Analytic study of the urn model for separation of sand

We present an analytic study of the urn model for separation of sand recently introduced by Lipowski and Droz (Phys. Rev. E 65, 031307 (2002)). We solve analytically the master equation and the first-passage problem. The analytic results confirm the numerical results obtained by Lipowski and Droz. We find that the stationary probability distribution and the shortest one among the characteristic times are governed by the same free energy. We also analytically derive the form of the critical probability distribution on the critical line, which supports their results obtained by numerically calculating Binder cumulants (cond-mat/0201472).Comment: 6 pages including 3 figures, RevTe

Two-way coupling of FENE dumbbells with a turbulent shear flow

We present numerical studies for finitely extensible nonlinear elastic (FENE) dumbbells which are dispersed in a turbulent plane shear flow at moderate Reynolds number. The polymer ensemble is described on the mesoscopic level by a set of stochastic ordinary differential equations with Brownian noise. The dynamics of the Newtonian solvent is determined by the Navier-Stokes equations. Momentum transfer of the dumbbells with the solvent is implemented by an additional volume forcing term in the Navier-Stokes equations, such that both components of the resulting viscoelastic fluid are connected by a two-way coupling. The dynamics of the dumbbells is given then by Newton's second law of motion including small inertia effects. We investigate the dynamics of the flow for different degrees of dumbbell elasticity and inertia, as given by Weissenberg and Stokes numbers, respectively. For the parameters accessible in our study, the magnitude of the feedback of the polymers on the macroscopic properties of turbulence remains small as quantified by the global energy budget and the Reynolds stresses. A reduction of the turbulent drag by up to 20% is observed for the larger particle inertia. The angular statistics of the dumbbells shows an increasing alignment with the mean flow direction for both, increasing elasticity and inertia. This goes in line with a growing asymmetry of the probability density function of the transverse derivative of the streamwise turbulent velocity component. We find that dumbbells get stretched referentially in regions where vortex stretching or bi-axial strain dominate the local dynamics and topology of the velocity gradient tensor.Comment: 20 pages, 10 Postscript figures (Figures 5 and 10 in reduced quality

The New White Flight

White charter school enclaves—defined as charter schools located in school districts that are thirty percent or less white, but that enroll a student body that is fifty percent or greater white— are emerging across the country. The emergence of white charter school enclaves is the result of a sobering and ugly truth: when given a choice, white parents as a collective tend to choose racially segregated, predominately white schools. Empirical research supports this claim. Empirical research also demonstrates that white parents as a collective will make that choice even when presented with the option of a more racially diverse school that is of good academic quality. Despite the connection between collective white parental choice and school segregation, greater choice continues to be injected into the school assignment process. School choice assignment policies, particularly charter schools, are proliferating at a substantial rate. As a result, parental choice rather than systemic design is creating new patterns of racial segregation and inequality in public schools. Yet the Supreme Court’s school desegregation jurisprudence insulates racial segregation in schools ostensibly caused by parental choice rather than systemic design from regulation. Consequently, the new patterns of racial segregation in public schools caused by collective white parental choice largely escapes regulation by courts. This article argues that the time has come to reconsider the legal and normative viability of regulating racial segregation in public schools caused by collective white parental choice. The article makes two important contributions to the legal literature on school desegregation. First, using white charter school enclaves as an example, it documents the ways in which school choice policies are being used to allow whites as a collective to satisfy their preference for segregated predominately white schools. Second, the article sets forth both constitutional and normative arguments for regulating the private choices that result in stark racial segregation patterns in public schools

An explicit KO-degree map and applications

The goal of this note is to study the analog in unstable ${{\mathbb A}^1}$-homotopy theory of the unit map from the motivic sphere spectrum to the Hermitian K-theory spectrum, i.e., the degree map in Hermitian K-theory. We show that "Suslin matrices", which are explicit maps from odd dimensional split smooth affine quadrics to geometric models of the spaces appearing in Bott periodicity in Hermitian K-theory, stabilize in a suitable sense to the unit map. As applications, we deduce that $K^{MW}_i(F) = GW^i_i(F)$ for $i \leq 3$, which can be thought of as an extension of Matsumoto's celebrated theorem describing $K_2$ of a field. These results provide the first step in a program aimed at computing the sheaf $\pi_{n}^{{\mathbb A}^1}({\mathbb A}^n \setminus 0)$ for $n \geq 4$.Comment: 36 Pages, Final version, to appear Journal of Topolog

