scholarly journals Universal Constraints on Relaxation Times for d-Level GKLS Master Equations

2017 ◽  
Vol 24 (04) ◽  
pp. 1740009
Author(s):  
Gen Kimura ◽  
Shigeru Ajisaka ◽  
Kyouhei Watanabe
Keyword(s):  
Relaxation Time ◽  
Relaxation Rate ◽  
Master Equation ◽  
Experimental Test ◽  
Relaxation Times ◽  
Master Equations ◽  
Complete Positivity ◽  
Relaxation Rates ◽  
Markovian Dynamics ◽  
Inverse Relaxation Time

In 1976, Gorini, Kossakowski, Sudarshan and Lindblad independently discovered a general form of master equations for an open quantum Markovian dynamics. In honor of all the authors, the equation is nowadays called the GKLS master equation. In this paper, we show universal constraints on the relaxation times valid for any d-level GKLS master equations, which is a generalization of the well-known constraints for 2-level systems. Specifically, we show that any relaxation rate, the inverse-relaxation time, is not greater than half of the sum of all relaxation rates. Since the relaxation times are measurable in experiments, our constraints provide a direct experimental test for the validity of the GKLS master equations, and hence for the conditions of the complete positivity and Markovianity.

Changes in contractility of frog muscle due to fatigue and inhibitors

1964 ◽  
Vol 206 (5) ◽  
pp. 1043-1048
Author(s):  
Manfred Brust
Keyword(s):  
Relaxation Rate ◽  
Relaxation Times ◽  
Frog Muscle ◽  
Relaxation Rates ◽  
Contraction Rate ◽  
Single Fibers ◽  
Continuous Activity ◽  
Frog Sartorius

Continuous activity in excised and curarized frog sartorius muscles reduced twitch tension, contraction rate, and half-relaxation rate, and increased contraction and half-relaxation times. These changes are essentially the same as those reported by others for single fibers. 0.05 mm 2,4-dinitrophenol (DNP), 1 mm NaN3, and 1 mm KCN reduced twitch and tetanus tension in rested muscles. DNP and KCN shortened contraction and half-relaxation times, but NaN3 induced a late prolongation. DNP and NaN3 reduced contraction and half-relaxation rates, but KCN enhanced them. DNP and NaN3 accentuated fatigue declines in tension output. KCN consistently induced twitch treppe, while tetanus tension declined as in unpoisoned fatigue. All the agents enhanced fatigue prolongations of contraction and half-relaxation times. DNP and NaN3 accelerated the fatigue declines of contraction and half-relaxation rates, but KCN retarded them. All inhibitor effects were at least partially reversible. These results differ in many respects from equivalent results obtained with mouse muscles. Known inhibitor mechanisms do not as yet account adequately for the present findings.

Contraction kinetics of red muscle in scup: mechanism for variation in relaxation rate along the length of the fish.

1997 ◽  
Vol 200 (9) ◽  
pp. 1297-1307 ◽  
Author(s):  
D M Swank ◽  
G Zhang ◽  
L C Rome
Keyword(s):  
Relaxation Rate ◽  
Relaxation Times ◽  
Muscle Length ◽  
Fiber Types ◽  
Myosin Isoforms ◽  
Relaxation Rates ◽  
Atpase Inhibitor ◽  
Pumping Rate ◽  
Red Muscle ◽  
The Difference

