An extension of Wiener integration with the use of operator theory

With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for these stochastic integrals. In our extension, we circumvent some of the limitations of the more widely used stochastic integral due to Wiener and Ito, i.e., stochastic integration with respect to Brownian motion. Finally we discuss the connection between the two approaches, as well as a priori estimates and applications.Comment: 13 page

Scanned Imaging Techniques for Surface NDE

A phase sensitive laser probe in which the focussed spot is small, as compared with the acoustic wavelength, is capable of measuring the complex distributions of a SAW field along prescribed scan lines. Using the probe, it is possible, on a defect free sample, to measure the SAW velocity surface with an accuracy of a few parts in 105. Such accuracy suggests that the technique is sufficiently sensitive to detect small changes in surface characteristics; the presence of a defect is revealed by perturbations in the relationship between various scans. The scattered radiation patterns from a surface crack irradiated by acoustic surface waves can be utilised to determine the defect size and location with improved accuracy. Results on deliberate and real cracks are presented

Minimal size of a barchan dune

Barchans are dunes of high mobility which have a crescent shape and propagate under conditions of unidirectional wind. However, sand dunes only appear above a critical size, which scales with the saturation distance of the sand flux [P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002); B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B {\bf{28,}} 321 (2002); G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E {\bf{64,}} 31305 (2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002) that this flux fetch distance is itself constant. Indeed, this could not explain the proto size of barchan dunes, which often occur in coastal areas of high litoral drift, and the scale of dunes on Mars. In the present work, we show from three dimensional calculations of sand transport that the size and the shape of the minimal barchan dune depend on the wind friction speed and the sand flux on the area between dunes in a field. Our results explain the common appearance of barchans a few tens of centimeter high which are observed along coasts. Furthermore, we find that the rate at which grains enter saltation on Mars is one order of magnitude higher than on Earth, and is relevant to correctly obtain the minimal dune size on Mars.Comment: 11 pages, 10 figure

Many Roads to Synchrony: Natural Time Scales and Their Algorithms

We consider two important time scales---the Markov and cryptic orders---that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the epsilon-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabilistic property of a process. Rather, it is a topological property and, moreover, it is not computable from any finite-state model other than the epsilon-machine. Via an exhaustive survey, we close by demonstrating that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes. We draw out the roles played in statistical mechanical spin systems by these two complementary length scales.Comment: 17 pages, 16 figures: http://cse.ucdavis.edu/~cmg/compmech/pubs/kro.htm. Santa Fe Institute Working Paper 10-11-02

Entropic bounds on coding for noisy quantum channels

In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if the loss is zero, quantum information can be perfectly transmitted at a rate measured by the quantum source entropy. By using block coding based on sequences of n entangled symbols, the average loss (defined as the overall loss of the joint n-symbol channel divided by n, when n tends to infinity) can be made lower than the loss for a single use of the channel. In this context, we examine several upper bounds on the rate at which quantum information can be transmitted reliably via a noisy channel, that is, with an asymptotically vanishing average loss while the one-symbol loss of the channel is non-zero. These bounds on the channel capacity rely on the entropic Singleton bound on quantum error-correcting codes [Phys. Rev. A 56, 1721 (1997)]. Finally, we analyze the Singleton bounds when the noisy quantum channel is supplemented with a classical auxiliary channel.Comment: 20 pages RevTeX, 10 Postscript figures. Expanded Section II, added 1 figure, changed title. To appear in Phys. Rev. A (May 98

On the possible role of elemental carbon in the formation of reduced chondrules

Recent experiments have been designed to produce chondrule textures via flash melting while simultaneously studying the nature of chondrule precursors. However, these experiments have only been concerned with silicate starting material. This is a preliminary report concerning what effects elemental carbon, when added to the silicate starting material, has on the origin of chondrules produced by flash melting

Investigation of four-year chemical composition and organic aerosol sources of submicron particles at the ATOLL site in northern France

This study presents the first long-term online measurements of submicron (PM1) particles at the ATOLL (ATmospheric Observations in liLLe) platform, in northern France. The ongoing measurements using an Aerosol Chemical Speciation Monitor (ACSM) started at the end of 2016 and the analysis presented here spans through December 2020. At this site, the mean PM1 concentration is 10.6 μg m-3, dominated by organic aerosols (OA, 42.3%) and followed by nitrate (28.9%), ammonium (12.3%), sulfate (8.6%), and black carbon (BC, 8.0%). Large seasonal variations of PM1 concentrations are observed, with high concentrations during cold seasons, associated with pollution episodes (e.g. over 100 μg m-3 in January 2017). To study OA origins over this multiannual dataset we performed source apportionment analysis using rolling positive matrix factorization (PMF), yielding two primary OA factors, a traffic-related hydrocarbon-like OA (HOA) and biomass-burning OA (BBOA), and two oxygenated OA (OOA) factors. HOA showed a homogeneous contribution to OA throughout the seasons (11.8%), while BBOA varied from 8.1% (summer) to 18.5% (winter), the latter associated with residential wood combustion. The OOA factors were distinguished between their less and more oxidized fractions (LO-OOA and MO-OOA, on average contributing 32% and 42%, respectively). During winter, LO-OOA is identified as aged biomass burning, so at least half of OA is associated with wood combustion during this season. Furthermore, ammonium nitrate is also a predominant aerosol component during cold-weather pollution episodes - associated with fertilizer usage and traffic emissions. This study provides a comprehensive analysis of submicron aerosol sources at the recently established ATOLL site in northern France from multiannual observations, depicting a complex interaction between anthropogenic and natural sources, leading to different mechanisms of air quality degradation in the region across different seasons

Energy minimization and AC demagnetization in a nanomagnet array

We study AC demagnetization in frustrated arrays of single-domain ferromagnetic islands, exhaustively resolving every (Ising-like) magnetic degree of freedom in the systems. Although the net moment of the arrays is brought near zero by a protocol with sufficiently small step size, the final magnetostatic energy of the demagnetized array continues to decrease for finer-stepped protocols and does not extrapolate to the ground state energy. The resulting complex disordered magnetic state can be described by a maximum-entropy ensemble constrained to satisfy just nearest-neighbor correlations.Comment: Published Versio

Thermodynamic efficiency of information and heat flow

A basic task of information processing is information transfer (flow). Here we study a pair of Brownian particles each coupled to a thermal bath at temperature $T_1$ and $T_2$, respectively. The information flow in such a system is defined via the time-shifted mutual information. The information flow nullifies at equilibrium, and its efficiency is defined as the ratio of flow over the total entropy production in the system. For a stationary state the information flows from higher to lower temperatures, and its the efficiency is bound from above by $\frac{{\rm max}[T_1,T_2]}{|T_1-T_2|}$. This upper bound is imposed by the second law and it quantifies the thermodynamic cost for information flow in the present class of systems. It can be reached in the adiabatic situation, where the particles have widely different characteristic times. The efficiency of heat flow|defined as the heat flow over the total amount of dissipated heat|is limited from above by the same factor. There is a complementarity between heat- and information-flow: the setup which is most efficient for the former is the least efficient for the latter and {\it vice versa}. The above bound for the efficiency can be [transiently] overcome in certain non-stationary situations, but the efficiency is still limited from above. We study yet another measure of information-processing [transfer entropy] proposed in literature. Though this measure does not require any thermodynamic cost, the information flow and transfer entropy are shown to be intimately related for stationary states.Comment: 19 pages, 1 figur