Checking the validity of truncating the cumulant hierarchy description of a small system

We analyze the behavior of the first few cumulant in an array with a small number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf 19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global coupling and derived an infinite hierarchy of differential equations for the cumulant moments. They focused on the behavior of infinite size systems using a strategy based on truncating the hierarchy. In this work we explore the reliability of such an approach to describe systems with a small number of elements. We carry out an extensive numerical analysis of the truncated hierarchy as well as numerical simulations of the full set of Langevin equations governing the dynamics. We find that the results provided by the truncated hierarchy for finite systems are at variance with those of the Langevin simulations for large regions of parameter space. The truncation of the hierarchy leads to a dependence on initial conditions and to the coexistence of states which are not consistent with the theoretical expectations based on the multidimensional linear Fokker-Planck equation for finite arrays

A unified approach for the solution of the Fokker-Planck equation

This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation. The unified features of the discrete singular convolution algorithm are discussed. It is demonstrated that different implementations of the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. Three benchmark stochastic systems, the repulsive Wong process, the Black-Scholes equation and a genuine nonlinear model, are employed to illustrate the robustness and to test accuracy of the present approach for the solution of the Fokker-Planck equation via a time-dependent method. An additional example, the incompressible Euler equation, is used to further validate the present approach for more difficult problems. Numerical results indicate that the present unified approach is robust and accurate for solving the Fokker-Planck equation.Comment: 19 page

Assembling the puzzle of superconducting elements: A Review

Superconductivity in the simple elements is of both technological relevance and fundamental scientific interest in the investigation of superconductivity phenomena. Recent advances in the instrumentation of physics under pressure have enabled the observation of superconductivity in many elements not previously known to superconduct, and at steadily increasing temperatures. This article offers a review of the state of the art in the superconductivity of elements, highlighting underlying correlations and general trends.Comment: Review, 10 pages, 11 figures, 97 references; to appear in Superc. Sci. Techno

Control of Spatial-Temporal Congested Traffic Patterns at Highway Bottlenecks

A microscopic theory of control of spatial-temporal congested traffic pattern at freeway bottlenecks is presented. Based on empirical spatial-temporal features of congested patterns at freeway bottlenecks which have recently been found, different control strategies for prevention or reducing of the patterns are simulated and compared. The studied control strategies include the on-ramp metering with feedback and automatic cruise control (ACC) vehicles. A recent microscopic traffic flow model within the author's three-phase traffic theory is used for validation of spatial-temporal congested pattern control.Comment: 19 pages, 7 figure

Petrophysical, Geochemical, and Hydrological Evidence for Extensive Fracture-Mediated Fluid and Heat Transport in the Alpine Fault's Hanging-Wall Damage Zone

Fault rock assemblages reflect interaction between deformation, stress, temperature, fluid, and chemical regimes on distinct spatial and temporal scales at various positions in the crust. Here we interpret measurements made in the hanging-wall of the Alpine Fault during the second stage of the Deep Fault Drilling Project (DFDP-2). We present observational evidence for extensive fracturing and high hanging-wall hydraulic conductivity (∼10−9 to 10−7 m/s, corresponding to permeability of ∼10−16 to 10−14 m2) extending several hundred meters from the fault's principal slip zone. Mud losses, gas chemistry anomalies, and petrophysical data indicate that a subset of fractures intersected by the borehole are capable of transmitting fluid volumes of several cubic meters on time scales of hours. DFDP-2 observations and other data suggest that this hydrogeologically active portion of the fault zone in the hanging-wall is several kilometers wide in the uppermost crust. This finding is consistent with numerical models of earthquake rupture and off-fault damage. We conclude that the mechanically and hydrogeologically active part of the Alpine Fault is a more dynamic and extensive feature than commonly described in models based on exhumed faults. We propose that the hydrogeologically active damage zone of the Alpine Fault and other large active faults in areas of high topographic relief can be subdivided into an inner zone in which damage is controlled principally by earthquake rupture processes and an outer zone in which damage reflects coseismic shaking, strain accumulation and release on interseismic timescales, and inherited fracturing related to exhumation