We studied possible mechanisms for the twofold difference in red muscle relaxation times between the posterior (207.2 ms) and anterior (98.4 ms) musculature of scup Stenotomus chrysops, which has been shown to have a large effect on power generation during swimming. This difference was not due to contamination of the anterior bundles with faster fiber types, as histological examination showed that all bundles contained more than 98.9% red fibers. Further, maximum velocities of shortening (Vmax) at 20 degrees C were nearly identical, 5.37 MLs-1 (where ML is muscle length) for the anterior musculature and 5.47 MLs-1 for the posterior musculature, suggesting that the difference in relaxation times was not due to a difference in the crossbridge detachment rates associated with different myosin isoforms. The possibility of differences in the Ca2+ pumping rate influencing relaxation rate was explored using cyclopiazonic acid (CPA), a sarcoplasmic reticulum (SR) Ca(2+)-ATPase inhibitor. The concentration of CPA could be adjusted to slow the relaxation rate of an anterior muscle to that of a posterior muscle. However, SDS gels showed no difference in the intensity of SR Ca(2+)-ATPase protein bands between muscle positions. These results suggest that differences in the Ca2+ pumping could account for the observed difference in relaxation rate, but do not support the simplest hypothesis that the difference in relaxation rates is due to differences in numbers of Ca2+ pumps. Other possible mechanisms for this difference are explored.

The Master Equation for the Dissociation of a Dilute Diatomic Gas. VI. Solution of Coupled Sets of Master Equations

1972 ◽  
Vol 50 (6) ◽  
pp. 897-906 ◽  
Author(s):  
D. L. S. McElwain ◽  
H. O. Pritchard
Keyword(s):  
Relaxation Time ◽  
Differential Equations ◽  
Master Equation ◽  
Normal Mode ◽  
Rate Constants ◽  
Vibrational Relaxation ◽  
Master Equations ◽  
Diatomic Gas ◽  
Full Solution ◽  
Mode Technique

Three coupled sets of master equations, representing the equilibration of [Formula: see text] via atoms only, have been solved by the normal-mode technique; the set of 57 simultaneous differential equations describing the H2/D2/2HD system was considered as a suitable trial model. It was found that at times (t) in excess of the longest vibrational relaxation time, even though some of the populations in the system appeared highly non-Boltzmann, all the phenomenological rate constants were well-behaved: they were either constant and obeyed the rate–quotient law, or they were dependent on t2.The paper concludes with a discussion of the information required before a full solution of the [Formula: see text] reaction could be contemplated, and suggests methods by which an approximation to such a solution could be obtained.

Skeletal muscle relaxation rate after fasting or hypocaloric feeding

1991 ◽  
Vol 71 (1) ◽  
pp. 204-209 ◽  
Author(s):  
M. L. Nishio ◽  
K. N. Jeejeebhoy
Keyword(s):  
Skeletal Muscle ◽  
Relaxation Rate ◽  
Muscle Fiber ◽  
Fiber Type ◽  
Muscle Relaxation ◽  
Relaxation Times ◽  
Exponential Phase ◽  
Relaxation Rates ◽  
Type Composition ◽  
Hypocaloric Feeding

The effect of malnutrition on skeletal muscle relaxation is not entirely clear; some studies indicate no change and others a slowing of the relaxation rate. We investigated whether these different results were due to type of malnutrition, muscle fiber type composition, or the index used to express relaxation rate. The effect of a 2-day fast (16% body wt loss) or 1 wk of hypocaloric feeding (22.6% wt loss) on relaxation rates of soleus and extensor digitorum longus (EDL) muscles was studied in situ with the use of anesthetized adult Wistar rats. Relaxation rates were assessed for twitch contractions using half-relaxation times and exponential phase half-times and for tetanic contractions using exponential phase half-times. The rate of relaxation was unaffected by fasting, whereas hypocaloric feeding reduced relaxation rates after twitch and tetanic contractions in both soleus and EDL muscles. We conclude that slowing of skeletal muscle relaxation rate occurs after 1 wk of hypocaloric feeding but not after 2 days of fasting. The slowing is independent of muscle fiber composition, type of contraction, or the index used to express relaxation rate.

