Kinetic theory of the standard map in the localized weak-stochasticity regime

2000 ◽  
Vol 64 (4) ◽  
pp. 379-396 ◽  
Author(s):  
R. BALESCU
Keyword(s):  
Kinetic Theory ◽  
Master Equation ◽  
Density Profile ◽  
Initial Density ◽  
Rate Of Change ◽  
Standard Map ◽  
Diffusive Regime ◽  
Memory Time ◽  
Order Of Magnitude ◽  
Curious Feature

The well-known Chirikov–Taylor standard map is studied using the methods of non-equilibrium statistical mechanics. It appears possible to simplify the master equation whenever the stochasticity parameter is small and the initial density profile is sharply localized in phase space: this defines the ‘localized weak-stochasticity’ (LWS) regime. The resulting equation of evolution of the density profile involves a convolution in time. Its most conspicuous feature is the absence of a ‘short’ intrinsic time scale: the memory time is infinite. The master equation can therefore not be Markovianized as in usual kinetic theory (or as in the diffusive regime of the standard map). Moreover, the initial value of the fluctuations influences the rate of change of the density profile at all times. Quite unexpectedly, the contributions of the two terms of the master equation to the density profile are of the same order of magnitude. As a result, they practically cancel each other. It is this curious feature that explains the suppression of the motion by the islands and the KAM barriers that is well known from the study of individual standard map orbits. The LWS approximation is valid for a limited time (which is very long when the initial localization is very sharp).

Lab experiments to quantify wind induced microstructural modifications of surface snow

2021 ◽  
Author(s):  
Benjamin Walter ◽  
Henning Löwe
Keyword(s):  
Wind Tunnel ◽  
Wind Velocity ◽  
Microstructural Evolution ◽  
Measurement Techniques ◽  
Initial Density ◽  
Rate Of Change ◽  
Snow Density ◽  
Vertical Heterogeneity ◽  
Surface Snow ◽  
Order Of Magnitude

<p>The microstructural evolution of surface snow under the influence of wind is hardly understood and poorly quantified, but crucial for polar and alpine snowpacks. Only few field studies addressed the process of wind affecting surface snow at the snow-atmosphere interface in detail. Available descriptions are based on empirical relations between snow density, wind velocity and air temperature. A microstructural picture discerning independent controls of snow crystal fragmentation, abrasion and sublimation is yet missing. </p><p>The goal of this project is to analyze the relevant physical processes responsible for wind induced microstructural modifications, and develop parametrizations from controlled wind-tunnel experiments. A ring-shaped wind tunnel (RWT) with an infinite fetch was used in a cold lab to quantify the snow microstructural evolution through systematic variations of flow, snow, and temperature conditions. For the drift experiments, dendritic fresh snow was produced in a WSL/SLF snowmaker and slowly added to the wind tunnel during the experiments simulating precipitation. Measurement techniques like X-ray tomography, SnowMicroPen, density cutters and IceCube were applied to characterize the snow density (ρ), specific surface area (SSA), particle size and shape and vertical layering before and after the highly dendritic new snow was exposed to the wind. </p><p>The vertical heterogeneity of the deposited snow was characterized by SnowMicroPen measurements, showing increasing densities towards the snow surface. Densification rates (normalized by the initial density ρ<sub>0</sub>) of the surface layer measured with a density cutter show an increase with increasing wind velocity and are two to three orders of magnitude higher than those measured for isothermal metamorphism, underlining the importance of accurately understanding wind induced microstructural modifications. Densification rates simulated with stat-of-the-art snow physical models span an order of magnitude, significantly deviating from the measured values. The SSA, measured with the IceCube instrument, decreases with a rate of change of approximately -0.1 h<sup>-1</sup>, which is an order of magnitude higher than the rates for isothermal metamorphism. We hypothesize that the smallest fragments disappear because of sublimation while being transported by the wind. </p><p>The results of this project will lead to an improved, fundamental understanding of optically and mechanically relevant microstructural properties of surface snow and are thus applicable to many cryospheric processes like avalanche formation, exchange of chemical species with the atmosphere, alpine and polar mass balances, or radiative transfer.</p>

scholarly journals Quantum kinetic theory. II. Simulation of the quantum Boltzmann master equation