Theoretical Criteria for Scattering Dark States in Nanostructured Particles

Nanostructures with multiple resonances can exhibit a suppressed or even completely eliminated scattering of light, called a scattering dark state. We describe this phenomenon with a general treatment of light scattering from a multiresonant nanostructure that is spherical or nonspherical but subwavelength in size. With multiple resonances in the same channel (i.e., same angular momentum and polarization), coherent interference always leads to scattering dark states in the low-absorption limit, regardless of the system details. The coupling between resonances is inevitable and can be interpreted as arising from far-field or near-field. This is a realization of coupled-resonator-induced transparency in the context of light scattering, which is related to but different from Fano resonances. Explicit examples are given to illustrate these concepts.Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (Contract W911NF-13-D-0001)National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Grant DMR-0819762

Traffic and Related Self-Driven Many-Particle Systems

Since the subject of traffic dynamics has captured the interest of physicists, many astonishing effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by so-called ``phantom traffic jams'', although they all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction of the traffic volume cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize in lanes, while similar systems are ``freezing by heating''? Why do self-organizing systems tend to reach an optimal state? Why do panicking pedestrians produce dangerous deadlocks? All these questions have been answered by applying and extending methods from statistical physics and non-linear dynamics to self-driven many-particle systems. This review article on traffic introduces (i) empirically data, facts, and observations, (ii) the main approaches to pedestrian, highway, and city traffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts like a general modelling framework for self-driven many-particle systems, including spin systems. Subjects such as the optimization of traffic flows and relations to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are discussed as well.Comment: A shortened version of this article will appear in Reviews of Modern Physics, an extended one as a book. The 63 figures were omitted because of storage capacity. For related work see http://www.helbing.org

Bedrock geology of DFDP-2B, central Alpine Fault, New Zealand

<p>During the second phase of the Alpine Fault, Deep Fault Drilling Project (DFDP) in the Whataroa River, South Westland, New Zealand, bedrock was encountered in the DFDP-2B borehole from 238.5–893.2 m Measured Depth (MD). Continuous sampling and meso- to microscale characterisation of whole rock cuttings established that, in sequence, the borehole sampled amphibolite facies, Torlesse Composite Terrane-derived schists, protomylonites and mylonites, terminating 200–400 m above an Alpine Fault Principal Slip Zone (PSZ) with a maximum dip of 62°. The most diagnostic structural features of increasing PSZ proximity were the occurrence of shear bands and reduction in mean quartz grain sizes. A change in composition to greater mica:quartz + feldspar, most markedly below c. 700 m MD, is inferred to result from either heterogeneous sampling or a change in lithology related to alteration. Major oxide variations suggest the fault-proximal Alpine Fault alteration zone, as previously defined in DFDP-1 core, was not sampled.</p

Type I Interferons Induce T Regulatory 1 Responses and Restrict Humoral Immunity during Experimental Malaria

We thank Christopher Hunter and Bob Axtell for critical feedback, and the Flow Cytometry Laboratory at OUHSC for technical assistance.Author Summary Humoral immunity is essential for host resistance to pathogens that trigger highly inflammatory immune responses, including Plasmodium parasites, the causative agents of malaria. Long-lived, secreted antibody responses depend on a specialized subset of CD4 T cells called T follicular helper (Tfh) cells. However, anti-Plasmodium humoral immunity is often short-lived, non-sterilizing, and immunity rapidly wanes, leaving individuals susceptible to repeated bouts of malaria. Here we explored the relationship between inflammatory type I interferons, the regulation of pathogen-specific CD4 T cell responses, and humoral immunity using models of experimental malaria and systemic virus infection. We identified that type I interferons promote the formation and accumulation of pathogen-specific CD4 T regulatory 1 cells that co-express interferon-gamma and interleukin-10. Moreover, we show that the combined activity of interferon-gamma and interleukin-10 limits the magnitude of infection-induced Tfh responses, the secretion of parasite-specific secreted antibody, and parasite control. Our study provides new insight into the regulation of T regulatory 1 responses and humoral immunity during inflammatory immune reactions against systemic infections.Yeshttp://www.plospathogens.org/static/editorial#pee