Spin–lattice relaxation of Fe3+ in rutile for X- and F-band transitions

1969 ◽  
Vol 47 (15) ◽  
pp. 1573-1583 ◽  
Author(s):  
G. J. Lichtenberger
Keyword(s):  
Relaxation Time ◽  
Temperature Dependence ◽  
Transition Probabilities ◽  
Relaxation Times ◽  
Lattice Relaxation ◽  
Spin Lattice Relaxation ◽  
Rate Equations ◽  
Relaxation Rates ◽  
Time Resolved ◽  
Spin Lattice

Detailed measurements of the angular and temperature dependence (1.6 °K to 4.2 °K) of the dominant spin–lattice relaxation rates of Fe3+ in rutile have been carried out for a number of strong transitions at 9.4 Gc and 121 Gc using the pulse saturation method. At 9.4 Gc, two relaxation time components were observed, ranging from 0.5 to 1.2 ms and 1.6 to 4.0 ms, respectively, at 4.2 °K. Assuming a relationship of the form log(relaxation time) = −n∙log(temperature), the temperature dependence factor n was found to be between 0.4 and 1.0. The single relaxation time resolved at F band had values from 0.7 to 1.0 ms at 4.2 °K, and n between 0.1 and 0.6. The corresponding relative relaxation rates were calculated from the direct process spin–phonon transition probabilities, assuming Debye elastic isotropy for rutile. Using a cubic spin–lattice coupling tensor, [Formula: see text] was found to be 0.5 and the rate equations for the six-level system were solved. The calculated effective relaxation times were successfully identified with the slower dominant relaxation component of the experimental data.

scholarly journals T2 mapping of the peritumoral infiltration zone of glioblastoma and anaplastic astrocytoma

2021 ◽  
pp. 197140092198932
Author(s):  
Timo Alexander Auer ◽  
Maike Kern ◽  
Uli Fehrenbach ◽  
Yasemin Tanyldizi ◽  
Martin Misch ◽  
...  
Keyword(s):  
Relaxation Time ◽  
Isocitrate Dehydrogenase ◽  
Anaplastic Astrocytoma ◽  
T2 Mapping ◽  
Relaxation Times ◽  
Region Of Interest ◽  
World Health ◽  
High Grade ◽  
High Grade Gliomas ◽  
Health Organization

Purpose To characterise peritumoral zones in glioblastoma and anaplastic astrocytoma evaluating T2 values using T2 mapping sequences. Materials and methods In this study, 41 patients with histopathologically confirmed World Health Organization high grade gliomas and preoperative magnetic resonance imaging examinations were retrospectively identified and enrolled. High grade gliomas were differentiated: (a) by grade, glioblastoma versus anaplastic astrocytoma; and (b) by isocitrate dehydrogenase mutational state, mutated versus wildtype. T2 map relaxation times were assessed from the tumour centre to peritumoral zones by means of a region of interest and calculated pixelwise by using a fit model. Results Significant differences between T2 values evaluated from the tumour centre to the peritumoral zone were found between glioblastoma and anaplastic astrocytoma, showing a higher decrease in signal intensity (T2 value) from tumour centre to periphery for glioblastoma ( P = 0.0049 – fit-model: glioblastoma –25.02± 19.89 (–54–10); anaplastic astrocytoma –5.57±22.94 (–51–47)). Similar results were found when the cohort was subdivided by their isocitrate dehydrogenase profile, showing an increased drawdown from tumour centre to periphery for wildtype in comparison to mutated isocitrate dehydrogenase ( P = 0.0430 – fit model: isocitrate dehydrogenase wildtype –10.35±16.20 (–51) – 0; isocitrate dehydrogenase mutated 12.14±21.24 (–15–47)). A strong statistical proof for both subgroup analyses ( P = 0.9987 – glioblastoma R2 0.93±0.08; anaplastic astrocytoma R2 0.94±0.15) was found. Conclusion Peritumoral T2 mapping relaxation time tissue behaviour of glioblastoma differs from anaplastic astrocytoma. Significant differences in T2 values, using T2 mapping relaxation time, were found between glioblastoma and anaplastic astrocytoma, capturing the tumour centre to the peritumoral zone. A similar curve progression from tumour centre to peritumoral zone was found for isocitrate dehydrogenase wildtype high grade gliomas in comparison to isocitrate dehydrogenase mutated high grade gliomas. This finding is in accordance with the biologically more aggressive behaviour of isocitrate dehydrogenase wildtype in comparison to isocitrate dehydrogenase mutated high grade gliomas. These results emphasize the potential of mapping techniques to reflect the tissue composition of high grade gliomas.