1997 ◽  
Vol 56 (1) ◽  
pp. 575-586 ◽  
Author(s):  
D. Jaksch ◽  
C. W. Gardiner ◽  
P. Zoller
Keyword(s):  
Kinetic Theory ◽  
Master Equation ◽  
Quantum Kinetic Theory

Storm surges in the North Sea during the winter 1953-4

1956 ◽  
Vol 235 (1201) ◽  
pp. 260-274 ◽  
Keyword(s):  
Sea Level ◽  
North Sea ◽  
Storm Surges ◽  
Rate Of Change ◽  
The North ◽  
Order Of Magnitude ◽  
The North Sea ◽  
Sea Ports ◽  
Phase Angles

Records of sea level for several North Sea ports for the winter of 1953-4 have been in vestigated. They were split into 14-day intervals, and each 14-day record was Fourieranalyzed to determine if any non-astronomical periods were present. There was evidence of some activity between 40 and 50 h period, and a determination of the phase angles at different ports showed that the activity could be due to a disturbance travelling southwards from the north of the North Sea. The disturbance was partly reflected somewhere near the line from Lowestoft to Flushing, so that one part returned past Flushing and Esbjerg towards Bergen while the other part travelled towards Dover, and there was evidence of its existence on the sea-current records taken near St Margaret's Bay. These results were confirmed by subtracting the predicted astronomical tidal levels from the observed values of sea level and cross-correlating the residuals so obtained for each port with those found at Lowestoft. The residuals at Lowestoft and Aberdeen were compared with the meteorological conditions, and it was found that, although they could be attributed to a large extent to conditions within the North Sea, there was an additional effect due to a travelling surge which was of the same order of magnitude at both Lowestoft and Aberdeen and which was closely related to the rate of change with time of the atmospheric pressure difference between Wick and Bergen.

MOTION DETECTION AND DIRECTION DETECTION IN LOCAL NEURAL NETS

1989 ◽  
Vol 01 (02) ◽  
pp. 187-192 ◽  
Author(s):  
H.-U. Bauer ◽  
T. Geisel
Keyword(s):  
Motion Detection ◽  
Pulse Velocity ◽  
Neural Nets ◽  
Global Network ◽  
Training Set ◽  
Backpropagation Algorithm ◽  
Short Term ◽  
Memory Time ◽  
Direction Detection ◽  
Order Of Magnitude

We present a model for motion and direction detection of moving pulses whose performance is independent of pulse velocity, size and shape. The input signal activates one row of instantaneous nodes and one row of time integrating input nodes acting as short-term memories. Motion detection is achieved locally by subnetworks which are trained with a synthetic training set using the backpropagation algorithm. The global network is constructed from these subnetworks, one for each position. We test its performance with different pulse shapes and sizes and find the response to be invariant in a window of pulse velocities an order of magnitude wide. The window can be shifted by adjusting the memory time of the input nodes.

scholarly journals In situ growth optimization in focused electron-beam induced deposition

2013 ◽  
Vol 4 ◽  
pp. 919-926 ◽  
Author(s):  
Paul M Weirich ◽  
Marcel Winhold ◽  
Christian H Schwalb ◽  
Michael Huth
Keyword(s):  
Electron Beam ◽  
Rate Of Change ◽  
In Situ Growth ◽  
Growth Optimization ◽  
Evolutionary Genetic ◽  
Order Of Magnitude ◽  
Electron Beam Induced Deposition ◽  
Deposition Processes ◽  
Fitness Parameter

We present the application of an evolutionary genetic algorithm for the in situ optimization of nanostructures that are prepared by focused electron-beam-induced deposition (FEBID). It allows us to tune the properties of the deposits towards the highest conductivity by using the time gradient of the measured in situ rate of change of conductance as the fitness parameter for the algorithm. The effectiveness of the procedure is presented for the precursor W(CO)6 as well as for post-treatment of Pt–C deposits, which were obtained by the dissociation of MeCpPt(Me)3. For W(CO)6-based structures an increase of conductivity by one order of magnitude can be achieved, whereas the effect for MeCpPt(Me)3 is largely suppressed. The presented technique can be applied to all beam-induced deposition processes and has great potential for a further optimization or tuning of parameters for nanostructures that are prepared by FEBID or related techniques.

