9,735 research outputs found
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
A simple solvable energy landscape model that shows a thermodynamic phase transition and a glass transition
When a liquid melt is cooled, a glass or phase transition can be obtained
depending on the cooling rate. Yet, this behavior has not been clearly captured
in energy landscape models. Here a model is provided in which two key
ingredients are considered based in the landscape, metastable states and their
multiplicity. Metastable states are considered as in two level system models.
However, their multiplicity and topology allows a phase transition in the
thermodynamic limit, while a transition to the glass is obtained for fast
cooling. By solving the corresponding master equation, the minimal speed of
cooling required to produce the glass is obtained as a function of the
distribution of metastable and stable states. This allows to understand cooling
trends due to rigidity considerations in chalcogenide glasses.Comment: 4 pages (letter), 2 figure
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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’
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
Water exchange at a hydrated platinum electrode is rare and collective
We use molecular dynamics simulations to study the exchange kinetics of water
molecules at a model metal electrode surface -- exchange between water
molecules in the bulk liquid and water molecules bound to the metal. This
process is a rare event, with a mean residence time of a bound water of about
40 ns for the model we consider. With analysis borrowed from the techniques of
rare-event sampling, we show how this exchange or desorption is controlled by
(1) reorganization of the hydrogen bond network within the adlayer of bound
water molecules, and by (2) interfacial density fluctuations of the bulk liquid
adjacent to the adlayer. We define collective coordinates that describe the
desorption mechanism. Spatial and temporal correlations associated with a
single event extend over nanometers and tens of picoseconds.Comment: 10 pages, 9 figure
Time scale for the onset of Fickian diffusion in supercooled liquids
We propose a quantitative measure of a time scale on which Fickian diffusion
sets in for supercooled liquids and use Brownian Dynamics computer simulations
to determine the temperature dependence of this onset time in a Lennard-Jones
binary mixture. The time for the onset of Fickian diffusion ranges between 6.5
and 31 times the relaxation time (the relaxation time is the
characteristic relaxation time of the incoherent intermediate scattering
function). The onset time increases faster with decreasing temperature than the
relaxation time. Mean squared displacement at the onset time increases
with decreasing temperature
Thermodynamics of Quantum Jump Trajectories
We apply the large-deviation method to study trajectories in dissipative
quantum systems. We show that in the long time limit the statistics of quantum
jumps can be understood from thermodynamic arguments by exploiting the analogy
between large-deviation and free-energy functions. This approach is
particularly useful for uncovering properties of rare dissipative trajectories.
We also prove, via an explicit quantum mapping, that rare trajectories of one
system can be realized as typical trajectories of an alternative system.Comment: 5 pages, 3 figure
Dynamics on the Way to Forming Glass: Bubbles in Space-time
We review a theoretical perspective of the dynamics of glass forming liquids
and the glass transition. It is a perspective we have developed with our
collaborators during this decade. It is based upon the structure of trajectory
space. This structure emerges from spatial correlations of dynamics that appear
in disordered systems as they approach non-ergodic or jammed states. It is
characterized in terms of dynamical heterogeneity, facilitation and excitation
lines. These features are associated with a newly discovered class of
non-equilibrium phase transitions. Equilibrium properties have little if
anything to do with it. The broken symmetries of these transitions are obscure
or absent in spatial structures, but they are vivid in space-time (i.e.,
trajectory space). In our view, the glass transition is an example of this
class of transitions. The basic ideas and principles we review were originally
developed through the analysis of idealized and abstract models. Nevertheless,
the central ideas are easily illustrated with reference to molecular dynamics
of more realistic atomistic models, and we use that illustrative approach here.Comment: 21 pages, 8 figures. Submitted to Annu. Rev. Phys. Che
Finite-temperature critical point of a glass transition
We generalize the simplest kinetically constrained model of a glass-forming
liquid by softening kinetic constraints, allowing them to be violated with a
small finite rate. We demonstrate that this model supports a first-order
dynamical (space-time) phase transition, similar to those observed with hard
constraints. In addition, we find that the first-order phase boundary in this
softened model ends in a finite-temperature dynamical critical point, which we
expect to be present in natural systems. We discuss links between this critical
point and quantum phase transitions, showing that dynamical phase transitions
in dimensions map to quantum transitions in the same dimension, and hence
to classical thermodynamic phase transitions in dimensions. We make these
links explicit through exact mappings between master operators, transfer
matrices, and Hamiltonians for quantum spin chains.Comment: 10 pages, 5 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
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