Convergence of continuous-time quantum walks on the line

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that depends on the initial state of the particle. This convergence behavior has recently been demonstrated for the simplest continuous-time random walk [see quant-ph/0408140]. In this brief report, we use a different technique to establish the same convergence for a very large class of continuous-time quantum walks, and we identify the limit distribution in the general case.Comment: Version to appear in Phys. Rev.

Automated method for study of drug metabolism

Commercially available equipment can be modified to provide automated system for assaying drug metabolism by continuous flow-through. System includes steps and devices for mixing drug with enzyme and cofactor in the presence of pure oxygen, dialyzing resulting metabolite against buffer, and determining amount of metabolite by colorimetric method

Conversion of acetate to lipids and co2 by liver of rats exposed to acceleration stress

Acetate conversion to lipids and carbon dioxide by exposure of rat liver to acceleration stres

Computer system for monitoring radiorepirometry data

System monitors expired breath patterns simultaneously from four small animals after they have been injected with carbon-14 substrates. It has revealed significant quantitative differences in oxidation patterns of glucose following such mild treatments of rats as a change in diet or environment

Geometric origin of scaling in large traffic networks

Large scale traffic networks are an indispensable part of contemporary human mobility and international trade. Networks of airport travel or cargo ships movements are invaluable for the understanding of human mobility patterns\cite{Guimera2005}, epidemic spreading\cite{Colizza2006}, global trade\cite{Imo2006} and spread of invasive species\cite{Ruiz2000}. Universal features of such networks are necessary ingredients of their description and can point to important mechanisms of their formation. Different studies\cite{Barthelemy2010} point to the universal character of some of the exponents measured in such networks. Here we show that exponents which relate i) the strength of nodes to their degree and ii) weights of links to degrees of nodes that they connect have a geometric origin. We present a simple robust model which exhibits the observed power laws and relates exponents to the dimensionality of 2D space in which traffic networks are embedded. The model is studied both analytically and in simulations and the conditions which result with previously reported exponents are clearly explained. We show that the relation between weight strength and degree is $s(k)\sim k^{3/2}$, the relation between distance strength and degree is $s^d(k)\sim k^{3/2}$ and the relation between weight of link and degrees of linked nodes is $w_{ij}\sim(k_ik_j)^{1/2}$ on the plane 2D surface. We further analyse the influence of spherical geometry, relevant for the whole planet, on exact values of these exponents. Our model predicts that these exponents should be found in future studies of port networks and impose constraints on more refined models of port networks.Comment: 17 pages, 5 figures, 1 tabl

Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences

We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$ measurements has any specified property. In many cases, product states are eigenstates of the projections, and therefore the result of measuring the property is determined. Thus we obtain a nonprobabilistic quantum analogue to the law of large numbers, the randomness property, and all other familiar almost-sure theorems of classical probability.Comment: 7 pages in LaTe

The delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation

It has been alleged in several papers that the so called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate how accurate are the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in $L_2$ norm to the DCTRWs than the telegraph equation. We conclude therefore that, first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs.Comment: 12 pages, 9 figure

Spectral absorption of visual pigments in stomatopod larval photoreceptors

Larval stomatopod eyes appear to be much simpler versions of adult compound eyes, lacking most of the visual pigment diversity and photoreceptor specializations. Our understanding of the visual pigment diversity of larval stomatopods, however, is based on four species, which severely limits our understanding of stomatopod eye ontogeny. To investigate several poorly understood aspects of stomatopod larval eye function, we tested two hypotheses surrounding the spectral absorption of larval visual pigments. First, we examined a broad range of species to determine if stomatopod larvae generally express a single, spectral class of photoreceptor. Using microspectrophotometry (MSP) on larvae captured in the field, we found data which further support this long-standing hypothesis. MSP was also used to test whether larval species from the same geographical region express visual pigments with similar absorption spectra. Interestingly, despite occupation of the same geographical location, we did not find evidence to support our second hypothesis. Rather, there was significant variation in visual pigment absorption spectra among sympatric species. These data are important to further our understanding of larval photoreceptor spectral diversity, which is beneficial to ongoing investigations into the ontogeny, physiology, and molecular evolution of stomatopod eyes. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s00359-015-1063-y) contains supplementary material, which is available to authorized users

Probability distribution of residence times of grains in models of ricepiles

We study the probability distribution of residence time of a grain at a site, and its total residence time inside a pile, in different ricepile models. The tails of these distributions are dominated by the grains that get deeply buried in the pile. We show that, for a pile of size $L$, the probabilities that the residence time at a site or the total residence time is greater than $t$, both decay as $1/t(\ln t)^x$ for $L^{\omega} \ll t \ll \exp(L^{\gamma})$ where $\gamma$ is an exponent $\ge 1$, and values of $x$ and $\omega$ in the two cases are different. In the Oslo ricepile model we find that the probability that the residence time $T_i$ at a site $i$ being greater than or equal to $t$, is a non-monotonic function of $L$ for a fixed $t$ and does not obey simple scaling. For model in $d$ dimensions, we show that the probability of minimum slope configuration in the steady state, for large $L$, varies as $\exp(-\kappa L^{d+2})$ where $\kappa$ is a constant, and hence $\gamma = d+2$.Comment: 13 pages, 23 figures, Submitted to Phys. Rev.

Coal desulfurization by low temperature chlorinolysis, phase 1

The reported activity covers laboratory scale experiments on twelve bituminous, sub-bituminous and lignite coals, and preliminary design and specifications for bench-scale and mini-pilot plant equipment