Kinetic Theory for a Dilute Gas of Particles with Spin. II. Relaxation Coefficients

1968 ◽  
Vol 23 (12) ◽  
pp. 1893-1902
Author(s):  
S. Hess ◽  
L. Waldmann
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Interaction Potential ◽  
Collision Operator ◽  
Dilute Gas ◽  
Order Of Magnitude ◽  
Generalized Boltzmann Equation ◽  
Linearized Collision Operator ◽  
Relaxation Coefficients

The relaxation coefficients to be discussed are given by collision brackets pertaining to the linearized collision operator of the generalized Boltzmann equation for particles with spin. The order of magnitude of various nondiagonal relaxation coefficients which are of interest for the SENFTLEBEN-BEENAKKER effect is investigated. Those nondiagonal relaxation coefficients which are linear in the nonsphericity parameter ε (ε essentially measures the ratio of the nonspherical and the spherical parts of the interaction potential), as well as some diagonal relaxation coefficients are expressed in terms of generalized Omega-integrals.

Plasma membrane H(+)-HCO3- transport in rat hepatocytes: a principal role for Na(+)-coupled HCO3- transport

1991 ◽  
Vol 261 (5) ◽  
pp. G803-G809 ◽  
Author(s):  
J. G. Fitz ◽  
S. D. Lidofsky ◽  
M. H. Xie ◽  
M. Cochran ◽  
B. F. Scharschmidt
Keyword(s):  
Plasma Membrane ◽  
Membrane Potential ◽  
Primary Culture ◽  
Basolateral Membrane ◽  
Rat Hepatocytes ◽  
Rate Of Change ◽  
Transport Capacity ◽  
Principal Role ◽  
Order Of Magnitude ◽  
Membrane Potential Difference

Na(+)-coupled HCO3- transport has been demonstrated in the basolateral membrane of hepatocytes, but there is uncertainty regarding its stoichiometry or capacity compared with other mechanisms of H(+)-HCO3- transport. After preincubation in medium free of Na+, either in the presence or absence of HCO3(-)-CO2, rat hepatocytes in primary culture were reexposed to Na+ or HCO3(-)-CO2 alone or in combination. Transporter electrogenicity was assessed by measuring membrane potential difference (PD), and the relative capacities of Na(+)-coupled HCO3- transport, Cl(-)-HCO3- exchange, and Na(+)-H+ exchange were assessed by measuring the magnitude and rate of change of intracellular pH (pHi) using BCECF. In the absence of Na+, exposure to HCO3- alone had no consistent effect on PD or pHi. In the absence of HCO3-, reexposure to Na+ depolarized cells by 3 +/- 1 mV and caused an amiloride-inhibitable increase in pHi of 0.031 +/- 0.02 units/min. In the presence of HCO3-, reexposure to Na+ hyperpolarized cells by -14 +/- 5 mV and increased pHi at a rate of 0.133 +/- 0.11 units/min; both the hyperpolarization and alkalinization were inhibited by SITS but unaffected by amiloride. These changes in PD indicate that Na(+)-coupled HCO3- transport is electrogenic, consistent with coupling of more than one HCO3- to each Na+. Furthermore, SITS-inhibitable Na(+)-dependent alkalinization exceeds amiloride-inhibitable Na(+)-dependent alkalinization by an order of magnitude, suggesting that the transport capacity of Na(+)-coupled HCO3- transport exceeds that of Na(+)-H+ exchange.(ABSTRACT TRUNCATED AT 250 WORDS)

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