# Manual A sup+ c inf inequality for Liouville-type equations with singular potentials

Cohen A Land of Liberty? Textbausteine und Tatigkeitsbeschreibungen 4. Auflage by Karsten Umnu? Hunt Obras Completas: El chiste y su relacion con lo inconciente vol. Fabozzi Series by David J. A phylogenetic approach to human prehistory by Q. Sixth Paper by Vandiver H. The calculational approach by Fokkinga M. Eine Abrechnung mit dem Amerika unter George W. Kilminster Autoimmune Diseases of the Skin. Shook Introduction to computer-intensive methods of data analysis in biology by Derek A. Einfuhrung in die Grundlagen der Literatursprache.

Nuclear Forces : Implications for U. Plummer Senza trucco. Nielsen Stupid white men-- and other sorry excuses for the state of the nation! Banach spaces of analytic functions and absolutely summing operators by Pelczynski A. Barrett Nachrichtentechnik: Eine Einfuhrung fur alle Studiengange, 6. Rice Tricarbonylchromium complexes of styrenes in radical copolymerization by Grishin D.

Turbomachinery and Other Applications by Murthy, S. Ultrafast electronic relaxation processes following two photoexcitation of nm in p-Fluorotoluene pFT have been investigated utilizing time -resolved photoelectron imaging coupled with time -resolved mass spectroscopy. While, the slower relaxation constant is attributed to the further internal conversion to the high levels of S0 from the secondarily populated S1 locating in the channel three region. Moreover, dynamical differences with benzene and toluene of analogous structures, including, specifically, the slightly slower relaxation rate of S2 and the evidently faster decay of S1, are also presented and tentatively interpreted as the substituent effects.

In addition, photoelectron kinetic energy and angular distributions reveal the feature of accidental resonances with low-lying Rydberg states the 3p, 4s and 4p states during the multi-photon ionization process, providing totally unexpected but very interesting information for pFT. Chemical exchange effects during refocusing pulses in constant- time CPMG relaxation dispersion experiments. In the analysis of the constant- time Carr-Purcell-Meiboom-Gill CT-CPMG relaxation dispersion experiment, chemical exchange parameters, such as rate of exchange and population of the exchanging species, are typically optimized using equations that predict experimental relaxation rates recorded as a function of effective field strength.

In this process, the effect of chemical exchange during the CPMG pulses is typically assumed to be the same as during the free-precession. This approximation may introduce systematic errors into the analysis of data because the number of CPMG pulses is incremented during the constant- time relaxation period, and the total pulse duration therefore varies as a function of the effective field strength. In order to estimate the size of such errors, we simulate the time -dependence of magnetization during the entire constant time period, explicitly taking into account the effect of the CPMG pulses on the spin relaxation rate.

We show that in general the difference in the relaxation dispersion profile calculated using a practical pulse width from that calculated using an extremely short pulse width is small, but under certain circumstances can exceed 1 s The difference increases significantly when CPMG pulses are miscalibrated. Using non-destructive photothermal techniques, it is possible to characterize non-homogenous materials to obtain its optical and thermal properties through photoacoustic spectroscopy PAS.

In photoacoustic PA phenomena, there are transient states of thermal excitation, when samples absorb the incident light; these states manifest an excitation process that generates the PA signal, being in direct relation with the non-radiative relaxation times with the sample absorbent centers. The objective of this study was to determine the non-radiative relaxation times associated with different absorbent centers of corn seeds Zea mays L.

A frequency scan was done at different wavelengths nm, nm and nm in order to obtain the non-radiative relaxation times with different types of maize seeds. The time -dependence of exchange-induced relaxation during modulated radio frequency pulses. The solution for the time evolution under the chemical exchange Hamiltonian in the tilted doubly rotating frame TDRF is presented.

Detailed derivation is specified to the case of a two-site chemical exchange system with complete randomization between jumps of the exchanging spins. The derived theory can be applied to describe the modulation of the chemical exchange relaxation rate constants when using a train of adiabatic pulses, such as the hyperbolic secant pulse. Theory presented is valid for quantification of the exchange-induced time -dependent rotating frame longitudinal T1rho,ex and transverse T2rho,ex relaxations in the fast chemical exchange regime.

Energy-level statistics and time relaxation in quantum systems. An important quantity is the survival probability P t , defined as the probability, at time t, to find the system in the original model state. Our main purpose is to analyze the influence of the discreteness and statistical properties of the spectrum on the behavior of P t. Since P t itself is a statistical quantity, we restrict our attention to its ensemble average , which is calculated analytically using random-matrix techniques, within certain approximations discussed in the text.

## Lectures On Differential Equations.pdf

We find, for , an exponential decay, followed by a revival, governed by the two-point structure of the statistical spectrum, thus giving a nonzero asymptotic value for large t's. The analytic result compares well with a number of computer simulations, over a time range discussed in the text. Observation of relaxation on time scale of core hole decay by coincidence photoelectron spectroscopy.

