Behavior of a Model Dynamical System with Applications to Weak Turbulence

We experimentally explore solutions to a model Hamiltonian dynamical system derived in Colliander et al., 2012, to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus. Our results include a statistical analysis of the evolution of data with localized amplitudes and random phases, which supports the conjecture that energy cascades are a generic phenomenon. We also identify stationary solutions, periodic solutions in an associated problem and find experimental evidence of hyperbolic behavior. Many of our results rely upon reframing the dynamical system using a hydrodynamic formulation.Comment: 22 pages, 14 figure

The Uses of Fear in Preventive Medicine

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A comparison of two magnetic ultra-cold neutron trapping concepts using a Halbach-octupole array

This paper describes a new magnetic trap for ultra-cold neutrons (UCNs) made from a 1.2 m long Halbach-octupole array of permanent magnets with an inner bore radius of 47 mm combined with an assembly of superconducting end coils and bias field solenoid. The use of the trap in a vertical, magneto-gravitational and a horizontal setup are compared in terms of the effective volume and ability to control key systematic effects that need to be addressed in high precision neutron lifetime measurements

Weierstrass's criterion and compact solitary waves

Weierstrass's theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it possible to identify some differential equations for which compact and even semicompact traveling solitary waves exist. In the framework of continuum mechanics, these differential equations correspond to bulk shear waves for a special class of constitutive laws.Comment: 4 page

Creep on seismogenic faults: Insights from analogue earthquake experiments

Tectonic faults display a range of slip behaviors including continuous and episodic slip covering rates of more than 10 orders of magnitude (m/s). The physical control of such kinematic observations remains ambiguous. To gain insight into the slip behavior of brittle faults we performed laboratory stick-slip experiments using a rock analogue, granular material. We realized conditions under which our seismogenic fault analogue shows a variety of slip behaviors ranging from slow, quasi continuous creep to episodic slow slip to dynamic rupture controlled by a limited number of parameters. We explore a wide parameter space by varying loading rate from those corresponding to interseismic to postseismic rates and normal loads equivalent to hydrostatic to lithostatic conditions at seismogenic depth. The experiments demonstrate that significant interseismic creep and earthquakes may not be mutually exclusive phenomena and that creep signals vary systematically with the fault’s seismic potential. Accordingly, the transience of interseismic creep scales with fault strength and seismic coupling as well as with the maturity of the seismic cycle. Loading rate independence of creep signals suggests that mechanical properties of faults (e.g. seismic coupling) can be inferred from shortterm observations (e.g. aftershock sequences). Moreover, we observe the number and size of small episodic slip events to systematically increase towards the end of the seismic cycle providing an observable proxy of the relative shear stress state on seismogenic faults. Modelling the data suggest that for very weak faults in a late stage of their seismic cycle, the observed creep systematics may lead to the chimera of a perennially creeping fault releasing stress by continuous creep and/or transient slow slip instead of large earthquakes

Interseismic deformation transients and precursory phenomena: Insights from stick-slip experiments with a granular fault zone

The release of stress in the lithosphere along active faults shows a wide range of behaviors spanning several spatial and temporal scales. It ranges from short-term localized slip via aseismic slip transients to long-term distributed slip along large fault zones. A single fault can show several of these behaviors in a complementary manner often synchronized in time or space. To study the multiscale fault slip behavior with a focus on interseismic deformation transients we apply a simpli�ed analog model experiment using a rate-and-state-dependent frictional granular material (glass beads) deformed in a ring shear tester. The analog model is able to show, in a reproducible manner, the full spectrum of natural fault slip behavior including transient creep and slow slip events superimposed on regular stick-slip cycles (analog seismic cycles). Analog fault slip behavior is systematically controlled by extrinsic parameters such as the system sti�ness, normal load on the fault, and loading rate. Accordingly, interseismic creep and slow slip events increase quantitatively with decreasing normal load, increasing sti�ness and loading rate. We observe two peculiar features in our analog fault model: (1) Absence of transients in the �final stage of the stick-slip cycle ("preseismic gap") and (2) "scale gaps" separating small interseismic slow (aseismic) events from large (seismic) fast events. Concurrent micromechanical processes, such as dilation, breakdown of force chains and granular packaging a�ect the frictional properties of the experimental fault zone and control interseismic strengthening and coseismic weakening. Additionally, interseismic creep and slip transients have a strong e�ect on the predictability of stress drops and recurrence times. Based on the strong kinematic similiarity between our fault analog and natural faults, our observations may set important constraints for time-dependent seismic hazard models along single faults