Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data

We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Moreover, we consider the extraction of physical observables from the lattice spectrum using the quantization condition. To illustrate the general framework, we calculate the volume-dependent three-particle spectrum in a simple model both below and above the three-particle threshold. The relation to existing approaches is discussed in detail.Comment: 36 pages, 9 figure

Electrolysis-based Parylene Balloon Actuators for Movable Neural Probes

In order to track a specific neuron and keep good sampling neural signals during chronic implantation, the neural probes are highly desired to have moving capability. This paper presents a novel electrolysis-based parylene balloon actuator fabricated with MEMS technology. The actuator is integrated with silicon probe to make it movable. A new fabrication technology has been developed to build a parylene balloon structure with silicon spring structure, electrolysis electrodes and electrolyte inside. By applying little current to electrolysis electrodes, high pressure is generated inside the parylene balloon by electrolysis. The spring structure is stretched with the parylene balloon expansion. Therefore the neural probe is moved by the actuation. The electrolysis actuator can generate large stain and pressure, requires modest electrical power and produces minimal heat. Due to the large volume expansion obtained via electrolysis, the small actuator can create a large force. The new electrolysis actuators for movable neural probes have been fabricated and validated

Electrolysis-based diaphragm actuators

This work presents a new electrolysis-based microelectromechanical systems (MEMS) diaphragm actuator. Electrolysis is a technique for converting electrical energy to pneumatic energy. Theoretically electrolysis can achieve a strain of 136 000% and is capable of generating a pressure above 200 MPa. Electrolysis actuators require modest electrical power and produce minimal heat. Due to the large volume expansion obtained via electrolysis, small actuators can create a large force. Up to 100 µm of movement was achieved by a 3 mm diaphragm. The actuator operates at room temperature and has a latching and reversing capability

Uniform polynomial rates of convergence for a class of L\'evy-driven controlled SDEs arising in multiclass many-server queues

We study the ergodic properties of a class of controlled stochastic differential equations (SDEs) driven by $\alpha$-stable processes which arise as the limiting equations of multiclass queueing models in the Halfin-Whitt regime that have heavy-tailed arrival processes. When the safety staffing parameter is positive, we show that the SDEs are uniformly ergodic and enjoy a polynomial rate of convergence to the invariant probability measure in total variation, which is uniform over all stationary Markov controls resulting in a locally Lipschitz continuous drift. We also derive a matching lower bound on the rate of convergence (under no abandonment). On the other hand, when all abandonment rates are positive, we show that the SDEs are exponentially ergodic uniformly over the above-mentioned class of controls. Analogous results are obtained for L\'evy-driven SDEs arising from multiclass many-server queues under asymptotically negligible service interruptions. For these equations, we show that the aforementioned ergodic properties are uniform over all stationary Markov controls. We also extend a key functional central limit theorem concerning diffusion approximations so as to make it applicable to the models studied here

Normal families and fixed points of iterates

Let F be a family of holomorphic functions and let K be a constant less than 4. Suppose that for all f in F the second iterate of f does not have fixed points for which the modulus of the multiplier is greater than K. We show that then F is normal. This is deduced from a result about the multipliers of iterated polynomials.Comment: 5 page

Analytic Lifshitz black holes in higher dimensions

We generalize the four-dimensional R^2-corrected z=3/2 Lifshitz black hole to a two-parameter family of black hole solutions for any dynamical exponent z and for any dimension D. For a particular relation between the parameters, we find the first example of an extremal Lifshitz black hole. An asymptotically Lifshitz black hole with a logarithmic decay is also exhibited for a specific critical exponent depending on the dimension. We extend this analysis to the more general quadratic curvature corrections for which we present three new families of higher-dimensional D>=5 analytic Lifshitz black holes for generic z. One of these higher-dimensional families contains as critical limits the z=3 three-dimensional Lifshitz black hole and a new z=6 four-dimensional black hole. The variety of analytic solutions presented here encourages to explore these gravity models within the context of non-relativistic holographic correspondence.Comment: 14 page