It is shown by a many-body theory that when the relaxation time of a metastable core hole state s to the most stable one is comparable to or shorter than core hole decay time of the former state s , a comparison between the singles noncoincidence photoelectron spectroscopy PES spectrum and the coincidence one provides a direct evidence of the relaxation. In principle the variation with photoelectron kinetic energy of relaxation or charge transfer CT time can be determined.

By singles measurement the correlation of a photoelectron generated by creation of the metastable states not only with an Auger electron generated by annihilation of the same core hole state but also with an Auger electron generated by annihilation of the stable state via relaxation of the metastable state, is completely lost, unless only the metastable state is observed by PES, whereas the correlation often manifests directly in the coincidence spectra.

Thus, compared to the coincidence spectroscopy the singles one is often much less capable of elucidating the competition between relaxation and core hole decay of a metastable state. Such examples are discussed. On-chip Brownian relaxation measurements of magnetic nanobeads in the time domain. In the time domain, a measurement is carried out in less than 30 s Deconvolution analysis to determine relaxation time spectra of internal friction peaks. A new method for analysis of an internal friction vs temperature peak to obtain an approximation of the spectrum of relaxation time responsible for the peak is described.

This method, referred to as direct spectrum analysis DSA , is shown to provide an accurate estimate of the distribution of relaxation times. Relaxation time measurements of white and grey matter in multiple sclerosis patients. In a patient population of some with definite, probable, and possible multiple sclerosis referred to us for MRI, some 40 suffering from definite MS were chosen randomly for relaxation time measurements of plaque-free grey and white matter.

T 1 values could not be used for diagnostic purposes owing to their broad standard deviation. Overall white matter T 2 was slightly higher in MS patients than in a non-MS population 94 ms versus 89 ms. Because these changes are not visible in MR images, relaxation time measurements may prove valuable for differential diagnosis.

Menstrual variation of breast volume and T2 relaxation times in cyclical mastalgia. Purpose: Hormonal activity causes breast volume to change during the menstrual cycle. One possible cause of this volume change is thought to be due to water retention or oedema within the tissues. We used magnetic resonance imaging MRI to study the variation in breast volume and 1 H Magnetic Resonance Spectroscopy MRS to measure T 2 relaxation times which are known to increase with increasing tissue water content.

We hypothesised that an increase in breast volume will elevate T 2 relaxation due to the presence of an increased water content within the breast. T 2 Relaxation time and volume were studied in fifteen control subjects and in a cohort of eight patients with cyclical mastalgia in order to determine whether changes in breast volume and T 2 relaxation times differed in controls and patients during menses, ovulation and premenses. Method: Breast volume was determined by the Cavalieri method in combination with point counting techniques on MR images and T 2 relaxation times of the water and fat in a voxel of breast tissue were obtained using 1 H Magnetic Resonance Spectroscopy MRS.

Results: Statistical analysis ANOVA demonstrated highly significant differences in breast volume between the three stages of the cycle p 2 of fat or water did not depend on stage of cycle. T-tests demonstrated no significant differences in T 2 of water or fat between patient and control groups.

The average T 2 relaxation time of water was lowest in the patient and control groups during ovulation and highest in the patient group during premenses. Conclusion: We have performed the first combined volumetric and spectroscopic study of women with cyclical mastalgia and demonstrated that the global changes in volumes and T 2 were not significantly different from normal menstrual variations.

The effects of bone on proton NMR relaxation times of surrounding liquids. Preliminary attempts by our group at UCSF to assess fat content of vertebral marrow in the lumbar spine using relaxation time information demonstrated that the presence of trabecular bone affects relaxation times. The objective of this work was a thorough study of the effects of bone on NMR relaxation characteristics of surrounding liquids. Trabecular bone from autopsy specimens was ground up and sifted into a series of powders with graded densities ranging from 0.

Each powder was placed first in n-saline and then in cottonseed oil. As bone density and surface to volume ratio increased, T1 decreased faster for saline than for oil. The T1s of oil were not affected since oil molecules are nonpolar, do not participate in significant intermolecular hydrogen bonding, and therefore would not be expected to interact strongly with the bone surface. These preliminary results suggest that water in contact with trabecular bone in vivo will exhibit shortened relaxation times.

T2 star relaxation times for assessment of articular cartilage at 3 T: a feasibility study. T2 mapping techniques use the relaxation constant as an indirect marker of cartilage structure, and the relaxation constant has also been shown to be a sensitive parameter for cartilage evaluation. Both parameters demonstrated similar spatial dependency, with longer values measured toward the articular surface for healthy articular cartilage.

No spatial variation was observed for cartilage repair tissue after MFX. Elkins, Madeline H. The observation that water proton relaxation rates were longer in tumors than in normal tissues provided a basis for the detection of human tumors by the NMR imaging technique. To evaluate the potentiality of P NMR spectroscopy as a diagnostic tool of the pathological state of tissues, T1 and T2 relaxation times have been measured for the phosphates of ATP, inorganic phosphate Pi , phosphomonoesters PME and phosphocreatine PCr in the P NMR spectra obtained in vivo for normal rat brain and rat brain tumors implanted in nude mice.

