Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Stability Concepts in Topological Dynamics by Nonstandard Methods

It is known that it is not possible to introduce C⁰ -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rⁿ. Classically these amount to considering the space of all systems on a given subset of Rⁿ as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

Clusters in an assembly of globally coupled bistable oscillators

We study the dynamics of an assembly of globally coupled bistable elements. We show that bistability of elements results in some new features of clustering in the assembly when there is global coupling. We provide conditions for the existence of stable amplitude-phase clusters and splay-phase states. Received 12 June 1998 and Received in final form 30 November 1998     

Statistical mechanics of money: how saving propensity affects its distribution

We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. Analogous to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or equilibrium probability distribution of money. When the agents do not save, the equilibrium money distribution becomes the usual Gibb's distribution, characteristic of non-interacting agents. However with saving, even for individual self-interest, the dynamics becomes cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering properties. Intriguing singularities are observed in the stationary money distribution in the market, as functions of the marginal saving propensity of the agents. Received 2 May 2000     

Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions

We improve the isospin dependent quantum molecular dynamical model by including isospin effects in the Skyrme potential and the momentum dependent interaction to obtain an isospin dependent Skyrme potential and an isospin dependent momentum interaction. We investigate the isospin effects of Skyrme potential and momentum dependent interaction on the isospin fractionation ratio and the dynamical mechanism in intermediate energy heavy ion collisions. It is found that the isospin dependent Skyrme potential and the isospin dependent momentum interaction produce some important isospin effects in the isospin fractionation ratio.     

Strain relaxation and surface morphology of high indium content InAlAs metamorphic buffers with reverse step

Low-temperature step-graded high indium content InAlAs (In% = 0.75) metamorphic buffer layers with reverse step layer grown on GaAs substrate by molecular beam epitaxy are investigated in this paper. The composition and the strain relaxation of the top InAlAs layer are determined by high-resolution triple-axis X-ray diffraction measurements, which show that the top InAlAs layer is nearly fully relaxed and the growth parameters for these samples have little influence on the strain relaxation ratio. Surface morphology is observed by reflection high-energy electron diffraction pattern and atomic force microscopy. The surface morphology is found to depend strongly on both the growth temperature and the As flux. Compared with other samples, the sample growth under the optimized conditions has the smallest value of root mean square surface roughness. Furthermore, the ω − 2θ and ω scans of the triple-axis X-ray diffraction and transmission electron microscopy result also show the sample grown under the optimized conditions has good crystalline quality.     

Thermochemistry of Surfactant-Templating of USY Zeolite

With the aim of understanding the thermochemistry of the introduction of mesoporosity in zeolites by using surfactants, high temperature oxide melt solution calorimetry was used to determine the change in the enthalpy of formation of USY zeolite before and after the introduction of mesoporosity. Our results confirm that this process only slightly destabilizes the zeolite by the additional surface area. However, this can be overcome by the stabilizing effect of the interactions between the surfactant and the zeolite framework.     

Light/Electricity Energy Conversion and Storage for a Hierarchical Porous In2S3@CNT/SS Cathode towards a Flexible Li-CO2 Battery

A photoinduced flexible Li-CO₂ battery with well-designed, hierarchical porous, and free-standing In₂S₃@CNT/SS (ICS) as a bifunctional photoelectrode to accelerate both the CO₂ reduction and evolution reactions (CDRR and CDER) is presented. The photoinduced Li-CO₂ battery achieved a record-high discharge voltage of 3.14 V, surpassing the thermodynamic limit of 2.80 V, and an ultra-low charge voltage of 3.20 V, achieving a round trip efficiency of 98.1 %, which is the highest value ever reported (<80 %) so far. These excellent properties can be ascribed to the hierarchical porous and free-standing structure of ICS, as well as the key role of photogenerated electrons and holes during discharging and charging processes. A mechanism is proposed for pre-activating CO₂ by reducing In³⁺ to In⁺ under light illumination. The mechanism of the bifunctional light-assisted process provides insight into photoinduced Li-CO₂ batteries and contributes to resolving the major setbacks of the system.