Proton magnetic relaxation of water sorbed by methaemoglobin crystals

1973 ◽  
Vol 331 (1587) ◽  
pp. 457-468 ◽  
Keyword(s):  
Relaxation Rate ◽  
Relaxation Times ◽  
Transverse Relaxation Rate ◽  
Ferric Ions ◽  
Transverse Relaxation ◽  
Water Binding ◽  
Adsorption Sites ◽  
Protein Molecules ◽  
Proton Magnetic Relaxation ◽  
Limiting Value

P. m. r. relaxation times ( T 1 and T 2 ) have been measured as a function of regain and temperature for water sorbed by lyophilized methaemoglobin. The purpose of the work was to gain information regarding the nature and extent of water binding by the protein molecules. The T 1 results are interpreted in terms of an exchange between the sixth ligand position of the Fe (III) and other adsorption sites on the protein. At high temperatures the relaxation rate at a given regain reaches a limiting value which allows the fraction of ferric ions hydrated to be calculated. Above 16% regain all the Fe (III) is hydrated. At 21 and 35% regains a maximum appears in the relaxation rate at about -46 °C indicating a contribution from a more mobile phase which produces a T 1 minimum at that temperature. The T 2 data are consistent with a model in which the main contribution to the transverse relaxation rate comes from a tightly bound fraction of the water with ω 0 Ƭ c ≫1. The temperature dependence of T 2 exhibits three different regions: ( a ) a low temperature region where lg T 2 ∝ T -1 ; ( b ) an intermediate region with a steeper increase of T 2 with temperature; and ( c ) a high temperature where T 2 levels off.

scholarly journals Theoretical Effect of Temperature on Threshold in the Hodgkin-Huxley Nerve Model

1966 ◽  
Vol 49 (5) ◽  
pp. 989-1005 ◽  
Author(s):  
Richard Fitzhugh
Keyword(s):  
Relaxation Time ◽  
Relaxation Times ◽  
Giant Axon ◽  
Temperature Curve ◽  
Effect Of Temperature ◽  
Threshold Temperature ◽  
Ionic Conductances ◽  
And Shifts ◽  
The Right ◽  
Increasing Temperature

In the squid giant axon, Sjodin and Mullins (1958), using 1 msec duration pulses, found a decrease of threshold with increasing temperature, while Guttman (1962), using 100 msec pulses, found an increase. Both results are qualitatively predicted by the Hodgkin-Huxley model. The threshold vs. temperature curve varies so much with the assumptions made regarding the temperature-dependence of the membrane ionic conductances that quantitative comparison between theory and experiment is not yet possible. For very short pulses, increasing temperature has two effects. (1) At lower temperatures the decrease of relaxation time of Na activation (m) relative to the electrical (RC) relaxation time favors excitation and decreases threshold. (2) For higher temperatures, effect (1) saturates, but the decreasing relaxation times of Na inactivation (h) and K activation (n) factor accommodation and increased threshold. The result is a U-shaped threshold temperature curve. R. Guttman has obtained such U-shaped curves for 50 µsec pulses. Assuming higher ionic conductances decreases the electrical relaxation time and shifts the curve to the right along the temperature axis. Making the conductances increase with temperature flattens the curve. Using very long pulses favors effect (2) over (1) and makes threshold increase monotonically with temperature.

scholarly journals Longer T2relaxation time is a marker of hypothalamic gliosis in mice with diet-induced obesity