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Transverse magnetic field effects on the relaxation time of the magnetization in Mn12 measured by 55Mn-NMR. The minima in the relaxation time at the fields for level crossing are due to the quantum tunneling of the magnetization. The shortening of the relaxation time under the application of H T is shown to be due mainly to the reduction of the energy barrier. We have shown how the relaxation times proliferate as the temperature is lowered. The anomalously wide distribution of relaxation times can be generated from a Gaussian distribution of energy barriers.

As temperature is decreased not only does the spread of relaxation times increase, but more importantly the width of the distribution of activation energies itself increases. Experimental investigations of relaxation times of gel electrolytes during polymerization by MR methods. Time stepping free numerical solution of linear differential equations: Krylov subspace versus waveform relaxation. The aim of this paper is two-fold.

First, we propose an efficient implementation of the continuous time waveform relaxation method based on block Krylov subspaces. Second, we compare this new implementation against Krylov subspace methods combined with the shift and invert technique. Source of non-arrhenius average relaxation time in glass-forming liquids. In this model, which is based on the fact that intermolecular interactions MR pulse sequences for selective relaxation time measurements: a phantom study. For comparison six imaging pulse sequences for relaxation time measurements were tested on the same phantom.

Estimation of T2 relaxation time of breast cancer: Correlation with clinical, imaging and pathological features. Of the breast cancers, 92 were invasive and 15 were ductal carcinoma in situ DCIS. Recently, the lattice Boltzmann method LBM has gained much attention for its ability to simulate fluid flows, and for its potential advantages over conventional CFD method.

The key advantages of LBM are, 1 suitability for parallel computations, 2 absence of the need to solve the time -consuming Poisson equation for pressure, and 3 ease with multiphase flows, complex geometries and interfacial dynamics may be treated. The LBM using relaxation technique was introduced by Higuerea and Jimenez to overcome some drawbacks of lattice gas automata LGA such as large statistical noise, limited range of physical parameters, non- Galilean invariance, and implementation difficulty in three-dimensional problem. Due to its extreme simplicity, the lattice BGK LBGK equation has become the most popular lattice Boltzmann model in spite of its well-known deficiencies, for example, in simulating high-Reynolds numbers flow.

Lallemand and Luo suggests that the use of a Multiple- Relaxation-Time MRT models are much more stable than LBGK, because the different relaxation times can be individually tuned to achieve 'optimal' stability. A lid-driven cavity flow is selected as the test problem because it has geometrically singular points in the flow, but geometrically simple.

In summary, LBM using MRT model introduces much less spatial oscillations near geometrical singular points, which is important for the successful simulation of higher Reynolds number flows. We developed the pulse sequence TOMROP T One by Multiple Read Out Pulses for determining precisely the spatial distribution of the longitudinal relaxation time T 1 in nuclear magnetic resonance NMR : a series of small-angle selection pulses is used to read out longitudinal magnetization from its initial state till thermal equilibrium.

Hence, one measurement will produce several images with different T 1 weightings whose pixel brilliance depends exponentially from read-out time. T 1 can be determined from these independent of initial magnetization and selection pulse angle. The measuring time corresponds to the time needed in multi-echo imaging for the determination of the transversal relaxation time T 2. We demonstrate this new method using head images of volunteers produced with a 0.

Isothermal structural relaxation of Fe40Ni40B20 metallic glass in the relaxation times spectrum model. The structural relaxation of amorphous as-quenched Fe40Ni40B20 sample was investigated during isothermal annealing at temperatures close to degrees C by: i the residual electrical resistance measured at liquid N-2 temperature; ii the in-situ electrical resistance; and iii the length.

Relaxation of the vibrational distribution function in N2 time varying discharges. Relaxation of the electron and vibrational distribution functions have been calculated in function of residence time in nitrogen electrical discharges and post-discharges. In the discharge the vibrational temperature get bigger with the residence time for t -2 s. In the post-discharge the vibrational distribution is evolving in such a manner that the high levels are overpopulated as the low vibrational level population is dropping.

Objective Our aim was to evaluate the cartilage cap of osteochondromas using T2 maps and to compare these values to those of normal patellar cartilage, from age and gender matched controls. Materials and Methods This study was approved by the Institutional Review Board and request for informed consent was waived. Temperature dependences of the spin-spin proton relaxation time , T2, have been shown for normal and tumorous tissues collected from kalus culture Nicotiana tabacum and from the plant Kalanchoe daigremontiana. For neoplastic plant tissues, time T2 was increased compared to that for intact plants, a finding similar to that for animal and human tissues.

