17,044 research outputs found
Non-local control in the conduction coefficients: well posedness and convergence to the local limit
We consider a problem of optimal distribution of conductivities in a system
governed by a non-local diffusion law. The problem stems from applications in
optimal design and more specifically topology optimization. We propose a novel
parametrization of non-local material properties. With this parametrization the
non-local diffusion law in the limit of vanishing non-local interaction
horizons converges to the famous and ubiquitously used generalized Laplacian
with SIMP (Solid Isotropic Material with Penalization) material model. The
optimal control problem for the limiting local model is typically ill-posed and
does not attain its infimum without additional regularization. Surprisingly,
its non-local counterpart attains its global minima in many practical
situations, as we demonstrate in this work. In spite of this qualitatively
different behaviour, we are able to partially characterize the relationship
between the non-local and the local optimal control problems. We also
complement our theoretical findings with numerical examples, which illustrate
the viability of our approach to optimal design practitioners
Time-Reversed EPR and the Choice of Histories in Quantum Mechanics
When a single photon is split by a beam splitter, its two `halves' can
entangle two distant atoms into an EPR pair. We discuss a time-reversed
analogue of this experiment where two distant sources cooperate so as to emit a
single photon. The two `half photons,' having interacted with two atoms, can
entangle these atoms into an EPR pair once they are detected as a single
photon. Entanglement occurs by creating indistinguishabilility between the two
mutually exclusive histories of the photon. This indistinguishabilility can be
created either at the end of the two histories (by `erasing' the single
photon's path) or at their beginning (by `erasing' the two atoms' positions).Comment: 6 pages, 5 figures. Presented at the Solvay Conference in Physics,
November 2001, Delphi, Greece. To be published in Quantum Computers and
Computing, 2002 and in the Proceedings of XXII Solvay Conference in Physics.
New York: World Scientific, 200
Nonlocal probes of thermalization in holographic quenches with spectral methods
We describe the application of pseudo-spectral methods to problems of
holographic thermal quenches of relevant couplings in strongly coupled gauge
theories. We focus on quenches of a fermionic mass term in a strongly coupled
N=4 supersymmetric Yang-Mills plasma, and the subsequent equilibration of the
system. From the dual gravitational perspective, we study the gravitational
collapse of a massive scalar field in asymptotically anti-de Sitter geometry
with a prescribed boundary condition for its non-normalizable mode. Access to
the full background geometry of the gravitational collapse allows for the study
of nonlocal probes of the thermalization process. We discuss the evolution of
the apparent and the event horizons, the two-point correlation functions of
operators of large conformal dimensions, and the evolution of the entanglement
entropy of the system. We compare the thermalization process from the viewpoint
of local (the one-point) correlation functions and these nonlocal probes,
finding that the thermalization time as measured by the probes is length
dependent, and approaches the thermalization time of the one-point function for
longer probes. We further discuss how the different energy scales of the
problem contribute to its thermalization.Comment: 83 pages, 25 figures. v2: Corrected constraint in equation (A.26),
which led to non-monotonic apparent horizons in our simulations. Replaced
most figures. Added equation (4.11). Added references [37], [38]. Added
acknowledgement. Corrected some typos. Most conclusions remain unchange
Stochastic symmetry-breaking in a gaussian Hopfield model
We study a ``two-pattern'' Hopfield model with Gaussian disorder. We find
that there are infinitely many pure states at low temperatures in this model,
and we find that the metastate is supported on an infinity of symmetric pairs
of pure states. The origin of this phenomenon is the random breaking of a
rotation symmetry of the distribution of the disorderComment: 31pp, AMSTe
A comparison of two models to predict nitrogen dynamics in organic agricultural systems
Two publicly available crop/soil models were compared. These were the EU-Rotate_N model (www.warwick.ac.uk/go/eurotaten) and the NDICEA model (www.ndicea.nl). Each simulation was also compared to measured data from an organically managed site in the English Midlands. Results showed that, overall, EU-Rotate_N gave a better estimation of soil mineral nitrogen, particularly after the incorporation of a long-term fertility-building crop. This model has a lot of flexibility but is aimed at researchers and requires more work before it is ready to be used by farmers or advisors. The NDICEA model is much simpler to use with a user-friendly interface
Quantum quenches of holographic plasmas
We employ holographic techniques to study quantum quenches at finite
temperature, where the quenches involve varying the coupling of the boundary
theory to a relevant operator with an arbitrary conformal dimension
2\leq\D\leq4. The evolution of the system is studied by evaluating the
expectation value of the quenched operator and the stress tensor throughout the
process. The time dependence of the new coupling is characterized by a fixed
timescale and the response of the observables depends on the ratio of the this
timescale to the initial temperature. The observables exhibit universal scaling
behaviours when the transitions are either fast or slow, i.e. when this ratio
is very small or very large. The scaling exponents are smooth functions of the
operator dimension. We find that in fast quenches, the relaxation time is set
by the thermal timescale regardless of the operator dimension or the precise
quenching rate.Comment: 60 pages, 10 figures, 3 appendice
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