Hydrodynamic singularities and clustering in a freely cooling inelastic gas

We employ hydrodynamic equations to follow the clustering instability of a freely cooling dilute gas of inelastically colliding spheres into a well-developed nonlinear regime. We simplify the problem by dealing with a one-dimensional coarse-grained flow. We observe that at a late stage of the instability the shear stress becomes negligibly small, and the gas flows solely by inertia. As a result the flow formally develops a finite time singularity, as the velocity gradient and the gas density diverge at some location. We argue that flow by inertia represents a generic intermediate asymptotic of unstable free cooling of dilute inelastic gases.Comment: 4 pages, 4 figure

Reproductive Genetic Testing: Issues and Options for Policymakers

Reproductive genetic testing offers prospective parents information about their risk of having a child with a genetic disease or characteristic. This information can be used to help prospective parents make reproductive decisions both before and during a pregnancy. Before pregnancy, prospective parents who know they have a risk of bearing a child with a genetic disease may choose to avoid pregnancy; use donated eggs, sperm or embryos; adopt, use in vitro fertilization followed by preimplantation genetic diagnosis to select those embryos free of a particular genetic mutation or pursue pregnancy better informed and prepared for the possibility of bearing an affected child. After pregnancy has begun, genetic testing can provide reassurance if tests are negative. Positive prenatal genetic test results can give parents time to prepare for the birth of a child with a particular disorder, or be used as the basis for a decision to terminate the pregnancy. Reproductive genetic testing raises a variety of concerns. Some care most that the tests are accurate and reliable. Yet, unlike drugs and medical devices, genetic tests - including those to test embryos and fetuses - are not required to meet standards of accuracy and reliability before they are marketed. Some agencies within the federal government regulate certain limited aspects of genetic testing, but there are gaps in the regulatory process. A genetic test can only identify the presence of a particular mutation or characteristics. It cannot ascribe social significance to that finding. Some worry about the potential uses of genetic tests. For example, they fear a world in which parents choose their child's height, eye color, intelligence level or other non-health-related trait. While these possibilities are all hypothetical, it is currently possible to choose the sex of one's child, and some believe this use of testing is inappropriate. Some also fear that as testing becomes increasingly available, people will face increased pressure to test, both to have the "very best baby" possible and to avoid the birth of an "unhealthy" child. Some people feel there should be limits on reproductive genetic testing. But what should those limits be? Who should set them? These questions raise ethical, social and legal issues that cannot be resolved by science and technology alone. Finally, concerns have been raised that access to genetic tests is not equitable, and that tests are not being delivered at the right time and with the appropriate context and counseling. To help inform public discussion and facilitate policymaking around these issues, the Genetics and Public Policy Center - funded by The Pew Charitable Trusts - has produced a report, Reproductive Genetic Testing: Issues and Options for Policymakers. This report presents a range of policy options that address genetic testing; it is supported by expert analysis that considers the potential effects, positive and negative, of a variety of different policy directions. The report develops policy options around four key areas of concern: (1) use of tests, (2) safety and accuracy, (3) access and (4) delivery. The options present a range of possible roles that federal and state governments and private entities could play in overseeing the development and use of these technologies, and describe the strengths and weaknesses of each approach. The options were developed by the Center through expert analysis and consultation with a variety of experts representing a wide range of political and religious viewpoints; the options were also informed by the results of the Center's extensive public opinion research. A companion report, Reproductive Genetic Testing: What America Thinks, reveals opinions about how regulation should be implemented and who should control regulation, ranging from no regulation at all to government regulation of both the safety and ethics surrounding the use of these tests

Theory of the vortex matter transformations in high Tc superconductor YBCO

Flux line lattice in type II superconductors undergoes a transition into a "disordered" phase like vortex liquid or vortex glass, due to thermal fluctuations and random quenched disorder. We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg -- Landau approach. The following T-H phase diagram of YBCO emerges. There are just two distinct thermodynamical phases, the homogeneous and the crystalline one, separated by a single first order transitions line. The line however makes a wiggle near the experimentally claimed critical point at 12T. The "critical point" is reinterpreted as a (noncritical) Kauzmann point in which the latent heat vanishes and the line is parallel to the T axis. The magnetization, the entropy and the specific heat discontinuities at melting compare well with experiments.Comment: 4 pages 3 figure

First principles theory of fluctuations in vortex liquids and solids

Consistent perturbation theory for thermodynamical quantities in type II superconductors in magnetic field at low temperatures is developed. It is complementary to the existing expansion valid at high temperatures. Magnetization and specific heat are calculated to two loop order and compare well to existing Monte Carlo simulations and experiments.Comment: 3 .ps fig. In press Phys. Rev.

Isotropic Transverse XY Chain with Energy- and Magnetization Currents

The ground-state correlations are investigated for an isotropic transverse XY chain which is constrained to carry either a current of magnetization J_M or a current of energy J_E. We find that the effect of nonzero J_M on the large-distance decay of correlations is twofold: i) oscillations are introduced and ii) the amplitude of the power law decay increases with increasing current. The effect of energy current is more complex. Generically, correlations in current carrying states are found to decay faster than in the J_E=0 states, contrary to expectations that correlations are increased by the presence of currents. However, increasing the current, one reaches a special line where the correlations become comparable to those of the J_E=0 states. On this line, the symmetry of the ground state is enhanced and the transverse magnetization vanishes. Further increase of the current destroys the extra symmetry but the transverse magnetization remains at the high-symmetry, zero value.Comment: 7 pages, RevTex, 4 PostScript figure

Progress in noncommutative function theory

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. We will show that these spaces of representations can be parameterized as unit balls of certain $W^{*}$-correspondences and the functions can be viewed as Schur class operator functions on these balls. We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory

Why the lowest Landau level approximation works in strongly type II superconductors

Higher than the lowest Landau level contributions to magnetization and specific heat of superconductors are calculated using Ginzburg - Landau equations approach. Corrections to the excitation spectrum around solution of these equations (treated perturbatively) are found. Due to symmetries of the problem leading to numerous cancellations the range of validity of the LLL approximation in mean field is much wider then a naive range and extends all the way down to $H = {H_{c2}(T)}/13$. Moreover the contribution of higher Landau levels is significantly smaller compared to LLL than expected naively. We show that like the LLL part the lattice excitation spectrum at small quasimomenta is softer than that of usual acoustic phonons. This enhanses the effect of fluctuations. The mean field calculation extends to third order, while the fluctuation contribution due to HLL is to one loop. This complements the earlier calculation of the LLL part to two loop order.Comment: 20 pages, Latex file, three figure