Border Security: Understanding Threats at U.S. Borders

[Excerpt] The United States confronts a wide array of threats at U.S. borders, ranging from terrorists who may have weapons of mass destruction, to transnational criminals smuggling drugs or counterfeit goods, to unauthorized migrants intending to live and work in the United States. Given this diversity of threats, how may Congress and the Department of Homeland Security (DHS) set border security priorities and allocate scarce enforcement resources? In general, DHS’s answer to this question is organized around risk management, a process that involves risk assessment and the allocation of resources based on a cost-benefit analysis. This report focuses on the first part of this process by identifying border threats and describing a framework for understanding risks at U.S. borders. DHS employs models to classify threats as relatively high- or low-risk for certain planning and budgeting exercises and to implement certain border security programs. Members of Congress may wish to use similar models to evaluate the costs and benefits of potential border security policies and to allocate border enforcement resources. This report discusses some of the issues involved in modeling border-related threats

Two Scenarios of Breaking Chaotic Phase Synchronization

Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break.Comment: 8 pages, 7 figure

A new model for mixing by double-diffusive convection (semi-convection): I. The conditions for layer formation

The process referred to as "semi-convection" in astrophysics and "double-diffusive convection in the diffusive regime" in Earth and planetary sciences, occurs in stellar and planetary interiors in regions which are stable according to the Ledoux criterion but unstable according to the Schwarzschild criterion. In this series of papers, we analyze the results of an extensive suite of 3D numerical simulations of the process, and ultimately propose a new 1D prescription for heat and compositional transport in this regime which can be used in stellar or planetary structure and evolution models. In a preliminary study of the phenomenon, Rosenblum et al. (2011) showed that, after saturation of the primary instability, a system can evolve in one of two possible ways: the induced turbulence either remains homogeneous, with very weak transport properties, or transitions into a thermo-compositional staircase where the transport rate is much larger (albeit still smaller than in standard convection). In this paper, we show that this dichotomous behavior is a robust property of semi-convection across a wide region of parameter space. We propose a simple semi-analytical criterion to determine whether layer formation is expected or not, and at what rate it proceeds, as a function of the background stratification and of the diffusion parameters (viscosity, thermal diffusivity and compositional diffusivity) only. The theoretical criterion matches the outcome of our numerical simulations very adequately in the numerically accessible "planetary" parameter regime, and can easily be extrapolated to the stellar parameter regime. Subsequent papers will address more specifically the question of quantifying transport in the layered case and in the non-layered case.Comment: Submitted to Ap

A new approach to partial synchronization in globally coupled rotators

We develop a formalism to analyze the behaviour of pulse--coupled identical phase oscillators with a specific attention devoted to the onset of partial synchronization. The method, which allows describing the dynamics both at the microscopic and macroscopic level, is introduced in a general context, but then the application to the dynamics of leaky integrate-and-fire (LIF) neurons is analysed. As a result, we derive a set of delayed equations describing exactly the LIF behaviour in the thermodynamic limit. We also investigate the weak coupling regime by means of a perturbative analysis, which reveals that the evolution rule reduces to a set of ordinary differential equations. Robustness and generality of the partial synchronization regime is finally tested both by adding noise and considering different force fields.Comment: 5 pages, 3 eps figure

Approximate resonance states in the semigroup decomposition of resonance evolution

The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.Comment: LaTex 22 pages 3 figure

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Asymptotically stable phase synchronization revealed by autoregressive circle maps

A new type of nonlinear time series analysis is introduced, based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit estimation scheme for the potentially underlying auto-regressive circle map (next phase map) guarantee the invertibility of reconstructed phase space trajectories to the original coordinates. The resulting Fourier approximated, Invertibility enforcing Phase Space map (FIPS map) is well suited to detect conditional asymptotic stability of coupled phases. This rather general synchronization criterion unites two existing generalisations of the old concept and can successfully be applied e.g. to phases obtained from ECG and airflow recordings characterizing cardio-respiratory interaction.Comment: PDF file, 232 KB, 24 pages, 3 figures; cheduled for Phys. Rev. E (Nov) 200

In Memoriam: Charles Wendell Carnahan

Charles Wendell Carnahan, 1903-1961. Ph.B. 1923, J.D. 1925, Univ. of Chicago; LL.M. 1937, Juris.Sc.D., 1942, Columbia Univ. Admitted to practice in Illinois, 1925; Missouri, 1943. Engaged in general practice with several law firms and alone, in Chicago, 1925-1930. Asst. Prof. of Law, Univ. of Louisville, 1930-1935; Assoc. Prof. 1935-1936; Prof. of Law 1936-1938; fellow Columbia Univ. 1936-1937; Prof. of Law, Washington Univ. since 1938; Zumbalen Prof. of the Law of Real Property since 1946. Visiting Prof. Univ. of Texas, Summer 1956. Attorney in home-office of General American Life Ins. Co., half-time 1943-1946. Editor, Cases and Materials on Conflict of Laws (1935). Co-Editor (with Taintor, Brown and Harper), Cases and Materials on Conflict of Laws (1950). Author, Conflict of Laws and Life Insurance Contracts (1942), (2d ed. 1958) ; The Dentist and the Law (1955), and of articles in various Law Reviews

Fingered growth in channel geometry: A Loewner equation approach

A simple model of Laplacian growth is considered, in which the growth takes place only at the tips of long, thin fingers. In a recent paper, Carleson and Makarov used the deterministic Loewner equation to describe the evolution of such a system. We extend their approach to a channel geometry and show that the presence of the side walls has a significant influence on the evolution of the fingers and the dynamics of the screening process, in which longer fingers suppress the growth of the shorter ones