The temperature dependences obtained were compared to analogous relations observed with animal tissues. Investigation of dielectric relaxation in systems with hierarchical organization: From time to frequency domain and back again. Relaxation in fractal structures was investigated theoretically starting from a simple model of a Cantorian tree and kinetic equations linking the change in the number of particles e. We numerically solved the system of differential equations obtained and determined the so-called cumulative distribution function of particles, which, in dielectric or mechanical relaxation parlance, is the same as the relaxation function of the system.

As a physical application, we studied the relationship between the dielectric relaxation in time -domain and the dielectric dispersion in the frequency-domain. Upon choosing appropriate rate constants, our model described accurately well-known non-exponential and non-Debye time - and frequency-domain functions, such as stretched exponentials, Havrilliak—Negami, and frequency power law.

Our approach opens the door to applying kinetic models to describe a wide array of relaxation processes, which traditionally have posed great challenges to theoretical modeling based on first principles. The dynamic electrical model DEM is employed for simulating the J-V characteristics for different bias scan rates and pre-poling conditions. Depending on the sign of the initial polarization normal or inverted hysteresis may be induced.

For fixed pre-poling conditions, the relaxation time , in relation to the bias scan rate, governs the magnitude of the dynamic hysteresis. Full Text Available Many pathologies can be identified by evaluating differences raised in the physical parameters of involved tissues. In a Magnetic Resonance Imaging MRI framework, spin-lattice T1 and spin-spin T2 relaxation time parameters play a major role in such an identification.

In this manuscript, a theoretical study related to the evaluation of the achievable performances in the estimation of relaxation times in MRI is proposed. After a discussion about the considered acquisition model, an analysis on the ideal imaging acquisition parameters in the case of spin echo sequences, i. In particular, the aim of the manuscript consists in providing an empirical rule for optimal imaging parameter identification with respect to the tissues under investigation.

Theoretical results are validated on different datasets in order to show the effectiveness of the presented study and of the proposed methodology. Measurement of short transverse relaxation times by pseudo-echo nutation experiments. Very short NMR transverse relaxation times may be difficult to measure by conventional methods. Nutation experiments constitute an alternative approach. Nutation is, in the rotating frame, the equivalent of precession in the laboratory frame.

It consists in monitoring the rotation of magnetization around the radio-frequency rf field when on-resonance conditions are fulfilled. Depending on the amplitude of the rf field, nutation may be sensitive to the two relaxation rates R1 and R2. A full theoretical development has been worked out for demonstrating how these two relaxation rates could be deduced from a simple nutation experiment, noticing however that inhomogeneity of the rf field may lead to erroneous results.

This has led us to devise new experiments which are the equivalent of echo techniques in the rotating frame pseudo spin-echo nutation experiment and pseudo gradient-echo experiment. Full equations of motion have been derived. Although complicated, they indicate that the sum of the two relaxation rates can be obtained very accurately and not altered by rf field inhomogeneity. This implies however an appropriate data processing accounting for the oscillations which are superposed to the echo decays and, anyway, theoretically predicted.

A series of experiments has been carried out for different values of the rf field amplitude on samples of water doped with a paramagnetic compound at different concentrations. Pragmatically, as R1 can be easily measured by conventional methods, its value is entered in the data processing algorithm which then returns exclusively the value of the transverse relaxation time. Very consistent results are obtained that way. Results: Statistical analysis ANOVA demonstrated highly significant differences in breast volume between the three stages of the cycle p relaxation time of water was lowest in the patient and control groups during ovulation and highest in the patient group during premenses.

In vivo measurements of T1 relaxation times of 31P-metabolites in human skeletal muscle. The T1 relaxation times were estimated for 31P-metabolites in human skeletal muscle. Five healthy volunteers were examined in a 1. The calculated T1 relaxation times ranged from 5. The field dependence of relaxation times of the C-1 carbon of glycogen was studied in vitro by natural-abundance 13 C NMR. T 1 is strongly field dependent, while T 2 does not change significantly with magnetic field.

T 1 and T 2 were also measured for rat hepatic glycogen enriched with [1- 13 C]glucose in vivo at 4. Calculations based on the rigid-rotor nearest-neighbor model give qualitatively good agreement with the T 1 field dependence with a best-fit correlation time of 6. A more accurate fit of T 1 data using a modified Lipari and Szabo approach indicates that internal fast motions dominate the T 1 relaxation in glycogen.

Dielectric relaxation spectroscopy was used to characterize the glass transition time , tg , of polydextrose, where the glass transition temperature, Tg , and water activity, aw relative humidity , were held constant during polydextrose relaxation. The tg was determined from a shift in the peak frequency of the imaginary capacitance spectrum with time.

It was found that when the peak frequency reaches 30 mHz, polydextrose undergoes glass transition. Glass transition time , tg , is the time for polydextrose to undergo glass transition at a specific Tg and aw. Results lead to a modified state diagram, where Tg is depressed with increasing aw. This curve forms a boundary: a below the boundary, polydextrose does not undergo glass transition and b above the boundary, polydextrose rapidly undergoes glass transition. As the boundary curve is specified by a tg value, it can assist in the selection of storage conditions.

