Internal displacement reactions in multicomponent oxides: Part II. Oxide solid solutions of wide composition range

As models of internal displacement reactions in oxide solid solutions, the following reactions were studied at 1273 K as a function of time: Fe + NixMg1-x)O = Ni + (FexMg1-x)O Fe + (Co0.5Mg0.5)O = Co + (Fe0.5Mg0.5)O In both reactions, Ni or Co in the starting oxide is displaced by Fe and the γ-(Ni-Fe) or (Co-Fe) alloy is precipitated. In the reaction zone, composition gradients develop in both product phases, viz., the oxide and the alloy precipitate. The Ni (or Co) concentration of the alloy precipitate increases towards the reaction front. In the product oxide, the "inert" Mg diffuses toward the reaction front along with the Fe, while the Ni (or Co) diffusion is in the opposite direction, towards the Fe/boundary. The shape of the composition profiles for Mg and Fe in the product oxide suggests that cross-coefficient terms in the generalized flux equations contribute significantly to the cation flux. The parabolic rate constants of reactions involving Fe/(NixMg1-x)O decrease by nearly four orders of magnitude when x decreases from 1 to 0.1

Internal displacement reactions in multicomponent oxides. Part I. Line compounds with narrow homogeneity range

As a model of an internal displacement reaction involving a ternary oxide "line" compound, the following reaction was studied at 1273 K as a function of time, t: Fe + NiTiO3 = "Ni" + "FeTiO3" Both polycrystalline and single-crystal materials were used as the starting NiTiO3 oxide. During the reaction, the Ni in the oxide compound is displaced by Fe and it precipitates as a γ-(Ni-Fe) alloy. The reaction preserves the starting ilmenite structure. The product oxide has a constant Ti concentration across the reaction zone, with variation in the concentration of Fe and Ni, consistent with ilmenite composition. In the case of single-crystal NiTiO3 as the starting oxide, the γ alloy has a "layered" structure and the layer separation is suggestive of Liesegang-type precipitation. In the case of polycrystalline NiTiO3 as the starting oxide, the alloy precipitates mainly along grain boundaries, with some particles inside the grains. A concentration gradient exists in the alloy across the reaction zone and the composition is >95 at. pct Ni at the reaction front. The parabolic rate constant for the reaction is kp = 1.3 × 10-12 m2 s-1 and is nearly the same for both single-crystal and polycrystalline oxides

Normal Form and Nekhoroshev stability for nearly-integrable Hamiltonian systems with unconditionally slow aperiodic time dependence

The aim of this paper is to extend the results of Giorgilli and Zehnder for aperiodic time dependent systems to a case of general nearly-integrable convex analytic Hamiltonians. The existence of a normal form and then a stability result are shown in the case of a slow aperiodic time dependence that, under some smallness conditions, is independent on the size of the perturbation.Comment: Corrected typo in the title and statement of Lemma 3.

Pressure-induced transient structural change of liquid germanium induced by high-energy picosecond laser pulses

The temporal evolution of the reflectivity of germanium at 514 nm upon irradiation with single high-energy picosecond laser pulses has been measured using a streak camera. It is found that, for a well-defined high fluence range, the reflectivity of the laser-induced molten phase attains a value of 0.85, considerably above the value reported for liquid Ge in thermal equilibrium (0.75). This behavior is consistent with a strong densification of the liquid phase remaining after the explosive vaporization of a thin surface layer. Within the specified fluence interval, this anomalously high reflectivity state is independent of the fluence and lasts tens of nanoseconds. Both characteristics point to the presence of a pressure-induced transient structural change in liquid germanium. © 2005 American Institute of Physics.Peer Reviewe

Reduction of a metapopulation genetic model to an effective one island model

We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than by artificially imposing a fixed population size. The increased complexity of the model is managed by employing techniques often used in the physical sciences, namely exploiting time-scale separation to eliminate fast variables and then constructing an effective model from the slow modes. Remarkably, an initial model with 2$\mathcal{D}$ variables, where $\mathcal{D}$ is the number of islands in the metapopulation, can be reduced to a model with a single variable. We analyze this effective model and show that the predictions for the probability of fixation of the alleles and the mean time to fixation agree well with those found from numerical simulations of the original model.Comment: 16 pages, 4 figures. Supplementary material: 22 pages, 3 figure

Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice

We investigate the connection between local and global dynamics in the Fermi -- Pasta -- Ulam (FPU) $\beta$ -- model from the point of view of stability of its simplest periodic orbits (SPOs). In particular, we show that there is a relatively high $q$ mode $(q=2(N+1)/{3})$ of the linear lattice, having one particle fixed every two oppositely moving ones (called SPO2 here), which can be exactly continued to the nonlinear case for $N=5+3m, m=0,1,2,...$ and whose first destabilization, $E_{2u}$, as the energy (or $\beta$) increases for {\it any} fixed $N$, practically {\it coincides} with the onset of a ``weak'' form of chaos preceding the break down of FPU recurrences, as predicted recently in a similar study of the continuation of a very low ($q=3$) mode of the corresponding linear chain. This energy threshold per particle behaves like $\frac{E_{2u}}{N}\propto N^{-2}$. We also follow exactly the properties of another SPO (with $q=(N+1)/{2}$) in which fixed and moving particles are interchanged (called SPO1 here) and which destabilizes at higher energies than SPO2, since $\frac{E_{1u}}{N}\propto N^{-1}$. We find that, immediately after their first destabilization, these SPOs have different (positive) Lyapunov spectra in their vicinity. However, as the energy increases further (at fixed $N$), these spectra converge to {\it the same} exponentially decreasing function, thus providing strong evidence that the chaotic regions around SPO1 and SPO2 have ``merged'' and large scale chaos has spread throughout the lattice.Comment: Physical Review E, 18 pages, 6 figure

Isomerization dynamics of a buckled nanobeam

We analyze the dynamics of a model of a nanobeam under compression. The model is a two mode truncation of the Euler-Bernoulli beam equation subject to compressive stress. We consider parameter regimes where the first mode is unstable and the second mode can be either stable or unstable, and the remaining modes (neglected) are always stable. Material parameters used correspond to silicon. The two mode model Hamiltonian is the sum of a (diagonal) kinetic energy term and a potential energy term. The form of the potential energy function suggests an analogy with isomerisation reactions in chemistry. We therefore study the dynamics of the buckled beam using the conceptual framework established for the theory of isomerisation reactions. When the second mode is stable the potential energy surface has an index one saddle and when the second mode is unstable the potential energy surface has an index two saddle and two index one saddles. Symmetry of the system allows us to construct a phase space dividing surface between the two "isomers" (buckled states). The energy range is sufficiently wide that we can treat the effects of the index one and index two saddles in a unified fashion. We have computed reactive fluxes, mean gap times and reactant phase space volumes for three stress values at several different energies. In all cases the phase space volume swept out by isomerizing trajectories is considerably less than the reactant density of states, proving that the dynamics is highly nonergodic. The associated gap time distributions consist of one or more `pulses' of trajectories. Computation of the reactive flux correlation function shows no sign of a plateau region; rather, the flux exhibits oscillatory decay, indicating that, for the 2-mode model in the physical regime considered, a rate constant for isomerization does not exist.Comment: 42 pages, 6 figure

Elasticity of semiflexible polymers in two dimensions

We study theoretically the entropic elasticity of a semi-flexible polymer, such as DNA, confined to two dimensions. Using the worm-like-chain model we obtain an exact analytical expression for the partition function of the polymer pulled at one end with a constant force. The force-extension relation for the polymer is computed in the long chain limit in terms of Mathieu characteristic functions. We also present applications to the interaction between a semi-flexible polymer and a nematic field, and derive the nematic order parameter and average extension of the polymer in a strong field.Comment: 16 pages, 3 figure

Three Open Questions for the Design of AI for Music Composition

This paper suggests three open questions for designing AI for music composition by reflecting on interviews with expert and novice composers. Our questions consider the role of AI as a mediator, the importance of a composer’s originality, and AI for building intuition

General Framework for phase synchronization through localized sets

We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange