RF circulator structures via offset lithography

Further developments are reported of the conductive lithographic film (CLF) process in which components of radio-frequency circulators are fabricated economically via offset lithography. The performance of centre conductor elements printed from silver-loaded inks on polymer substrates is compared with that of conventional solid copper structures

On the Fluctuation Relation for Nose-Hoover Boundary Thermostated Systems

We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas of particles, and the thermostats are modelled by two Nos\'e-Hoover thermostats applied at the boundaries of the system. The transient fluctuation relation, which holds only for a precise choice of the initial ensemble, is verified at all times, as expected. Times longer than the mesoscopic scale, needed for local equilibrium to be settled, are required if a different initial ensemble is considered. This shows how the transient fluctuation relation asymptotically leads to the steady state relation when, as explicitly checked in our systems, the condition found in [D.J. Searles, {\em et al.}, J. Stat. Phys. 128, 1337 (2007)], for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase space contraction rate \zL and of the dissipation function \zW, a similar relaxation regime at shorter averaging times is found. The quantity \zW satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale; the quantity \zL appears to begin a monotonic convergence after such times. This is consistent with the fact that \zW and \zL differ by a total time derivative, and that the tails of the probability distribution function of \zL are Gaussian.Comment: Major revision. Fig.10 was added. Version to appear in Journal of Statistical Physic

Printed analogue filter structures

The authors report progress in conductive lithographic film (CLF) technology, which uses the offset lithographic printing process to form electrically conductive patterns on flexible substrates. Networks of planar passive components and interconnects fabricated simultaneously via the CLF process form notch filter networks at 85 kHz

Lyapunov Exponent Pairing for a Thermostatted Hard-Sphere Gas under Shear in the Thermodynamic Limit

We demonstrate why for a sheared gas of hard spheres, described by the SLLOD equations with an iso-kinetic Gaussian thermostat in between collisions, deviations of the conjugate pairing rule for the Lyapunov spectrum are to be expected, employing a previous result that for a large number of particles $N$, the iso-kinetic Gaussian thermostat is equivalent to a constant friction thermostat, up to $1/\sqrt{N}$ fluctuations. We also show that these deviations are at most of the order of the fourth power in the shear rate.Comment: 4 pages, to appear in Rapid Comm., Phys. Rev.

The Steady State Fluctuation Relation for the Dissipation Function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.Comment: 30 pages, 1 figur

Biominerals - source and inspiration for novel advanced materials

Biomineralization seems an odd sort of word. How can you combine biology and minerals? However, a quick look around brings to light many familiar objects that are examples of biominerals. Most dramatic are the coral reefs and sea shells of the marine environment (calcium carbonate) and human bone and teeth (calcium hydroxyapatite) but there are many other examples. In the past 10 years, an increasing number of biominerals has been reported (Table 1). Interest in the biological and chemical processes that lead to biomineralization, howeyer, has only developed rather recently. Early observations were made by paleontologists who were interested in the preservation, through geological time, of the hard parts of organisms such as shells and skeletons but only in 1989 did the field really come of age with the almost simultaneous publication of three monographs covering current knowledge of the biological, biochemical, chemical and taxonomic aspects of biomineralization (Mann et al. 1989; Lowenstam & Weiner 1989; Simkiss & Wilbur 1989)

Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle

Recently Wang et al. carried out a laboratory experiment, where a Brownian particle was dragged through a fluid by a harmonic force with constant velocity of its center. This experiment confirmed a theoretically predicted work related integrated (I) Transient Fluctuation Theorem (ITFT), which gives an expression for the ratio for the probability to find positive or negative values for the fluctuations of the total work done on the system in a given time in a transient state. The corresponding integrated stationary state fluctuation theorem (ISSFT) was not observed. Using an overdamped Langevin equation and an arbitrary motion for the center of the harmonic force, all quantities of interest for these theorems and the corresponding non-integrated ones (TFT and SSFT, resp.) are theoretically explicitly obtained in this paper. While the (I)TFT is satisfied for all times, the (I)SSFT only holds asymptotically in time. Suggestions for further experiments with arbitrary velocity of the harmonic force and in which also the ISSFT could be observed, are given. In addition, a non-trivial long-time relation between the ITFT and the ISSFT was discovered, which could be observed experimentally, especially in the case of a resonant circular motion of the center of the harmonic force.Comment: 20 pages, 3 figure

Group explicit methods for hyperbolic equations

AbstractHere the strategy of the group explicit (GE) methods is applied to the numerical solution of hyperbolic partial differential equations. Theoretical aspects of the stability, consistency, convergence and truncation errors of this new class of methods are presented with supporting numerical evidence

A linear multistep numerical integration scheme for solving systems of ordinary differential equations with oscillatory solutions

AbstractIn [1], a set of convergent and stable two-point formulae for obtaining the numerical solution of ordinary differential equations having oscillatory solutions was formulated. The derivation of these formulae was based on a non-polynomial interpolant which required the prior analytic evaluation of the higher order derivatives of the system before proceeding to the solution. In this paper, we present a linear multistep scheme of order four which circumvents this (often tedious) initial preparation. The necessary starting values for the integration scheme are generated by an adaptation of the variable order Gragg-Bulirsch-Stoer algorithm as formulated in [2]

The numerical solution of an elliptic P.D.E. with periodic boundary conditions in a rectangular region by the spectral resolution method

AbstractIn this paper a new block matrix factorisation strategy is considered utilising the spectral resolution method for the solution of an elliptic partial differential equation with periodic boundary conditions in a rectangle