Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows

G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are Hamilton-Jacobi equations with convex ($L^1$ type) but non-coercive Hamiltonians. Viscous G-equations arise from either numerical approximations or regularizations by small diffusion. The nonlinear eigenvalue $\bar H$ from the cell problem of the viscous G-equation can be viewed as an approximation of the inviscid turbulent flame speed $s_T$. An important problem in turbulent combustion theory is to study properties of $s_T$, in particular how $s_T$ depends on the flow amplitude $A$. In this paper, we will study the behavior of $\bar H=\bar H(A,d)$ as $A\to +\infty$ at any fixed diffusion constant $d > 0$. For the cellular flow, we show that $$\bar H(A,d)\leq O(\sqrt {\mathrm {log}A}) \quad \text{for all $d>0$}.$$ Compared with the inviscid G-equation ($d=0$), the diffusion dramatically slows down the front propagation. For the shear flow, the limit \nit $\lim_{A\to +\infty}{\bar H(A,d)\over A} = \lambda (d) >0$ where $\lambda (d)$ is strictly decreasing in $d$, and has zero derivative at $d=0$. The linear growth law is also valid for $s_T$ of the curvature dependent G-equation in shear flows.Comment: 27 pages. We improve the upper bound from no power growth to square root of log growt

Ground state of a polydisperse electrorheological solid: Beyond the dipole approximation

The ground state of an electrorheological (ER) fluid has been studied based on our recently proposed dipole-induced dipole (DID) model. We obtained an analytic expression of the interaction between chains of particles which are of the same or different dielectric constants. The effects of dielectric constants on the structure formation in monodisperse and polydisperse electrorheological fluids are studied in a wide range of dielectric contrasts between the particles and the base fluid. Our results showed that the established body-centered tetragonal ground state in monodisperse ER fluids may become unstable due to a polydispersity in the particle dielectric constants. While our results agree with that of the fully multipole theory, the DID model is much simpler, which offers a basis for computer simulations in polydisperse ER fluids.Comment: Accepted for publications by Phys. Rev.

Characterizations of Cross-Bridges in the Presence of Saturating Concentrations of MgAMP-PNP in Rabbit Permeabilized Psoas Muscle

Several earlier studies have led to different conclusions about the complex of myosin with MgAMP-PNP. It has been suggested that subfragment 1 of myosin (S1)-MgAMP-PNP forms an S1-MgADP-like state, an intermediate between the myosin S1-MgATP and myosin S1-MgADP states or a mixture of cross-bridge states. We suggest that the different states observed result from the failure to saturate S1 with MgAMP-PNP. At saturating MgAMP-PNP, the interaction of myosin S1 with actin is very similar to that which occurs in the presence of MgATP. 1) At 1°C and 170 mM ionic strength the equatorial x-ray diffraction intensity ratio I11/I10 decreased with an increasing MgAMP-PNP concentration and leveled off by ∼20 mM MgAMP-PNP. The resulting ratio was the same for MgATP-relaxed fibers. 2) The two dimensional x-ray diffraction patterns from MgATP-relaxed and MgAMP-PNP-relaxed bundles are similar. 3) The affinity of S1-MgAMP-PNP for the actin-tropomyosin-troponin complex in solution in the absence of free calcium is comparable with that of S1-MgATP. 4) In the presence of calcium, I11/I10 decreased toward the relaxed value with increasing MgAMP-PNP, signifying that the affinity between cross-bridge and actin is weakened by MgAMP-PNP. 5) The degree to which the equatorial intensity ratio decreases as the ionic strength increases is similar in MgAMP-PNP and MgATP. Therefore, results from both fiber and solution studies suggest that MgAMP-PNP acts as a non hydrolyzable MgATP analogue for myosin

Privacy Architectures: Reasoning About Data Minimisation and Integrity

Privacy by design will become a legal obligation in the European Community if the Data Protection Regulation eventually gets adopted. However, taking into account privacy requirements in the design of a system is a challenging task. We propose an approach based on the specification of privacy architectures and focus on a key aspect of privacy, data minimisation, and its tension with integrity requirements. We illustrate our formal framework through a smart metering case study.Comment: appears in STM - 10th International Workshop on Security and Trust Management 8743 (2014

