On C*-algebras related to constrained representations of a free group

We consider representations of the free group $F_2$ on two generators such that the norm of the sum of the generators and their inverses is bounded by $\mu\in[0,4]$. These $\mu$-constrained representations determine a C*-algebra $A_{\mu}$ for each $\mu\in[0,4]$. We prove that these C*-algebras form a continuous bundle of C*-algebras over $[0,4]$ and calculate their K-groups.Comment: 9 page

Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes

The phase transition of Reissner-Nordstr\"om black holes in $(n+1)$-dimensional anti-de Sitter spacetime is studied in details using the thermodynamic analogy between a RN-AdS black hole and a van der Waals liquid gas system. We first investigate critical phenomena of the RN-AdS black hole. The critical exponents of relevant thermodynamical quantities are evaluated. We find identical exponents for a RN-AdS black hole and a Van der Waals liquid gas system. This suggests a possible universality in the phase transitions of these systems. We finally study the thermodynamic behavior using the equilibrium thermodynamic state space geometry and find that the scalar curvature diverges exactly at the van der Waals-like critical point where the heat capacity at constant charge of the black hole diverges.Comment: 18 pages, 5 figure

Well-posedness of the Viscous Boussinesq System in Besov Spaces of Negative Order Near Index s=−1s=-1

This paper is concerned with well-posedness of the Boussinesq system. We prove that the $n$ ($n\ge2$) dimensional Boussinesq system is well-psoed for small initial data $(\vec{u}_0,\theta_0)$ ($\nabla\cdot\vec{u}_0=0$) either in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times{B}^{-1}_{p,r}$ or in ${B^{-1,1}_{\infty,\infty}}\times{B}^{-1,\epsilon}_{p,\infty}$ if $r\in[1,\infty]$, $\epsilon>0$ and $p\in(\frac{n}{2},\infty)$, where $B^{s,\epsilon}_{p,q}$ ($s\in\mathbb{R}$, $1\leq p,q\leq\infty$, $\epsilon>0$) is the logarithmically modified Besov space to the standard Besov space $B^{s}_{p,q}$. We also prove that this system is well-posed for small initial data in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times({B}^{-1}_{\frac{n}{2},1}\cap{B^{-1,1}_{\frac{n}{2},\infty}})$.Comment: 18 page

Soliton with a Pion Field in the Global Color Symmetry Model

We calculate the property of the global color symmetry model soliton with the pion field being included explicitly. The calculated results indicate that the pion field provides a strong attraction so that the eigen-energy of a quark and the mass of a soliton reduce drastically, in contrast to those with only the sigma field.Comment: 15 pages, 2 figure

A tracking algorithm for the stable spin polarization field in storage rings using stroboscopic averaging

Polarized protons have never been accelerated to more than about $25$GeV. To achieve polarized proton beams in RHIC (250GeV), HERA (820GeV), and the TEVATRON (900GeV), ideas and techniques new to accelerator physics are needed. In this publication we will stress an important aspect of very high energy polarized proton beams, namely the fact that the equilibrium polarization direction can vary substantially across the beam in the interaction region of a high energy experiment when no countermeasure is taken. Such a divergence of the polarization direction would not only diminish the average polarization available to the particle physics experiment, but it would also make the polarization involved in each collision analyzed in a detector strongly dependent on the phase space position of the interacting particle. In order to analyze and compensate this effect, methods for computing the equilibrium polarization direction are needed. In this paper we introduce the method of stroboscopic averaging, which computes this direction in a very efficient way. Since only tracking data is needed, our method can be implemented easily in existing spin tracking programs. Several examples demonstrate the importance of the spin divergence and the applicability of stroboscopic averaging.Comment: 39 page

Kinetic pinning and biological antifreezes

Biological antifreezes protect cold-water organisms from freezing. An example are the antifreeze proteins (AFPs) that attach to the surface of ice crystals and arrest growth. The mechanism for growth arrest has not been heretofore understood in a quantitative way. We present a complete theory based on a kinetic model. We use the `stones on a pillow' picture. Our theory of the suppression of the freezing point as a function of the concentration of the AFP is quantitatively accurate. It gives a correct description of the dependence of the freezing point suppression on the geometry of the protein, and might lead to advances in design of synthetic AFPs.Comment: 4 pages, 4 figure

Effects of Electromagnetic Field on the Dynamical Instability of Cylindrical Collapse

The objective of this paper is to discuss the dynamical instability in the context of Newtonian and post Newtonian regimes. For this purpose, we consider non-viscous heat conducting charged isotropic fluid as a collapsing matter with cylindrical symmetry. Darmois junction conditions are formulated. The perturbation scheme is applied to investigate the influence of dissipation and electromagnetic field on the dynamical instability. We conclude that the adiabatic index $\Gamma$ has smaller value for such a fluid in cylindrically symmetric than isotropic sphere

The effects of age on cerebral activations: internally versus externally driven processes

Numerous studies using functional magnetic resonance imaging (fMRI) have described increased or decreased regional brain activations in older as compared to younger adults. This seeming inconsistency may reflect differences in the psychological constructs examined across studies. We hypothesized that behavioral tasks/contrasts engaging internally and externally driven processes are each associated with age-related decreases and increases, respectively, in cerebral activations. We examined the fMRI data of 103 healthy adults, 18–72 years of age, performing a stop signal task (SST), in which a frequent “go” signal triggered a prepotent response and a less frequent “stop” signal prompted inhibition of this response. Greater internally driven processes lead to stop successes (SS) as compared to stop errors (SE), and to speeding up instead of slowing down in go trials. Conversely, externally driven processes contribute to SE trials, which resulted from habitual, unmonitored responses triggered by the go signal (as compared to SS trials), and involved perceptual and cognitive processes elicited by the stop signal (as compared to go trials). Consistent with our hypothesis, the results showed age-related decreases and increases in cerebral activations each during these respective internally and externally driven processes. These findings further elucidate the influence of age on cognitive functioning and provide an additional perspective to understand the imaging literature of aging

Quantum Anomalous Hall Effect in Hg1−y_{1-y}Mny_{y}Te Quantum Wells

The quantum Hall effect is usually observed when the two-dimensional electron gas is subjected to an external magnetic field, so that their quantum states form Landau levels. In this work we predict that a new phenomenon, the quantum anomalous Hall effect, can be realized in Hg$_{1-y}$Mn$_{y}$Te quantum wells, without the external magnetic field and the associated Landau levels. This effect arises purely from the spin polarization of the $Mn$ atoms, and the quantized Hall conductance is predicted for a range of quantum well thickness and the concentration of the $Mn$ atoms. This effect enables dissipationless charge current in spintronics devices.Comment: 5 pages, 3 figures. For high resolution figures see final published version when availabl