18,141 research outputs found
On the universal Representation of the Scattering Matrix of Affine Toda Field Theory
By exploiting the properties of q-deformed Coxeter elements, the scattering
matrices of affine Toda field theories with real coupling constant related to
any dual pair of simple Lie algebras may be expressed in a completely generic
way. We discuss the governing equations for the existence of bound states, i.e.
the fusing rules, in terms of q-deformed Coxeter elements, twisted q-deformed
Coxeter elements and undeformed Coxeter elements. We establish the precise
relation between these different formulations and study their solutions. The
generalized S-matrix bootstrap equations are shown to be equivalent to the
fusing rules. The relation between different versions of fusing rules and
quantum conserved quantities, which result as nullvectors of a doubly
q-deformed Cartan like matrix, is presented. The properties of this matrix
together with the so-called combined bootstrap equations are utilised in order
to derive generic integral representations for the scattering matrix in terms
of quantities of either of the two dual algebras. We present extensive
case-by-case data, in particular on the orbits generated by the various Coxeter
elements.Comment: 57 page
Weak disorder expansion for localization lengths of quasi-1D systems
A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength
Understanding and Improving the Wang-Landau Algorithm
We present a mathematical analysis of the Wang-Landau algorithm, prove its
convergence, identify sources of errors and strategies for optimization. In
particular, we found the histogram increases uniformly with small fluctuation
after a stage of initial accumulation, and the statistical error is found to
scale as with the modification factor . This has implications
for strategies for obtaining fast convergence.Comment: 4 pages, 2 figures, to appear in Phys. Rev.
Collective Diffusion and a Random Energy Landscape
Starting from a master equation in a quantum Hamiltonian form and a coupling
to a heat bath we derive an evolution equation for a collective hopping process
under the influence of a stochastic energy landscape. There results different
equations in case of an arbitrary occupation number per lattice site or in a
system under exclusion. Based on scaling arguments it will be demonstrated that
both systems belong below the critical dimension to the same universality
class leading to anomalous diffusion in the long time limit. The dynamical
exponent can be calculated by an expansion. Above the
critical dimension we discuss the differences in the diffusion constant for
sufficient high temperatures. For a random potential we find a higher mobility
for systems with exclusion.Comment: 15 pages, no figure
Approaches and tools to manipulate the carbonate chemistry
Although the chemistry of ocean acidifi cation is very well understood (see chapter 1), its impact on marine organisms and ecosystems remains poorly known. The biological response to ocean acidifi cation is a recent field
of research, the fi rst purposeful experiments have only been carried out as late as the 1980s (Agegian, 1985)
and most were not performed until the late 1990s. The potentially dire consequences of ocean acidifi cation
have attracted the interest of scientists and students with a limited knowledge of the carbonate chemistry and
its experimental manipulation. Perturbation experiments are one of the key approaches used to investigate
the biological response to elevated p(CO2). Such experiments are based on measurements of physiological or
metabolic processes in organisms and communities exposed to seawater with normal and altered carbonate chemistry. The basics of the carbonate chemistry must be understood to perform meaningful CO2 perturbation experiments (see chapter 1). Briefl y, the marine carbonate system considers
€ CO2 ∗(aq) [the sum of CO2 and H2CO3], € HCO3 −, € CO3 2−,
H+, € OH− , and several weak acid-base systems of which borate-boric acid (€ B(OH)4 − , B(OH)3) is the most
important. As discussed by Dickson (chapter 1), if two components of the carbonate chemistry are known, all
the other components can be calculated for seawater with typical nutrient concentrations at given temperature,
salinity, and pressure. One of the possible pairs is of particular interest because both components can be
measured with precision, accuracy, and are conservative in the sense that their concentrations do not change
with temperature or pressure. Dissolved inorganic carbon (DIC) is the sum of all dissolved inorganic carbon
species while total alkalinity (AT) equals € [HCO3 − ] + 2
€ [CO3 2− ] + € [B(OH)4 − ] + € [OH− ] - [H+] + minor components, and refl ects the excess of proton acceptors over proton donors with respect to a zero level of protons (see chapter 1 for a detailed defi nition). AT is determined by the titration of seawater with a strong acid and thus can also be regarded as a measure of the buffering capacity. Any changes in any single component of the carbonate system will lead to changes in several, if not all, other components. In other words, it is not possible to vary a single component of the carbonate system while keeping all other components constant. This interdependency
in the carbonate system is important to consider when performing CO2 perturbation experiments.
To adjust seawater to different p(CO2) levels, the carbonate system can be manipulated in various ways that
usually involve changes in AT or DIC. The goal of this chapter is (1) to examine the benefi ts and drawbacks of
various manipulation methods used to date and (2) to provide a simple software package to assist the design
of perturbation experiments
Current reversal and exclusion processes with history-dependent random walks
A class of exclusion processes in which particles perform history-dependent
random walks is introduced, stimulated by dynamic phenomena in some biological
and artificial systems. The particles locally interact with the underlying
substrate by breaking and reforming lattice bonds. We determine the
steady-state current on a ring, and find current-reversal as a function of
particle density. This phenomenon is attributed to the non-local interaction
between the walkers through their trails, which originates from strong
correlations between the dynamics of the particles and the lattice. We
rationalize our findings within an effective description in terms of
quasi-particles which we call front barriers. Our analytical results are
complemented by stochastic simulations.Comment: 5 pages, 6 figure
Mapping the interstellar medium in galaxies with Herschel/SPIRE
The standard method of mapping the interstellar medium in a galaxy, by observing the molecular gas in the CO 1-0 line and the atomic gas in the 21-cm line, is largely limited with current telescopes to galaxies in the nearby universe. In this letter, we use SPIRE observations of the galaxies
M99 and M100 to explore the alternative approach of mapping the interstellar medium using the continuum emission from the dust. We have compared the methods by measuring the relationship between the star-formation rate and the surface density of gas in the galaxies using both
methods. We find the two methods give relationships with a similar dispersion, confirming that observing the continuum emission from the dust is a promising method of mapping the interstellar medium in galaxies
The Herschel Space Observatory view of dust in M81
We use Herschel Space Observatory data to place observational constraints on the peak and Rayleigh-Jeans slope of dust emission observed at 70−500 μm in the nearby spiral galaxy M81. We find that the ratios of wave bands between 160 and 500 μm are primarily dependent on radius but that the ratio of 70 to 160 μm emission shows no clear dependence on surface brightness or radius. These
results along with analyses of the spectral energy distributions imply that the 160−500 μm emission traces 15−30 K dust heated by evolved stars in the bulge and disc whereas the 70 μm emission includes dust heated by the active galactic nucleus and young stars in star forming regions
Radial distribution of gas and dust in spiral galaxies: The case of M 99 (NGC 4254) and M 100 (NGC 4321)
By combining Herschel-SPIRE data with archival Spitzer, H i , and CO maps, we investigate the spatial distribution of gas and dust in the two famous grand-design spirals M 99 and M 100 in the Virgo cluster. Thanks to the unique resolution and sensitivity of the Herschel-SPIRE photometer, we are for the first time able to measure the distribution and extent of cool, submillimetre (submm)-emitting dust inside and beyond the optical radius. We compare this with the radial variation in both the gas mass and the metallicity. Although we adopt a model-independent, phenomenological approach, our analysis provides important insights. We find the dust extending to at least the optical radius of the galaxy and showing breaks in its radial profiles at similar positions as the stellar distribution. The colour indices f350/f500 and f250/f350 decrease radially consistent with the temperature decreasing with radius. We also find evidence of an increasing gas to dust ratio with radius in the outer regions of both galaxies
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