This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fac...This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].展开更多
Ephedra comprises approximately 50 species, which are roughly equally distributed between the Old and New World deserts, but not in the intervening regions （amphitropical range）. Great heterogeneity in the substitut...Ephedra comprises approximately 50 species, which are roughly equally distributed between the Old and New World deserts, but not in the intervening regions （amphitropical range）. Great heterogeneity in the substitution rates of Gnetales （Ephedra, Gnetum, and Welwitschia） has made it difficult to infer the ages of the major divergence events in Ephedra, such as the timing of the Beringian disjunction in the genus and the entry into South America. Here, we use data from as many Gnetales species and genes as available from GenBank and from a recent study to investigate the timing of the major divergence events. Because of the tradeoff between the amount of missing data and taxon/gene sampling, we reduced the initial matrix of 265 accessions and 12 loci to 95 accessions and 10 loci, and further to 42 species （and 7736 aligned nucleotides） to achieve stationary distributions in the Bayesian molecular clock runs. Results from a relaxed clock with an uncorrelated rates model and fossil-based calibration reveal that New World species are monophyletic and diverged from their mostly Asian sister clade some 30 mya, fitting with many other Beringian disjunctions. The split between the single North American and the single South American clade occurred approximately 25 mya, well before the closure of the Panamanian Isthmus. Overall, the biogeographic history of Ephedra appears dominated by long-distance dispersal, but finer-scale studies are needed to test this hypothesis.展开更多
In order to understand whether the ameliorating effect on old ages memory disorder by the root of Salvia miltiorhiza is related to the acetylcholinesterase （ACHE） inhibition, two main ingredients, salvianolic acid B...In order to understand whether the ameliorating effect on old ages memory disorder by the root of Salvia miltiorhiza is related to the acetylcholinesterase （ACHE） inhibition, two main ingredients, salvianolic acid B （1） and rosmarinic acid （2）, which were isolated from S. miltiorhiza water extract, were investigated in vitro by NMR relaxation rate in this work. The results showed that the proton selective relaxation rates and the molecular rotational correlation time of proton pairs for compounds 1 and 2 increased significantly by adding of AChE in mixing solution. The study reveals that the two compounds might bind to the enzyme and have ACHE inhibitory effect, which could contribute to the ameliorating effect at some extent on old ages memory disorder.展开更多
The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is ob...The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.展开更多
A relaxation-rate formula is presented for the entropic lattice Boltzmann model(ELBM) - a discrete kinetic theory for hydrodynamics. The simple formula not only guarantees the discrete time H-theorem but also gives fu...A relaxation-rate formula is presented for the entropic lattice Boltzmann model(ELBM) - a discrete kinetic theory for hydrodynamics. The simple formula not only guarantees the discrete time H-theorem but also gives full consideration to the consistency with hydrodynamics. The relaxation rate calculated with the formula effectively characterizes the drastic changes of the flow fields. By using this formula, the computational cost of the ELBM is significantly reduced and the model now can be efficiently used for a broad range of applications including high Reynolds number flows.展开更多
Adaption of circadian rhythms in behavioral and physiological activities to the external light–dark cycle is achieved through the main clock, i.e., the suprachiasmatic nucleus(SCN) of the brain in mammals. It has bee...Adaption of circadian rhythms in behavioral and physiological activities to the external light–dark cycle is achieved through the main clock, i.e., the suprachiasmatic nucleus(SCN) of the brain in mammals. It has been found that the SCN neurons differ in the amplitude relaxation rate, which represents the rigidity of the neurons to the external amplitude disturbance. Thus far, the appearance of that difference has not been explained. In the present study, an alternative explanation based on the Poincare′ model is given which takes into account the effect of the difference in the entrainment range of the SCN. Both our simulation results and theoretical analyses show that the largest entrainment range is obtained with suitable difference in the case that only a part of SCN neurons are sensitive to the light information. Our findings may give an alternative explanation for the appearance of that difference(heterogeneity) and shed light on the effects of the heterogeneity in the neuronal properties on the collective behaviors of the SCN neurons.展开更多