The methodology can also be used to calculate the stress- relaxation viscosity of polydextrose as a function of Tg and aw , which is important when characterizing the flow properties of polydextrose initially in powder form. Deducting the temperature dependence of the structural relaxation time in equilibrium far below the nominal Tg by aging the decoupled conductivity relaxation to equilibrium.

State of health assessment for lithium batteries based on voltage— time relaxation measure. The degradation rate strongly depends on stress conditions during use and even at rest. Thus, accurate and rapid diagnosis of battery state of health SOH is necessary for electric vehicle manufacturers to manage their vehicle fleets and warranties. The presented method is based on the monitoring of U relax over aging. U relax is the open-circuit voltage of the battery measured after full charging and 30 min of rest.

A linear dependence between U relax and remaining capacity is noted. This correlation is demonstrated for three different commercial battery technologies different chemistries aged under different calendar and power cycling aging conditions. It was determined that the difference between two U relax voltages measured at two different aging states is proportional to SOH E decay.

This method could also be a highly useful and rapid tool for a complete battery pack diagnosis. Nuclear magnetic resonance relaxation times for human lung cancer and lung tissues. We investigated the nuclear magnetic resonance NMR relaxation times , T 1 and T 2 , for lung cancer tissue, and other samples of lung tissue obtained from surgical specimens.

The samples were nine squamous cell carcinomas, five necrotic squamous cell carcinomas, 15 adenocarcinomas, two benign mesotheliomas, and 13 fibrotic lungs. The relaxation times were measured with a 90 MHz NMR spectrometer and the results were correlated with histological changes. The values of T 1 and T 2 for squamous cell carcinoma and mesothelioma were significantly longer than those of adenocarcinoma and fibrotic lung tissue. There were no significant differences in values of T 1 and T 2 between adenocarcinoma and lung tissue.

The values of T 1 and T 2 for benign mesothelioma were similar to those of squamous cell carcinoma, which suggested that increases in T 1 and T 2 are not specific to malignant tissues. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity.

The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. From all the derived dielectric parameters, molecular interactions are interpreted through hydrogen bonding. Relaxation time of normal breast tissues. Changes with age and variations during the menstrual cycle. The influence of age on the relaxation times of normal breast parenchyma and its surrounding fatty tissue were evaluated, and the variations during a normal menstrual cycle were analyzed using an ultra low field 0.

Thirty-nine healthy volunteers aged 21 to 59 years were examined to determine T1 and T2 relaxation times , and 8 of these volunteers were studied once weekly during one menstrual cycle. The only significant trend was an increase in the T2 of breast parenchyma with increasing age. Dean, K. University Central Hospital, Turku Finland. Characterization of relaxation processes in interacting vortex matter through a time -dependent correlation length.

Vortex lines in type-II superconductors display complicated relaxation processes due to the intricate competition between their mutual repulsive interactions and pinning to attractive point or extended defects. We perform extensive Monte Carlo simulations for an interacting elastic line model with either point-like or columnar pinning centers. From measurements of the space- and time -dependent height-height correlation function for lateral flux line fluctuations, we extract a characteristic correlation length that we use to investigate different non-equilibrium relaxation regimes. The specific time dependence of this correlation length for different disorder configurations displays characteristic features that provide a novel diagnostic tool to distinguish between point-like pinning centers and extended columnar defects.

Evaluation of relaxation time measurements by magnetic resonance imaging. A phantom study. Several circumstances may explain the great variation in reported proton T1 and T2 relaxation times usually seen. This study was designed to evaluate the accuracy of relaxation time measurements by magnetic resonance imaging MRI operating at 1. Using a phantom of nine boxes with different Measurements performed on a large water phantom in order to evaluate the homogeneity Changing the gradient field strength apparently had no influence on the T2 values recorded.

Consequently diffusion processes seem without significance. It is concluded Full Text Available Complexation between anionic and cationic polyelectrolytes results in solid-like precipitates or liquid-like coacervate depending on the added salt in the aqueous medium. However, the boundary between these polymer-rich phases is quite broad and the associated changes in the polymer relaxation in the complexes across the transition regime are poorly understood. In this work, the relaxation dynamics of complexes across this transition is probed over a wide timescale by measuring viscoelastic spectra and zero-shear viscosities at varying temperatures and salt concentrations for two different salt types.

We find that the complexes exhibit time -temperature superposition TTS at all salt concentrations, while the range of overlapped-frequencies for time -temperature-salt superposition TTSS strongly depends on the salt concentration Cs and gradually shifts to higher frequencies as Cs is decreased. The sticky-Rouse model describes the relaxation behavior at all Cs. However, collective relaxation of polyelectrolyte complexes gradually approaches a rubbery regime and eventually exhibits a gel-like response as Cs is decreased and limits the validity of TTSS.