2013 ◽  
Vol 304 (11) ◽  
pp. E1245-E1250 ◽  
Author(s):  
Donghoon Lee ◽  
Joshua P. Thaler ◽  
Kathryn E. Berkseth ◽  
Susan J. Melhorn ◽  
Michael W. Schwartz ◽  
...  
Keyword(s):  
Relaxation Time ◽  
High Field ◽  
Relaxation Times ◽  
Quantitative Mri ◽  
Human Studies ◽  
Mri Findings ◽  
Diet Induced Obesity ◽  
Magnetic Resonance Imaging Mri ◽  
The Right ◽  
Mr Brain

A hallmark of brain injury from infection, vascular, neurodegenerative, and other disorders is the development of gliosis, which can be detected by magnetic resonance imaging (MRI). In rodent models of diet-induced obesity (DIO), high-fat diet (HFD) consumption rapidly induces inflammation and gliosis in energy-regulating regions of the mediobasal hypothalamus (MBH), and recently we reported MRI findings suggestive of MBH gliosis in obese humans. Thus, noninvasive imaging may obviate the need to assess MBH gliosis using histopathological end points, an obvious limitation to human studies. To investigate whether quantitative MRI is a valid tool with which to measure MBH gliosis, we performed analyses, including measurement of T2relaxation time from high-field MR brain imaging of mice fed HFD and chow-fed controls. Mean bilateral T2relaxation time was prolonged significantly in the MBH, but not in the thalamus or cortex, of HFD-fed mice compared with chow-fed controls. Histological analysis confirmed evidence of increased astrocytosis and microglial accumulation in the MBH of HFD-fed mice compared with controls, and T2relaxation times in the right MBH correlated positively with mean intensity of glial fibrillary acidic protein staining (a marker of astrocytes) in HFD-fed animals. Our findings indicate that T2relaxation time obtained from high-field MRI is a useful noninvasive measurement of HFD-induced gliosis in the mouse hypothalamus with potential for translation to human studies.

Textural and pore size analysis of carbonates from integrated core and nuclear magnetic resonance logging: An Arbuckle study

2015 ◽  
Vol 3 (1) ◽  
pp. SA77-SA89 ◽  
Author(s):  
John Doveton ◽  
Lynn Watney
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Relaxation Time ◽  
Magnetic Resonance ◽  
Pore Size ◽  
Relaxation Times ◽  
T2 Relaxation Time ◽  
T2 Relaxation ◽  
Nmr Logging ◽  
The Core ◽  
Nuclear Magnetic

The T2 relaxation times recorded by nuclear magnetic resonance (NMR) logging are measures of the ratio of the internal surface area to volume of the formation pore system. Although standard porosity logs are restricted to estimating the volume, the NMR log partitions the pore space as a spectrum of pore sizes. These logs have great potential to elucidate carbonate sequences, which can have single, double, or triple porosity systems and whose pores have a wide variety of sizes and shapes. Continuous coring and NMR logging was made of the Cambro-Ordovician Arbuckle saline aquifer in a proposed CO2 injection well in southern Kansas. The large data set gave a rare opportunity to compare the core textural descriptions to NMR T2 relaxation time signatures over an extensive interval. Geochemical logs provided useful elemental information to assess the potential role of paramagnetic components that affect surface relaxivity. Principal component analysis of the T2 relaxation time subdivided the spectrum into five distinctive pore-size classes. When the T2 distribution was allocated between grainstones, packstones, and mudstones, the interparticle porosity component of the spectrum takes a bimodal form that marks a distinction between grain-supported and mud-supported texture. This discrimination was also reflected by the computed gamma-ray log, which recorded contributions from potassium and thorium and therefore assessed clay content reflected by fast relaxation times. A megaporosity class was equated with T2 relaxation times summed from 1024 to 2048 ms bins, and the volumetric curve compared favorably with variation over a range of vug sizes observed in the core. The complementary link between grain textures and pore textures was fruitful in the development of geomodels that integrates geologic core observations with petrophysical log measurements.

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