Relaxation rate is a very crucial parameter in physics.For the water surface wave,its relaxation rate is directly relevantto the response time of disturbed spectrum returning back to its quasi-steady state.It is diffi...Relaxation rate is a very crucial parameter in physics.For the water surface wave,its relaxation rate is directly relevantto the response time of disturbed spectrum returning back to its quasi-steady state.It is difficult to be calculated directly asa function of different oceanographic and meteorological parameters.Previous researches were mainly based on experimentalmeasurements or parameterization.In this paper,a method based on the liner array charge-coupled device(CCD)is proposed tomeasure the relaxation rate of the water surface wave.Compared with the traditional methods?it can obtain the information ofsurface wave and current synchronously,and works well under a multi wind-wave environment.Wind wav^tank experimentswere carried out based on this method.The good consistency between the results calculated by this method and the traditionalrelaxation rate models shows the validity of the proposed method.This method can be further used to study the modulation theoryof surface waves by currents.展开更多
There was a slow-relaxing tail of skeletal muscles in vitro upon the inhibition of Ca2+-pump by cyclopiazonic acid (CPA). Herein, a new linearly-combined bi-exponential model to resolve this slow-relaxing tail from th...There was a slow-relaxing tail of skeletal muscles in vitro upon the inhibition of Ca2+-pump by cyclopiazonic acid (CPA). Herein, a new linearly-combined bi-exponential model to resolve this slow-relaxing tail from the fast-relaxing phase was investigated for kinetic analysis of the isometric relaxation process of Bufo gastrocnemius in vitro, in comparison to the single exponential model and the classical bi-exponential model. During repetitive stimulations at a 2-s interval by square pulses of a 2-ms duration at 12 V direct currency (DC), the isometric tension of Bufo gastrocnemius was recorded at 100 Hz. The relaxation curve with tensions falling from 90% of the peak to the 15th datum before next stimulation was analyzed by three exponential models using a program in MATLAB 6.5. Both the goodness of fit and the distribution of the residuals for the best fitting sup- ported the comparable validity of this new bi-exponential model for kinetic analysis of the relaxation process of the control muscles. After CPA treatment, however, this new bi-exponential model showed an obvious statistical superiority for kinetic analysis of the muscle relaxation process, and it gave the estimated rest tension consistent to that by experimentation, whereas both the classical bi-exponential model and the single exponential model gave biased rest tensions. Moreover, after the treatment of muscles by CPA, both the single exponential model and the classical bi-exponential model yielded lowered relaxation rates, nevertheless, this new bi-exponential model had relaxation rates of negligible changes except much higher rest tensions. These results suggest that this novel linearly-combined bi-exponential model is desirable for kinetic analysis of the relaxation process of muscles with altered Ca2+-pumping activity.展开更多
In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hy...In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate O（√δ） in L1 norm as the relaxation time δ tends to zero.展开更多
The rate of elapsed polymerization of polyhydroxyethylacrylate in gelatin has been studied to investigate the effect of co-monomers consumption at a given dose. The polymer gel dosimeters consisted of 2%～4% N,N-methy...The rate of elapsed polymerization of polyhydroxyethylacrylate in gelatin has been studied to investigate the effect of co-monomers consumption at a given dose. The polymer gel dosimeters consisted of 2%～4% N,N-methyelene-bis-acrylamide cross-linker,2%～4% 2-hydroxyethylacrylate monomer and gelatin at 3% and 5%. The dosimeters were irradiated by using 60Co teletherapy γ-ray source up to 20 Gy at a constant dose rate. The relaxation rate of water proton in the dosimeters at different doses and co-monomer concentrations were measured using a nuclear magnetic resonance spectroscopy. The rate of elapsed polymerization decreases with increasing the dose and the initial concentration of co-monomers. The rate of consumption of co-monomers increases with an increase of the polymerization and the gelatin content of the polymer gel.展开更多
At the present time, a number of various ways of sportspersons’ special physical capability (SPC) based mainly on training and competitive loadings ramp up. They are effective enough to reach the main goal, but none ...At the present time, a number of various ways of sportspersons’ special physical capability (SPC) based mainly on training and competitive loadings ramp up. They are effective enough to reach the main goal, but none of them provides sportspersons’ health safety. Moreover, with the increase in volume and intensity of the loadings, which in sport have almost reached their limits, the sport traumatism and morbidity rate grow progressively. Proceeding from this, there was an evident necessity for the search of conceptually new ways for a simultaneous solution of these two the most complex and, in the opinion of many research workers, almost incompatible problems—the problem of achieving the highest levels of special physical working capacity, and the problem of sportspersons’ health maintenance and improving-associated by us into one general problem of human motor activity efficiency enhancement. Therefore it is necessary to physiologically substantiated the basic methods and principles of special relaxation training, directed on increase of efficiency of process of training of sportsmen at all stages of the development of athletic skills. Under the efficiency of the motor activity, we understand achieve the highest levels of the special physical performance while maintaining sports longevity and health of athletes.展开更多
基金The subject is supported by National Natural Sciences Foundation of China(10001036)
文摘This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].