The modified relaxation time function: A novel analysis technique for relaxation processes. Application to high-temperature molybdenum internal friction peaks. The modified relaxation time MRT function, which is based on a general linear viscoelastic formalism, has several important mathematical properties that greatly simplify the analysis of relaxation processes. In this work, the MRT is applied to the study of the relaxation damping peaks in deformed molybdenum at high temperatures.

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The dependence of experimental data from these relaxation processes with temperature are adequately described by a Havriliak-Negami HN function, and the MRT makes it possible to find a relation between the parameters of the HN function and the activation energy of the process. The analysis reveals that for the relaxation peak appearing at temperatures below K, the physical mechanism is related to a vacancy-diffusion-controlled movement of dislocations.

In contrast, when the peak appears at temperatures higher than K, the damping is controlled by a mechanism of diffusion in the low-temperature tail of the peak, and in the high-temperature tail of the peak the creation plus diffusion of vacancies at the dislocation line occurs. The water proton spin-lattice relaxation times in virus-infected cells.

The water proton spin-lattice relaxation times in HEp-2 cell cultures were determined immediately after 1 h of polio-virus adsorption. The shortening of the water T 1 was closely related to the multiplicity of infection, allowing direct inspections of the virus-cell interaction since the first steps of the infectious cycle. Virus-induced structural and conformational changes of cell constituents were suggested to be detectable by NMR investigation of cell water.

Determining the structural relaxation times deep in the glassy state of the pharmaceutical Telmisartan. By using the dielectric relaxation method proposed recently by Casalini and Roland Phys. Unequivocal comparison cannot be made in the case of Telmisartan because its beta-loss peak is extremely broad, and the CM predicts only an order of magnitude agreement between the primitive relaxation frequency and the beta-peak frequency.

We also made an attempt to analyze all isothermal and aging susceptibility data after transformation into the electric modulus representation. Our results suggest that the electric modulus representation may be useful as an alternative to analyze aging data, especially in the case of highly polar glassformers having a large ratio of low frequency and high frequency dielectric. Two- relaxation-time lattice Boltzmann method and its application to advective-diffusive-reactive transport. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments.

These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. The TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena.

Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments. Bulk viscosity of strongly interacting matter in the relaxation time approximation. We show how thermal mean field effects can be incorporated consistently in the hydrodynamical modeling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent.

The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio of the bulk viscosity to its relaxation time. Pseudopotential multi- relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio. The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention.

In the present work, the modified forcing scheme for the pseudopotential multi- relaxation-time lattice Boltzmann model developed by Li Q et al. E 87 ] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi- relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity.

By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multi- relaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling.

Asymptotic description of two metastable processes of solidification for the case of large relaxation time. The interaction length is proportional to a small parameter, and the relaxation time is proportional to a constant. The asymptotic solutions describing two metastable processes are constructed and justified. The soliton type solution describes the first stage of separation in alloy, when a set of ''superheated liquid'' appears inside the ''solid'' part. The Van der Waals type solution describes the free interface dynamics for large time.

The smoothness of temperature is established for large time and the Mullins-Sekerka problem describing the free interface is derived. Relaxation dynamics and thermophysical properties of vegetable oils using time -domain reflectometry. Dielectric relaxation studies of vegetable oils are important for insights into their hydrogen bonding and intermolecular dynamics. The frequency and temperature dependence of dielectric constants and dielectric loss factors were determined for coconut, peanut, soya bean, sunflower, palm, and olive oils.

The dielectric permittivity spectra for each of the studied vegetable oils are explained using the Debye model with their complex dielectric permittivity analyzed using the Havriliak-Negami equation. Calculation and analysis of these thermodynamic parameters agrees with the determined dielectric parameters, giving insights into the temperature dependence of the molecular dynamics of these systems. Full Text Available Terminal cancer patients face not only issues unique to their diseases, but also issues rooted in their previous life experiences, including physical, social, psychological, and spiritual pain.

I attended an elderly terminal cancer patient in a Japanese hospital, observing and conversing with her as she went through the process of examining her life and faith. Magnetic resonance studies on the brain edema by the administration of the osmotic agents; Special references to the relaxation times. Subjects were 11 patients who were composed of 4 gliomas, 2 metastatic brain tumors, 2 meningiomas, 2 hypertensive intracerebral hematomas, and a C-P angle tumor. Scanning was done before injection, just after injection, and post injection until 2 hours with passing times.

We regarded the peritumoral or perihemorrahgical low density area on the CT scan as the edema, and then, relaxation times of the edema was obtained from the ROI of the calculated images corresponding to the surrounding low density area on the CT scan. The results were as follows. Normal white matter, in the same way, showed the decreasing tendency, but the degree of the decreasing was more clearly in the edematous areas than in the white matter.

In most cases, relaxation times decreased just after injection. But in a few cases, relaxation times increased just after injection, transiently. In some cases, decreased relaxation times continued more than 2 hours, in the other cases, relaxation times increased at 2 hours. In the current MR systems, there are considerably large standard deviations and inequality in the magnetic field, therefore, further investigations should be done moreover. Elastic models for the non-Arrhenius relaxation time of glass-forming liquids. We first review the phenomenology of viscous liquids and the standard models used for explaining the non-Arrhenius average relaxation time.