Approach to the semiconductor cavity QED in high-Q regimes with q-deformed boson

The high density Frenkel exciton which interacts with a single mode microcavity field is dealed with in the framework of the q-deformed boson. It is shown that the q-defomation of bosonic commutation relations is satisfied naturally by the exciton operators when the low density limit is deviated. An analytical expression of the physical spectrum for the exciton is given by using of the dressed states of the cavity field and the exciton. We also give the numerical study and compare the theoretical results with the experimental resultsComment: 6 pages, 2 figure

Impurity Energy Level Within The Haldane Gap

An impurity bond $J{'}$ in a periodic 1D antiferromagnetic, spin 1 chain with exchange $J$ is considered. Using the numerical density matrix renormalization group method, we find an impurity energy level in the Haldane gap, corresponding to a bound state near the impurity bond. When $J{'}<J$ the level changes gradually from the edge of the Haldane gap to the ground state energy as the deviation $dev=(J-J{'})/J$ changes from 0 to 1. It seems that there is no threshold. Yet, there is a threshold when $J{'}>J$. The impurity level appears only when the deviation $dev=(J{'}-J)/J{'}$ is greater than $B_{c}$, which is near 0.3 in our calculation.Comment: Latex file,9 pages uuencoded compressed postscript including 4 figure

Adiponectin Prevents Diabetic Premature Senescence of Endothelial Progenitor Cells and Promotes Endothelial Repair by Suppressing the p38 MAP Kinase/p16INK4A Signaling Pathway

OBJECTIVE - A reduced number of circulating endothelial progenitor cells (EPCs) are casually associated with the cardiovascular complication of diabetes. Adiponectin exerts multiple protective effects against cardiovascular disease, independent of its insulin-sensitizing activity. The objective of this study was to investigate whether adiponectin plays a role in modulating the bioavailability of circulating EPCs and endothelial repair. RESEARCH DESIGN AND METHODS - Adiponectin knockout mice were crossed with db+/- mice to produce db/db diabetic mice without adiponectin. Circulating number of EPCs were analyzed by flow cytometry. Reendothelialization was evaluated by staining with Evans blue after wire-induced carotid injury. RESULTS - In adiponectin knockout mice, the number of circulating EPCs decreased in an age-dependent manner compared with the wild-type controls, and this difference was reversed by the chronic infusion of recombinant adiponectin. In db/db diabetic mice, the lack of adiponectin aggravated the hyperglycemia-induced decrease in circulating EPCs and also diminished the stimulatory effects of the PPARγ agonist rosiglitazone on EPC production and reendothelialization. In EPCs isolated from both human peripheral blood and mouse bone marrow, treatment with adiponectin prevented high glucose-induced premature senescence. At the molecular level, adiponectin decreased high glucose-induced accumulation of intracellular reactive oxygen species and consequently suppressed activation of p38 MAP kinase (MAPK) and expression of the senescence marker p16INK4A. CONCLUSIONS - Adiponectin prevents EPC senescence by inhibiting the ROS/p38 MAPK/p16 INK4A signaling cascade. The protective effects of adiponectin against diabetes vascular complications are attributed in part to its ability to counteract hyperglycemia-mediated decrease in the number of circulating EPCs. © 2010 by the American Diabetes Association.published_or_final_versio

Coherent States for Quantum Compact Groups

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the $q$--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}Comment: 25 page

Superradiance of low density Frenkel excitons in a crystal slab of three-level atoms: Quantum interference effect

We systematically study the fluorescence of low density Frenkel excitons in a crystal slab containing $N_T$ V-type three-level atoms. Based on symmetric quasi-spin realization of SU(3) in large $N$ limit, the two-mode exciton operators are invoked to depict various collective excitations of the collection of these V-type atoms starting from their ground state. By making use of the rotating wave approximation, the light intensity of radiation for the single lattice layer is investigated in detail. As a quantum coherence effect, the quantum beat phenomenon is discussed in detail for different initial excitonic states. We also test the above results analytically without the consideration of the rotating wave approximation and the self-interaction of radiance field is also included.Comment: 18pages, 17 figures. Resubmit to Phys. Rev.