Roughness-induced critical phenomena in a turbulent flow

I present empirical evidence that turbulent flows are closely analogous to critical phenomena, from a reanalysis of friction factor measurements in rough pipes. The data collapse found here corresponds to Widom scaling near critical points, and implies that a full understanding of turbulence requires explicit accounting for boundary roughness

Children with language delay referred to Dutch speech and hearing centres: caseload characteristics

Background: Early detection and remediation of language disorders are important in helping children to establish appropriate communicative and social behaviour and acquire additional information about the world through the use of language. In the Netherlands, children with (a suspicion of) language disorders are referred to speech and hearing centres for multidisciplinary assessment. Reliable data are needed on the nature of language disorders, as well as the age and source of referral, and the effects of cultural and socioeconomic profiles of the population served in order to plan speech and language therapy service provision. Aims: To provide a detailed description of caseload characteristics of children referred with a possible language disorder by generating more understanding of factors that might influence early identification. Methods & Procedures: A database of 11,450 children was analysed consisting of data on children, aged 2–7 years (70% boys, 30% girls), visiting Dutch speech and hearing centres. The factors analysed were age of referral, ratio of boys to girls, mono- and bilingualism, nature of the language delay, and language profile of the children. Outcomes & Results: Results revealed an age bias in the referral of children with language disorders. On average, boys were referred 5 months earlier than girls, and monolingual children were referred 3 months earlier than bilingual children. In addition, bilingual children seemed to have more complex problems at referral than monolingual children. They more often had both a disorder in both receptive and expressive language, and a language disorder with additional (developmental) problems. Conclusions & Implications: This study revealed a bias in age of referral of young children with language disorders. The results implicate the need for objective language screening instruments and the need to increase the awareness of staff in primary child healthcare of red flags in language development of girls and multilingual children aiming at earlier identification of language disorders in these children. What this paper adds What is already known on the subject Identifying language disorders before children enter school can foster the initiation of early interventions before these problems interfere with formal education and behavioural adjustment. Information on caseload characteristics is important to plan speech and language therapy service provision. There are only a few studies on the caseload characteristics of children at first referral for language assessment. What this paper adds to existing knowle

Wall-Resolved Large Eddy Simulations of Transonic Shock-Induced Flow Separation

This paper reports the wall-resolved large eddy simulations of shock-induced boundary layer separation over an axisymmetric bump for a flow Mach number of 0.875 and a chord-based Reynolds number of 2.763 million. The incoming boundary layer has a momentum-thickness Reynolds number of 6600 at one and a half chord lengths upstream of the leading edge. The calculations simulate the experiment by Bachalo and Johnson (AIAA Journal, Vol. 24, No. 3, 1986), except that the tunnel walls are ignored and the simulations are performed assuming free air with as many as 24 billion grid points. The effects of domain span, grid resolution and time step on the predictions are examined. The results are found to show some sensitivity to the studied parameters. Owing to the outer boundary conditions, the predicted surface pressure distribution as well as the flow separation and reattachment locations tend to agree better with the experimental results from the larger (6 6 ft) tunnel than those from the smaller (2 2 ft) tunnel. The predicted Reynolds shear stress profiles in the separated region differ by as much as 31%from the experimental results that were only obtained in the smaller tunnel. The most accurate surface pressure distribution obtained in this study lies within the scatter of the measurements taken in the two facilities

Effects of gas density on the structure of liquid jets in still gases

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77334/1/AIAA-11098-570.pd

Friction factor for turbulent flow in rough pipes from Heisenberg's closure hypothesis

We show that the main results of the analysis of the friction factor for turbulent pipe flow reported in G. Gioia and P. Chakraborty (GC), Phys. Rev. Lett. 96, 044502 (1996) can be recovered by assuming the Heisenberg closure hypothesis for the turbulent spectrum. This highlights the structural features of the turbulent spectrum underlying GC's analysis.Comment: 19 pages, 7 figures. Accepted for publication in Physical Review

Branching of the Falkner-Skan solutions for λ < 0

The Falkner-Skan equation f'" + ff" + λ(1 - f'^2) = 0, f(0) = f'(0) = 0, is discussed for λ < 0. Two types of problems, one with f'(∞) = 1 and another with f'(∞) = -1, are considered. For λ = 0- a close relation between these two types is found. For λ < -1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f' - 1. The numerical results indicate that the solution branches with f'(∞) = 1 and those with f'(∞) = -1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for λ < -1, is presented.