Then the focus is turned to the so-called elastic models, arguing that these models are all equivalent in the Einstein approximation where the short- time We finally discuss the connection between the elastic models and two well-established research fields of condensed-matter physics: point defects in crystals and solid-state diffusion T 2 relaxation time of hyaline cartilage in presence of different gadolinium-based contrast agents. The transverse relaxation time , T 2 , of native cartilage is used to quantify cartilage degradation.

T 2 is frequently measured after contrast administration, assuming that the impact of gadolinium-based contrast agents on cartilage T 2 is negligible. To verify this assumption the depth-dependent variation of T 2 in the presence of gadopentetate dimeglumine, gadobenate dimeglumine and gadoteridol was investigated.

## A Sup C Inf Inequality For Liouville Type Equations With Singular Potentials

Transverse high-spatial-resolution T 1 - and T 2 -maps were simultaneously acquired on a 1. The mean values in different cartilage layers were compared for global variance using the Kruskal-Wallis test and pairwise using the Mann-Whitney U-test. Eleven hours after contrast administration significant differences p cartilage thickness were close to 1.

The change in T 2 relaxation rate was similar to the change in T 1. Cartilage T 2 measurements after contrast administration will lead to systematic errors in the quantification of cartilage degradation. A novel NMR experiment comprising adiabatic fast passage techniques for the measurement of heteronuclear self- relaxation rates in fully 15N-enriched proteins is described.

Heteronuclear self- relaxation is monitored by performing adiabatic fast passage AFP experiments at variable adiabaticity e. The experiment encompasses gradient- selection and sensitivity-enhancement. It is shown that transverse relaxation rates derived with this method are in good agreement with the ones measured by the classical Carr-Purcell-Meiboom-Gill CPMG sequences.

Musculoskeletal MRI at 3. The purpose of this study was to measure and compare the relaxation times of musculoskeletal tissues at 3. We used the measured relaxation times to help design 7. The measured relaxation times were used to help develop high resolution 7. Parameters for musculoskeletal protocols at 7. Jordan, Caroline D. Objective: The purpose of this study was to measure and compare the relaxation times of musculoskeletal tissues at 3. Materials and methods: We measured the T 1 and T 2 relaxation times of cartilage, muscle, synovial fluid, bone marrow and subcutaneous fat at both 3.

The T 1 relaxation times were measured using a spin-echo inversion recovery sequence with six inversion times. The T 2 relaxation times were measured using a spin-echo sequence with seven echo times. The accuracy of both the T 1 and T 2 measurement techniques was verified in phantoms at both magnetic field strengths. Results: The T 1 relaxation times in all tissues at 7.

Conclusion: The T 1 and T 2 changes were within the expected ranges. Radiation self-polarization of electrons moving in a magnetic field. When electrons move in a magnetic field, synchrotron radiation gives rise to transitions accompanied by the electron spin reorientation.

In this case, it is essential that the transition probability depends on the spin orientation; as a result electron polarization takes place with the spin orientation being predominantly opposite to the direction of the magnetic field. This effect has been called ''radiative self-polarization of electrons''.

The present work is concerned with the question how the choice of the spin operator will affect the self-polarization degree and relaxation time. The problem has been solved for a vector spin operator. Full Text Available We introduce a magnetohydrodynamic model of boundary-layer equations for conducting viscous fluids. This model is applied to study the effects of free convection currents with thermal relaxation time on the flow of a viscous conducting fluid. The method of the matrix exponential formulation for these equations is introduced. The resulting formulation together with the Laplace transform technique is applied to a variety problems.

The effects of a plane distribution of heat sources on the whole and semispace are studied. Numerical results are given and illustrated graphically for the problem. Laplace transform is used. The solution in Laplace transform domain has been obtained using a direct method and its inversion is calculated numerically using a method based on Fourier series expansion technique.

Finally, the effects of the two fractional parameters thermo and magneto on variable fields distributions are made. Numerical results are represented graphically. Predicting how nanoconfinement changes the relaxation time of a supercooled liquid. The properties of nanoconfined fluids can be strikingly different from those of bulk liquids. A basic unanswered question is whether the equilibrium and dynamic consequences of confinement are related to each other in a simple way. We study this question by simulation of a liquid comprising asymmetric dumbbell-shaped molecules, which can be deeply supercooled without crystallizing.

We find that the dimensionless structural relaxation times -spanning six decades as a function of temperature, density, and degree of confinement-collapse when plotted versus excess entropy. The data also collapse when plotted versus excess isochoric heat capacity, a behavior consistent with the existence of isomorphs in the bulk and confined states. MR spectroscopy of liver in overweight children and adolescents: Investigation of 1H T2 relaxation times at 3 T.

