "blind" pursuer, certain roads in the network have been
instrumented with Unattended Ground Sensors (UGSs) that detect the evader's
passage. When the pursuer arrives at an instrumented node, the UGS therein
informs the pursuer if and when the evader visited the node. The pursuer's
motion is not restricted to the road network. In addition, the pursuer can
choose to wait/loiter for an arbitrary time at any UGS location/node. At time
0, the evader passes by an entry node on his way towards one of the exit nodes.
The pursuer also arrives at this entry node after some delay and is thus
informed about the presence of the intruder/evader in the network, whereupon
the chase is on - the pursuer is tasked with capturing the evader. Because the
pursuer is "blind", capture entails the pursuer and evader being collocated at
an UGS location. If this happens, the UGS is triggered and this information is
instantaneously relayed to the pursuer, thereby enabling capture. On the other
hand, if the evader reaches one of the exit nodes without being captured, he is
deemed to have escaped. We provide an algorithm that computes the maximum
initial delay at the entry node for which capture is guaranteed. The algorithm
also returns the corresponding optimal pursuit policy
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An integral equation method for a boundary value problem arising in unsteady water wave problems
In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result
is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem.
Keywords. Boundary integral equation method, Water waves, Laplace’
Computer Assembly of Cluster-Forming Amphiphilic Dendrimers
Recent theoretical studies have predicted a new clustering mechanism for soft
matter particles that interact via a certain kind of purely repulsive, bounded
potentials. At sufficiently high densities, clusters of overlapping particles
are formed in the fluid, which upon further compression crystallize into cubic
lattices with density-independent lattice constants. In this work we show that
amphiphilic dendrimers are suitable colloids for the experimental realization
of this phenomenon. Thereby, we pave the way for the synthesis of such
macromolecules, which form the basis for a novel class of materials with
unusual properties.Comment: 4 pages, 4 figures, 1 tabl
The Most Detailed Picture Yet of an Embedded High-mass YSO
High-mass star formation is not well understood chiefly because examples are
deeply embedded, relatively distant, and crowded with sources of emission.
Using VLA and VLBA observations of water and SiO maser emission, we have mapped
in detail the structure and proper motion of material 20-500 AU from the
closest high-mass YSO, radio source-I in the Orion KL region. We observe
streams of material driven in a rotating, wide angle, bipolar wind from the
surface of an edge-on accretion disk. The example of source-I provides strong
evidence that high-mass star formation proceeds via accretionComment: typo corrected and word added to abstract 6 pages including 4 B&W
figures. To appear in the Proceeding of IAU Symposium 221, Star Formation at
High Angular Resolution, Editors M. Burton, R. Jayawardhana & T. Bourke,
Astronomical Society of the Pacifi
Dynamical Exchanges in Facilitated Models of Supercooled liquids
We investigate statistics of dynamical exchange events in coarse--grained
models of supercooled liquids in spatial dimensions , 2, and 3. The
models, based upon the concept of dynamical facilitation, capture generic
features of statistics of exchange times and persistence times. Here,
distributions for both times are related, and calculated for cases of strong
and fragile glass formers over a range of temperatures. Exchange time
distributions are shown to be particularly sensitive to the model parameters
and dimensions, and exhibit more structured and richer behavior than
persistence time distributions. Mean exchange times are shown to be Arrhenius,
regardless of models and spatial dimensions. Specifically, , with being the excitation concentration. Different dynamical
exchange processes are identified and characterized from the underlying
trajectories. We discuss experimental possibilities to test some of our
theoretical findings.Comment: 11 pages, 14 figures, minor corrections made, paper published in
Journal of Chemical Physic
The projection of a nonlocal mechanical system onto the irreversible generalized Langevin equation, II: Numerical simulations
The irreversible generalized Langevin equation (iGLE) contains a
nonstationary friction kernel that in certain limits reduces to the GLE with
space-dependent friction. For more general forms of the friction kernel, the
iGLE was previously shown to be the projection of a mechanical system with a