基金supported,in part,by the National Science Foundation (USA)-Emerging Frontiers,Assembling the Tree of Life,Collaborative Research:Gymnosperms on the Tree of Life:Resolving the Phylogeny of Seed Plants (Grant No. EF-0629657 to SMI-B)supported by the Swedish Research Council (grants to CR)
文摘Ephedra comprises approximately 50 species, which are roughly equally distributed between the Old and New World deserts, but not in the intervening regions （amphitropical range）. Great heterogeneity in the substitution rates of Gnetales （Ephedra, Gnetum, and Welwitschia） has made it difficult to infer the ages of the major divergence events in Ephedra, such as the timing of the Beringian disjunction in the genus and the entry into South America. Here, we use data from as many Gnetales species and genes as available from GenBank and from a recent study to investigate the timing of the major divergence events. Because of the tradeoff between the amount of missing data and taxon/gene sampling, we reduced the initial matrix of 265 accessions and 12 loci to 95 accessions and 10 loci, and further to 42 species （and 7736 aligned nucleotides） to achieve stationary distributions in the Bayesian molecular clock runs. Results from a relaxed clock with an uncorrelated rates model and fossil-based calibration reveal that New World species are monophyletic and diverged from their mostly Asian sister clade some 30 mya, fitting with many other Beringian disjunctions. The split between the single North American and the single South American clade occurred approximately 25 mya, well before the closure of the Panamanian Isthmus. Overall, the biogeographic history of Ephedra appears dominated by long-distance dispersal, but finer-scale studies are needed to test this hypothesis.
基金The authors are grateful for supports by the National Natural Science Foundation of China （No. 90409015 and 20473013）.
文摘In order to understand whether the ameliorating effect on old ages memory disorder by the root of Salvia miltiorhiza is related to the acetylcholinesterase （ACHE） inhibition, two main ingredients, salvianolic acid B （1） and rosmarinic acid （2）, which were isolated from S. miltiorhiza water extract, were investigated in vitro by NMR relaxation rate in this work. The results showed that the proton selective relaxation rates and the molecular rotational correlation time of proton pairs for compounds 1 and 2 increased significantly by adding of AChE in mixing solution. The study reveals that the two compounds might bind to the enzyme and have ACHE inhibitory effect, which could contribute to the ameliorating effect at some extent on old ages memory disorder.
文摘The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11471185,11801030,and 11861131004)
文摘A relaxation-rate formula is presented for the entropic lattice Boltzmann model(ELBM) - a discrete kinetic theory for hydrodynamics. The simple formula not only guarantees the discrete time H-theorem but also gives full consideration to the consistency with hydrodynamics. The relaxation rate calculated with the formula effectively characterizes the drastic changes of the flow fields. By using this formula, the computational cost of the ELBM is significantly reduced and the model now can be efficiently used for a broad range of applications including high Reynolds number flows.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11875042,11505114,and 10975099)the Program for Professor of Special Appointment(Orientational Scholar)at Shanghai Institutions of Higher Learning,China(Grant Nos.QD2015016 and D-USST02)
文摘Adaption of circadian rhythms in behavioral and physiological activities to the external light–dark cycle is achieved through the main clock, i.e., the suprachiasmatic nucleus(SCN) of the brain in mammals. It has been found that the SCN neurons differ in the amplitude relaxation rate, which represents the rigidity of the neurons to the external amplitude disturbance. Thus far, the appearance of that difference has not been explained. In the present study, an alternative explanation based on the Poincare′ model is given which takes into account the effect of the difference in the entrainment range of the SCN. Both our simulation results and theoretical analyses show that the largest entrainment range is obtained with suitable difference in the case that only a part of SCN neurons are sensitive to the light information. Our findings may give an alternative explanation for the appearance of that difference(heterogeneity) and shed light on the effects of the heterogeneity in the neuronal properties on the collective behaviors of the SCN neurons.