## Read Legacy: A Novel

Objective: The objective was to investigate T 2 relaxation values and to optimize hepatic fat quantification using proton MR spectroscopy 1 H MRS at 3 T in overweight and obese children and adolescents. Subjects: The study included consecutive children and adolescents with a body mass index above the 97th percentile according to age and sex. T 2 relaxation values and hepatic fat content corrected for the T 2 relaxation effects were calculated. Results: T 2 values for water ranged from 22 ms to 42 ms mean value 28 ms and T 2 values for fat ranged from 36 ms to 99 ms mean value 64 ms.

It is necessary to measure T 2 relaxation values and to correct the spectra for the T 2 relaxation effects in order to obtain an accurate estimate of the hepatic fat content. Coupled kinetic equations for fermions and bosons in the relaxation-time approximation. Kinetic equations for fermions and bosons are solved numerically in the relaxation-time approximation for the case of one-dimensional boost-invariant geometry.

Fermions are massive and carry baryon number, while bosons are massless. The conservation laws for the baryon number, energy, and momentum lead to two Landau matching conditions, which specify the coupling between the fermionic and bosonic sectors and determine the proper- time dependence of the effective temperature and baryon chemical potential of the system. The numerical results illustrate how a nonequilibrium mixture of fermions and bosons approaches hydrodynamic regime described by the Navier-Stokes equations with appropriate forms of the kinetic coefficients.

The shear viscosity of a mixture is the sum of the shear viscosities of fermion and boson components, while the bulk viscosity is given by the formula known for a gas of fermions, however, with the thermodynamic variables characterising the mixture. Thus, we find that massless bosons contribute in a nontrivial way to the bulk viscosity of a mixture, provided fermions are massive. We further observe the hydrodynamization effect, which takes place earlier in the shear sector than in the bulk one.

The numerical studies of the ratio of the longitudinal and transverse pressures show, to a good approximation, that it depends on the ratio of the relaxation and proper times only. This behavior is connected with the existence of an attractor solution for conformal systems. In this paper we provide a quantum field theoretical study on the shear and bulk relaxation times. First, we find Kubo formulas for the shear and the bulk relaxation times , respectively. They are found by examining response functions of the stress-energy tensor.

We use general properties of correlation functions and the gravitational Ward identity to parametrize analytical structures of the Green functions describing both sound and diffusion mode.

We find that the hydrodynamic limits of the r We find that the hydrodynamic limits of the real parts of the respective energy-momentum tensor correlation functions provide us with the method of computing both the shear and bulk viscosity relaxation times. The relaxation time is shown to be inversely related to the thermal width as it should be. The measurement of very short spin-lattice, or longitudinal, relaxation SLR times i.

The ability to measure such fast SLR data on amorphous Si and copper-chromium-tin spinel led to an understanding of the role of exchange interaction in affecting spin-lattice relaxation , while the data on polymer resins doped with rare-earth ions provided evidence of spin-fracton relaxation Pescia et al. But such fast SLR times are not measurable by the most commonly used techniques of saturation- and inversion-recovery Poole, ; Alger, , which only measure spin-lattice relaxation times longer than s.

A summary of relevant experimental data is presented in Table 1. Detection of early gamma-postirradiation effects in murine spleen by proton NMR relaxation times. It was our aim to evaluate the potential of proton relaxation times for the early detection of radiation-induced spleen changes. Female Swiss mice were irradiated with doses ranging from 0. The body weight, the spleen weight and the spleen water content of single animals were determined.

Measurements of longitudinal T1 and transversal T2 proton relaxation times of the spleen samples were performed in a 0. Histological examinations of the control and irradiated organs were performed. NMR measurements during the first five days after irradiation showed that total body gamma-irradiation with doses from 1. Significant shortening in T2 was observed for the spleen of animals irradiated with a dose of 4 Gy. Histological examinations demonstrated subnormal architecture in slices derived from animals irradiated with 2 Gy and 4 Gy.

The fluctuations of the spleen T1 and T2 of irradiated mice are correlated with relative spleen weight and can be used to estimate radiation induced changes in this organ. Towards quantitative measurements of relaxation times and other parameters in the brain. The nature and physical significance of the relaxation times T1 and T2 and of proton density are described. Methods of measuring T1 and T2 are discussed with emphasis on the establishment of precision and the maintenance of accuracy. Reported standards of success are briefly reviewed.

Although early hopes of disease diagnosis by tissue characterisation were not realised, strict scientific method and careful calibration have made it pracitcable to apply relaxation time measurement to research into disease process. Serial measurements in patients and correlation with similar studies in animal models, biopsy results and autopsy material taken together have provided new knowledge about cerebral oedema, water compartmentation, alcoholism and the natural history of multiple sclerosis.

There are prospects of using measurement to monitor treatment in other diseases with diffuse brain abnormalities invisible on the usual images. Secondarily derived parameters and notably the quantification of blood-brain barrier defect after injection of Gadolinium-DTPA also offer prospects of valuable data. Quasiparticle energy distribution and relaxation times in a tunnel-injected superconductor.