Single crystal growth from light, volatile, and reactive materials using lithium and calcium flux

We present a method for the solution growth of single crystals from reactive Li and Ca melts and its application to the synthesis of several, representative compounds. Among these, single crystalline Li3N, Li2(Li{1-x}Tx)N with T = {Mn, Fe, Co}, LiCaN, Li2C2, LiRh, and LiIr from Li-rich flux as well as Ca2N, CaNi2, CaNi3, YbNi2, Y2Ni7, and LaNi5 from Ca-rich flux could be obtained. Special emphasize is given on the growth of nitrides using commercially available Li3N and Ca3N2 powders as the nitrogen source instead of N2 gas.Comment: 40 pages, 20 figures, reference list update

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