基金National Natural Science Foundation of China(No.41276185)
文摘Relaxation rate is a very crucial parameter in physics.For the water surface wave,its relaxation rate is directly relevantto the response time of disturbed spectrum returning back to its quasi-steady state.It is difficult to be calculated directly asa function of different oceanographic and meteorological parameters.Previous researches were mainly based on experimentalmeasurements or parameterization.In this paper,a method based on the liner array charge-coupled device(CCD)is proposed tomeasure the relaxation rate of the water surface wave.Compared with the traditional methods?it can obtain the information ofsurface wave and current synchronously,and works well under a multi wind-wave environment.Wind wav^tank experimentswere carried out based on this method.The good consistency between the results calculated by this method and the traditionalrelaxation rate models shows the validity of the proposed method.This method can be further used to study the modulation theoryof surface waves by currents.
基金Project supported by the National Natural Science Foundation of China (No. 30472139)the Education Commission for the First Batch of Excellent Young Teachers in Universities of Chongqing City, China
文摘There was a slow-relaxing tail of skeletal muscles in vitro upon the inhibition of Ca2+-pump by cyclopiazonic acid (CPA). Herein, a new linearly-combined bi-exponential model to resolve this slow-relaxing tail from the fast-relaxing phase was investigated for kinetic analysis of the isometric relaxation process of Bufo gastrocnemius in vitro, in comparison to the single exponential model and the classical bi-exponential model. During repetitive stimulations at a 2-s interval by square pulses of a 2-ms duration at 12 V direct currency (DC), the isometric tension of Bufo gastrocnemius was recorded at 100 Hz. The relaxation curve with tensions falling from 90% of the peak to the 15th datum before next stimulation was analyzed by three exponential models using a program in MATLAB 6.5. Both the goodness of fit and the distribution of the residuals for the best fitting sup- ported the comparable validity of this new bi-exponential model for kinetic analysis of the relaxation process of the control muscles. After CPA treatment, however, this new bi-exponential model showed an obvious statistical superiority for kinetic analysis of the muscle relaxation process, and it gave the estimated rest tension consistent to that by experimentation, whereas both the classical bi-exponential model and the single exponential model gave biased rest tensions. Moreover, after the treatment of muscles by CPA, both the single exponential model and the classical bi-exponential model yielded lowered relaxation rates, nevertheless, this new bi-exponential model had relaxation rates of negligible changes except much higher rest tensions. These results suggest that this novel linearly-combined bi-exponential model is desirable for kinetic analysis of the relaxation process of muscles with altered Ca2+-pumping activity.
基金partially supported by the NSFC(11371349)National Basic Research Program of China(973 Program)(2011CB808002)
文摘In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate O（√δ） in L1 norm as the relaxation time δ tends to zero.
文摘The rate of elapsed polymerization of polyhydroxyethylacrylate in gelatin has been studied to investigate the effect of co-monomers consumption at a given dose. The polymer gel dosimeters consisted of 2%～4% N,N-methyelene-bis-acrylamide cross-linker,2%～4% 2-hydroxyethylacrylate monomer and gelatin at 3% and 5%. The dosimeters were irradiated by using 60Co teletherapy γ-ray source up to 20 Gy at a constant dose rate. The relaxation rate of water proton in the dosimeters at different doses and co-monomer concentrations were measured using a nuclear magnetic resonance spectroscopy. The rate of elapsed polymerization decreases with increasing the dose and the initial concentration of co-monomers. The rate of consumption of co-monomers increases with an increase of the polymerization and the gelatin content of the polymer gel.
文摘At the present time, a number of various ways of sportspersons’ special physical capability (SPC) based mainly on training and competitive loadings ramp up. They are effective enough to reach the main goal, but none of them provides sportspersons’ health safety. Moreover, with the increase in volume and intensity of the loadings, which in sport have almost reached their limits, the sport traumatism and morbidity rate grow progressively. Proceeding from this, there was an evident necessity for the search of conceptually new ways for a simultaneous solution of these two the most complex and, in the opinion of many research workers, almost incompatible problems—the problem of achieving the highest levels of special physical working capacity, and the problem of sportspersons’ health maintenance and improving-associated by us into one general problem of human motor activity efficiency enhancement. Therefore it is necessary to physiologically substantiated the basic methods and principles of special relaxation training, directed on increase of efficiency of process of training of sportsmen at all stages of the development of athletic skills. Under the efficiency of the motor activity, we understand achieve the highest levels of the special physical performance while maintaining sports longevity and health of athletes.
