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We develop a method of finding analytical sotutions of the Bogolyubov-de Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose- Einstein condensation
Two-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at top and bottom and periodic boundary conditions in the horizontal direction is investigated by means of numerical simulation and bifurcation-analysis techniques. As the bouyancy forces increase, the primary stationary and symmetric convection rolls undergo successive Hopf bifurcations, bifurcations to traveling waves, and phase lockings. We pay attention to symmetry breaking and its connection with the generation of large-scale horizontal flows. Calculations of Lyapunov exponents indicate that at a Rayleigh number of 2.3×105 no temporal chaos is reached yet, but the system moves nonchaotically on a 4-torus in phase space.
Control of noise-induced oscillations of a pendulum with a rondomly vibrating suspension axis
(1997)
The pendant drop technique was used to determine p/A isotherms of docosanic acid spread on the drop surface of an aqueous polymer solution. Two water soluble polymers were used, poly(dimethyl-diallyl-ammoniumchloride) and sodium poly(styrene sulfonate-b-ethylethylene). By fast changes of the drop volume, the monolayers were compressed and dilated. The stress relaxation was monitored and surface rheological dilation parameters were obtained. It is shown that the fatty acid monolayer can be mechanically stabilized by both interacting anionic and cationic polymers. In the case of the anionic polymer, the interaction becomes more pronounced in the presence of salts in the subphase (counterions). Brewster angle microscopy shows that the typical tilt-orientation of crystalline domains of the fatty acid monolayers transforms into a more uniform and fluid-like structure caused by the polymer/monolayer interaction. The surface rheological behavior is dramatically influenced by the polymer binding. The interaction results in surface dilational viscoelastic properties and show that there is a strong resistance against expansion of the complex fatty acid/polymer layer.
The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.
We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from theenvironment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of thegrand- canonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau-Ginzburg functional which - despite the non- interacting nature of the system - displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is base on the grand-canonical ensemble. We show that for an ideal Bose gas neither are the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir.
Electrochemical polymerization of functionalized thiohene derivatives for immobilization of proteins
(1997)
We discuss the exact particle number counting statistics of degenerate ideal Bose gases in the microcanonical, canonical, and grand-canonical ensemble, respectively, for various trapping potentials. We then invoke the Maxwell's Demon ensemble [P. Navez et al., Phys. Rev. Lett.(1997)] and show that for large total number of particles the root-mean-square fluctuation of the condensate occupation scales delta n0 proportional to [T/Tc]r Ns with scaling exponents r=3/2, s=1/2 for the 3D harmonic oscillator trapping potential, and r=1, s=2/3 for the 3D box. We derive an explicit expression for r and s in terms of spatial dimension D and spectral index sigma of the single- particle energy spectrum. Our predictions also apply to systems where Bose-Einstein condensation does not occur. We point out that the condensate fluctuations in the microcanonical and canonical ensemble respect the principle of thermodynamic equivalence.
In modern political philosophy social contract theory is the most prominent approach to individual rights and fair institutions. According to social contract theory the system of rights in a society ought to be justified by reconstructing its basic features as a contract between the mutually unconcerned members of society. This paper explores whether social contract theory can successfully be applied to justify rights of future generations. Three competing views are analysed: Rawls's theory of justice, Hobbes's radical liberalism and Gauthier's bargaining framework based on the Lockean proviso.
The paper is an enquiry into dynamic social contract theory. The social contract defines the rules of resource use. An intergenerational social contract in an economy with a single exhaustible resource is examined within a framework of an overlapping generations model. It is assumed that new generations do not accept the old social contract, and access to resources will be renegotiated between any incumbent generation and their successors. It turns out that later generations will be in an unfortunate position regardless of their bargaining power.
This paper opens a series of discussion papers which report about the findings of a research project within the Phare-ACE Programme of the European Union. We, a group of Bulgarian, German, Greek, Polish and Scottish economists and agricultural economists, undertake this research to provide An Integrated Analysis of Industrial Policies and Social Security Systems in Countries in Transition.1 This paper outlines the basic motivation for such study.
Biosensors for food analysis
(1997)
Weak gravitational lensing by large-scale structure affects the determination of the cosmological deceleration parameter q0. We find that the lensing induced dispersions on truly standard candles are 0.04 and 0.02 mag at redshift z = 1 and z = 0.5, respectively, in a COBE-normalized cold dark matter universe with Omega 0 = 0.40, Lamda 0 = 0.6, H = 65 km s-1 Mpc-1, and sigma 8 = 0.79. It is shown that one would observe q0 = -0.395^{+0.125}_{-0.095} and q0 = - 0.398^{+0.048}_{-0.077} (the error bars are 2 sigma limits) with standard candles with zero intrinsic dispersion at redshift z = 1 and z = 0.5, respectively, compared to the truth of q0 = -0.400. A standard COBE normalized Omega 0 = 1 CDM model would produce three times as much variance and a mixed (hot and cold) dark matter model would lead to an intermediate result. One unique signature of this dispersion effect is its non-Gaussianity. Although the lensing induced dispersion at lower redshift is still significantly smaller than the currently best observed (total) dispersion of 0.12 mag in a sample of type Ia supernovae, selected with the multicolor light curve shape method, it becomes significant at higher redshift. We show that there is an optimal redshift, in the range z ~ 0.5--2.0 depending on the amplitude of the intrinsic dispersion of the standard candles, at which q0 can be most accurately determined.
Reconstruction of nonlinear time delay models from data by the use of optimal transformations
(1997)
Starting from recent approaches in mental model research, it is argued that (1) logical inference rules are used in order to construct mental cliques from learned sentiment relations, and (2) social context cues (operationalized as primes) play a crucial role in activating such rules. Transitivity and Anti- transitivity are taken as examples, and are shown as core constituents of such models. In a first experiment, priming was achieved by announcing the sorting of fictitious persons in either TWO or THREE cliques. Thirty-one subjects studied eight sets of sentiment relations among these persons that either did or did not satisfy their primed clique expectations. They showed longer study times and more requests for additional information in the case of inconsistent fits between prime and set. Their sorting solutions also showed clear priming effects. A second experiment (n = 30) showed that when undergoing a recognition test after seeing the relation sets, subjects tended to confuse model-consistent distractors with information they had actually seen. In a third experiment (n=30) the results from Experiment 1 were replicated using more realistic learning materials.