time-dependent Hamiltonian. [R. Hernandez, J. Chem. Phys. 110, 7701 (1999)] In
the present work, the corresponding open Hamiltonian system is further
explored. Numerical simulations of this mechanical system illustrate that the
time dependence of the observed total energy and the correlations of the
solvent force are in precise agreement with the projected iGLE.Comment: 8 pages, 9 figures, submitted to J. Chem. Phy
A statistical mechanics framework for static granular matter
The physical properties of granular materials have been extensively studied
in recent years. So far, however, there exists no theoretical framework which
can explain the observations in a unified manner beyond the phenomenological
jamming diagram [1]. This work focuses on the case of static granular matter,
where we have constructed a statistical ensemble [2] which mirrors equilibrium
statistical mechanics. This ensemble, which is based on the conservation
properties of the stress tensor, is distinct from the original Edwards ensemble
and applies to packings of deformable grains. We combine it with a field
theoretical analysis of the packings, where the field is the Airy stress
function derived from the force and torque balance conditions. In this
framework, Point J characterized by a diverging stiffness of the pressure
fluctuations. Separately, we present a phenomenological mean-field theory of
the jamming transition, which incorporates the mean contact number as a
variable. We link both approaches in the context of the marginal rigidity
picture proposed by [3, 4].Comment: 21 pages, 15 figure
Spin-torque switching: Fokker-Planck rate calculation
We describe a new approach to understanding and calculating magnetization
switching rates and noise in the recently observed phenomenon of "spin-torque
switching". In this phenomenon, which has possible applications to information
storage, a large current passing from a pinned ferromagnetic (FM) layer to a
free FM layer switches the free layer. Our main result is that the spin-torque
effect increases the Arrhenius factor in the switching rate, not
by lowering the barrier , but by raising the effective spin temperature .
To calculate this effect quantitatively, we extend Kramers' 1940 treatment of
reaction rates, deriving and solving a Fokker-Planck equation for the energy
distribution including a current-induced spin torque of the Slonczewski type.
This method can be used to calculate slow switching rates without long-time
simulations; in this Letter we calculate rates for telegraph noise that are in
good qualitative agreement with recent experiments. The method also allows the
calculation of current-induced magnetic noise in CPP (current perpendicular to
plane) spin valve read heads.Comment: 11 pages, 8 figures, 1 appendix Original version in Nature format,
replaced by Phys. Rev. Letters format. No substantive change
Molecular packing and chemical association in liquid water simulated using ab initio hybrid Monte Carlo and different exchange-correlation functionals
In the free energy of hydration of a solute, the chemical contribution is
given by the free energy required to expel water molecules from the
coordination sphere and the packing contribution is given by the free energy
required to create the solute-free coordination sphere (the observation volume)
in bulk water. With the SPC/E water model as a reference, we examine the
chemical and packing contributions in the free energy of water simulated using
different electron density functionals. The density is fixed at a value
corresponding to that for SPC/E water at a pressure of 1 bar. The chemical
contribution shows that water simulated at 300 K with BLYP is somewhat more
tightly bound than water simulated at 300 K with the revPBE functional or at
350 K with the BLYP and BLYP-D functionals. The packing contribution for
various radii of the observation volume is studied. In the size range where the
distribution of water molecules in the observation volume is expected to be
Gaussian, the packing contribution is expected to scale with the volume of the
observation sphere. Water simulated at 300 K with the revPBE and at 350 K with
BLYP-D or BLYP conforms to this expectation, but the results suggest an earlier
onset of system size effects in the BLYP 350 K and revPBE 300 K systems than
that observed for either BLYP-D 350 K or SPC/E. The implication of this
observation for constant pressure simulations is indicated. For water simulated
at 300 K with BLYP, in the size range where Gaussian distribution of occupation
is expected, we instead find non-Gaussian behavior, and the packing
contribution scales with surface area of the observation volume, suggesting the
presence of heterogeneities in the system
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