27,078 research outputs found

    Anomalous reaction-transport processes: the dynamics beyond the Mass Action Law

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    In this paper we reconsider the Mass Action Law (MAL) for the anomalous reversible reaction ABA\rightleftarrows B with diffusion. We provide a mesoscopic description of this reaction when the transitions between two states AA and BB are governed by anomalous (heavy-tailed) waiting-time distributions. We derive the set of mesoscopic integro-differential equations for the mean densities of reacting and diffusing particles in both states. We show that the effective reaction rate memory kernels in these equations and the uniform asymptotic states depend on transport characteristics such as jumping rates. This is in contradiction with the classical picture of MAL. We find that transport can even induce an extinction of the particles such that the density of particles AA or BB tends asymptotically to zero. We verify analytical results by Monte Carlo simulations and show that the mesoscopic densities exhibit a transient growth before decay.Comment: 4 pages, 3 figure

    A survey of low-velocity collisional features in Saturn's F ring

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    Small (~50km scale), irregular features seen in Cassini images to be emanating from Saturn's F ring have been termed mini-jets by Attree et al. (2012). One particular mini-jet was tracked over half an orbital period, revealing its evolution with time and suggesting a collision with a local moonlet as its origin. In addition to these data we present here a much more detailed analysis of the full catalogue of over 800 F ring mini-jets, examining their distribution, morphology and lifetimes in order to place constraints on the underlying moonlet population. We find mini-jets randomly located in longitude around the ring, with little correlation to the moon Prometheus, and randomly distributed in time, over the full Cassini tour to date. They have a tendency to cluster together, forming complicated `multiple' structures, and have typical lifetimes of ~1d. Repeated observations of some features show significant evolution, including the creation of new mini-jets, implying repeated collisions by the same object. This suggests a population of <~1km radius objects with some internal strength and orbits spread over 100km in semi-major axis relative to the F ring but with the majority within 20km. These objects likely formed in the ring under, and were subsequently scattered onto differing orbits by, the perturbing action of Prometheus. This reinforces the idea of the F ring as a region with a complex balance between collisions, disruption and accretion.Comment: 21 pages, 12 figures. Accepted for publication in Icarus. Supplementary information available at http://www.maths.qmul.ac.uk/~attree/mini-jets

    The 10 to the 8th power bit solid state spacecraft data recorder

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    The results are summarized of a program to demonstrate the feasibility of Bubble Domain Memory Technology as a mass memory medium for spacecraft applications. The design, fabrication and test of a partially populated 10 to the 8th power Bit Data Recorder using 100 Kbit serial bubble memory chips is described. Design tradeoffs, design approach and performance are discussed. This effort resulted in a 10 to the 8th power bit recorder with a volume of 858.6 cu in and a weight of 47.2 pounds. The recorder is plug reconfigurable, having the capability of operating as one, two or four independent serial channel recorders or as a single sixteen bit byte parallel input recorder. Data rates up to 1.2 Mb/s in a serial mode and 2.4 Mb/s in a parallel mode may be supported. Fabrication and test of the recorder demonstrated the basic feasibility of Bubble Domain Memory technology for such applications. Test results indicate the need for improvement in memory element operating temperature range and detector performance

    Adequacy of the Weekly Benefit Amount

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    Analysis of complex contagions in random multiplex networks

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    We study the diffusion of influence in random multiplex networks where links can be of rr different types, and for a given content (e.g., rumor, product, political view), each link type is associated with a content dependent parameter cic_i in [0,][0,\infty] that measures the relative bias type-ii links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their "perceived" proportion of active neighbors exceeds a threshold \tau. Namely, a node connected to mim_i active neighbors and kimik_i-m_i inactive neighbors via type-ii links will turn active if cimi/ciki\sum{c_i m_i}/\sum{c_i k_i} exceeds its threshold \tau. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature.Comment: Revised 06/08/12. 11 Pages, 3 figure

    Coexistence of ferro- and antiferromagnetic order in Mn-doped Ni2_2MnGa

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    Ni-Mn-Ga is interesting as a prototype of a magnetic shape-memory alloy showing large magnetic field induced strains. We present here results for the magnetic ordering of Mn-rich Ni-Mn-Ga alloys based on both experiments and theory. Experimental trends for the composition dependence of the magnetization are measured by a vibrating sample magnetometer (VSM) in magnetic fields of up to several tesla and at low temperatures. The saturation magnetization has a maximum near the stoichiometric composition and it decreases with increasing Mn content. This unexpected behaviour is interpreted via first-principles calculations within the density-functional theory. We show that extra Mn atoms are antiferromagnetically aligned to the other moments, which explains the dependence of the magnetization on composition. In addition, the effect of Mn doping on the stabilization of the structural phases and on the magnetic anisotropy energy is demonstrated.Comment: 4 pages, 3 figure
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