Transience and recurrence of random walks on percolation clusters in an ultrametric space

We study existence of percolation in the hierarchical group of order $N$, which is an ultrametric space, and transience and recurrence of random walks on the percolation clusters. The connection probability on the hierarchical group for two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)}, \delta>-1$, with $c_k=C_0+C_1\log k+C_2k^\alpha$, non-negative constants $C_0, C_1, C_2$, and $\alpha>0$. Percolation was proved in Dawson and Gorostiza (2013) for $\delta0$, with $\alpha>2$. In this paper we improve the result for the critical case by showing percolation for $\alpha>0$. We use a renormalization method of the type in the previous paper in a new way which is more intrinsic to the model. The proof involves ultrametric random graphs (described in the Introduction). The results for simple (nearest neighbour) random walks on the percolation clusters are: in the case $\delta<1$ the walk is transient, and in the critical case $\delta=1, C_2>0,\alpha>0$, there exists a critical $\alpha_c\in(0,\infty)$ such that the walk is recurrent for $\alpha<\alpha_c$ and transient for $\alpha>\alpha_c$. The proofs involve graph diameters, path lengths, and electric circuit theory. Some comparisons are made with behaviours of random walks on long-range percolation clusters in the one-dimensional Euclidean lattice.Comment: 27 page

Understanding the Role of Behavior and Cognitions in a Group Exercise Setting

The first purpose of the present study examined whether individuals with different exercise behaviors (classified by attendance) experienced different or similar cognitive patterns. It was hypothesized that different behavior would lead to different cognitive appraisals. It was predicted that there would be a difference between the three behavioral frequency groups with regard to self-efficacy measures and goal measures. The second purpose of the study was to describe, evaluate and observe whether social factors were associated with participating in exercise in groups. It was hypothesized that those who engage in exercise classes would elicit a social focus. Participants for the study included 39 females who registered in-group fitness classes at a mid-sized university. Attendance over the 10-week course was assessed and participants completed a self-report questionnaire during week seven. The attendance data were used to create 3 exercise frequency groups (regular attenders, sporadic attenders, and dropouts) based on ACSM’s exercise guidelines. Analysis of Variance (ANOVA), means and frequencies were used to describe the data. There were no significant differences on measures of self-efficacy. Continued research is necessary to investigate the benefit of social suport in a group exercise setting, as well as to better understand how self-regulation through self-efficacy and goal factors influences and is influenced by actual behavior

Hierarchical equilibria of branching populations

The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group $\Omega_N$ consisting of families of individuals undergoing critical branching random walk and in addition these families also develop according to a critical branching process. Strong transience of the random walk guarantees existence of an equilibrium for this two-level branching system. In the limit $N\to\infty$ (called the hierarchical mean field limit), the equilibrium aggregated populations in a nested sequence of balls $B^{(N)}_\ell$ of hierarchical radius $\ell$ converge to a backward Markov chain on $\mathbb{R_+}$. This limiting Markov chain can be explicitly represented in terms of a cascade of subordinators which in turn makes possible a description of the genealogy of the population.Comment: 62 page

Fabrication and test of lightweight honeycomb sandwich structures Final report

Fabrication and testing of lightweight honeycomb sandwich structure

Twisted semilocal strings in the MSSM

The standard electroweak model is extended by means of a second Brout-Englert-Higgs-doublet. The symmetry breaking potential is chosen is such a way that (i) the Lagrangian possesses a custodial symmetry, (ii) a stationary, axially symmetric ansatz of the bosonic fields consistently reduces the Euler-Lagrange equations to a set of differential equations. The potential involves, in particular, a direct interaction between the two doublets. Stationary, axially-symmetric solutions of the classical equations are constructed. Some of them can be assimilated to embedded Nielsen-Olesen strings. From these solutions there are bifurcations and new solutions appear which exhibit the characteristics of the recently constructed twisted semilocal strings. A special emphasis is set on "doubly-twisted" solutions for which the two doublets present different time-dependent phase factors. They are regular and have a finite energy which can be lower than the energy of the embedded twisted solution. Electric-type solutions, such that the fields oscillate asymptotically far from the symmetry-axis, are also reported.Comment: 17 pages, 11 figures, discussion extended, new solutions obtaine

Study and applications of retrodirective and self-adaptive electromagnetic wave controls to a Mars probe Quarterly report, 1 Oct. - 31 Dec. 1965

Design feasibility and applications of adaptive antenna circuits for deep space communication - antenna concepts, environmental effects, and phase lock loops and adaptive circuitr

Investigation of phase-separated electronic states in 1.5µm GaInNAs/GaAs heterostructures by optical spectroscopy

We report on the comparative electronic state characteristics of particular GaInNAs/GaAs quantum well structures that emit near 1.3 and 1.5 µm wavelength at room temperature. While the electronic structure of the 1.3 µm sample is consistent with a standard quantum well, the 1.5 µm sample demonstrate quite different characteristics. By using photoluminescence sPLd excitation spectroscopy at various detection wavelengths, we demonstrate that the macroscopic electronic states in the 1.5 µm structures originate from phase-separated quantum dots instead of quantum wells. PL measurements with spectrally selective excitation provide further evidence for the existence of composition-separated phases. The evidence is consistent with phase segregation during the growth leading to two phases, one with high In and N content which accounts for the efficient low energy 1.5 µm emission, and the other one having lower In and N content which contributes metastable states and only emits under excitation in a particular wavelength range

Pulmonary arterial remodeling revealed by microfocal x-ray tomography

Animal models and micro-CT imaging are useful for understanding the functional consequences of, and identifying the genes involved in, the remodeling of vascular structures that accompanies pulmonary vascular disease. Using a micro-CT scanner to image contrast-enhanced arteries in excised lungs from fawn hooded rats (a strain genetically susceptible to hypoxia induced pulmonary hypertension), we found that portions of the pulmonary arterial tree downstream from a given diameter were morphometrically indistinguishable. This \u27self-consistency\u27 property provided a means for summarizing the pulmonary arterial tree architecture and mechanical properties using a parameter vector obtained from measurements of the contiguous set of vessel segments comprising the longest (principal) pathway and its branches over a range of vascular pressures. This parameter vector was used to characterize the pulmonary vascular remodeling that occurred in rats exposed to a hypoxic (11.5% oxygen) environment and provided the input to a hemodynamic model relating structure to function. The major effect of the remodeling was a longitudinally (pulmonary artery to arterioles) uniform decrease in vessel distensibility that resulted in a 90% increase in arterial resistance. Despite the almost uniform change in vessel distensibility, over 50% of the resistance increase was attributable to vessels with unstressed diameters less than 125 microns