In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure ...In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure are derived unconditionally,while the previous works require certain time-step restrictions.The analysis is based on an iterated time-discrete system,with which the error function is split into a temporal error and a spatial error.The τ-independent(τ is the time stepsize)error estimate between the numerical solution and the solution of the time-discrete system is proven by a rigorous analysis,which implies that the numerical solution in L^(∞)-norm is bounded.Thus optimal error estimates can be obtained in a traditional way.Numerical results are provided to confirm the theoretical analysis.展开更多
To increase the detectability of split Hopkinson pressure bar （SHPB） of low-impedance materials, modifications were conducted on traditional SHPB apparatus with a PMMA tube to output transmitted signal, and weak sig...To increase the detectability of split Hopkinson pressure bar （SHPB） of low-impedance materials, modifications were conducted on traditional SHPB apparatus with a PMMA tube to output transmitted signal, and weak signals were further amplified by semiconductor strain gauges. Experiments on soft rubbers and cushioning foam materials were carried out. In order to analyze the accuracy of the experimental results, the stress equilibrium issues involved in the assumptions of SHPB were investigated. First, by way of re-constructing loading process of incident wave, the stress- strain curve was obtained, along with the stress equilibrium ratio of specimen. Secondly, the influences on the accuracy of stress-strain curves were investigated through the elastic modulus comparisons. And the results illustrate that the bilinear incident wave from experiments can ensure the stress equilibrium deformation of specimen after 2 normalized times, much sooner than ramp incident waves. Moreover, it even facilitates specimen deformation with a constant strain rate. The results confirm that the detectability of the modified SHPB can be down to tens kPa with enough accuracy level.展开更多
The effect of diffusion on thermoelastic thin plates is investigated. The governing equations for thin thermoelastic diffusion plates under three different laws of heat and diffusion transmission are derived. By the C...The effect of diffusion on thermoelastic thin plates is investigated. The governing equations for thin thermoelastic diffusion plates under three different laws of heat and diffusion transmission are derived. By the C0-semigroup theory, the well-posedness of the proposed equations is shown.展开更多
We construct the Hirota bilinear form of the nonlocal Boussinesq（nlBq） equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator togethe...We construct the Hirota bilinear form of the nonlocal Boussinesq（nlBq） equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.展开更多
Bitcoin has gained its popularity for almost 10 years as a ＂secure and anonymous digital currency＂. However, according to several recent researches, we know that it can only provide pseudonymity rather than real ano...Bitcoin has gained its popularity for almost 10 years as a ＂secure and anonymous digital currency＂. However, according to several recent researches, we know that it can only provide pseudonymity rather than real anonymity, and privacy has been one of the main concerns in the system similar to Bitcoin. Ring signature is a good method for those users who need better anonymity in cryptocurrency. It was first proposed by Rivest et al. based upon the discrete logarithm problem （DLP） assumption in 2006, which allows a user to sign a message anonymously on behalf of a group of users even without their coordination. The size of ring signature is one of the dominating parameters, and constant-size ring signature （where signature size is independent of the ring size） is much desirable. Otherwise, when the ring size is large, the resultant ring signature becomes unbearable for power limited devices or leads to heavy burden over the communication network. Though being extensively studied, currently there are only two approaches for constant-size ring signature. Achieving practical constant-size ring signature is a long-standing open problem since its introduction. In this work, we solve this open question. We present a new constant-size ring signature scheme based on bilinear pairing and accumulator, which is provably secure under the random oracle （RO） model. To the best of our knowledge, it stands for the most practical ring signature up to now.展开更多
The importance of anharmonic effect in dissociation of molecular systems especially clusters has been noted. In this paper, we shall study the effect of coupled anharmonic oscillator of the standard bilinear form (SBF...The importance of anharmonic effect in dissociation of molecular systems especially clusters has been noted. In this paper, we shall study the effect of coupled anharmonic oscillator of the standard bilinear form (SBF) Morse oscillator (MO) potential on unimolecular reaction. We shall use the systematic theoretical approach, YL method, proposed by Yao and Lin (YAO L, et. al. J Phys Chem A, 2007, 111(29): 6722-6729), which can evaluate anharmonic effects on the rate constants based on the transition state theory. In treating the anharmonic effect with the Morse oscillator potential on unimolecular reactions under collision-free conditions by using the RRKM (Rice-Ramsperger-Kassel-Marcus) theory, the in-verse Laplace transformation of the partition functions was used to obtain the total amount of state and density of state by using the first-order and the second-order approximations of the saddle-point method. To demonstrate the anharmonic effect of the SBF Morse model, we choose some model systems and a real reaction as examples.展开更多
基金supported by National Natural Science Foundation of China(No.11671369)the Doctoral Starting Foundation of Zhengzhou University of Aeronautics(No.63020390).
文摘In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure are derived unconditionally,while the previous works require certain time-step restrictions.The analysis is based on an iterated time-discrete system,with which the error function is split into a temporal error and a spatial error.The τ-independent(τ is the time stepsize)error estimate between the numerical solution and the solution of the time-discrete system is proven by a rigorous analysis,which implies that the numerical solution in L^(∞)-norm is bounded.Thus optimal error estimates can be obtained in a traditional way.Numerical results are provided to confirm the theoretical analysis.
基金Supported by the National Natural Science Foundation(11272267,11102168,10932008)111 Project(B07050)
文摘To increase the detectability of split Hopkinson pressure bar （SHPB） of low-impedance materials, modifications were conducted on traditional SHPB apparatus with a PMMA tube to output transmitted signal, and weak signals were further amplified by semiconductor strain gauges. Experiments on soft rubbers and cushioning foam materials were carried out. In order to analyze the accuracy of the experimental results, the stress equilibrium issues involved in the assumptions of SHPB were investigated. First, by way of re-constructing loading process of incident wave, the stress- strain curve was obtained, along with the stress equilibrium ratio of specimen. Secondly, the influences on the accuracy of stress-strain curves were investigated through the elastic modulus comparisons. And the results illustrate that the bilinear incident wave from experiments can ensure the stress equilibrium deformation of specimen after 2 normalized times, much sooner than ramp incident waves. Moreover, it even facilitates specimen deformation with a constant strain rate. The results confirm that the detectability of the modified SHPB can be down to tens kPa with enough accuracy level.
文摘The effect of diffusion on thermoelastic thin plates is investigated. The governing equations for thin thermoelastic diffusion plates under three different laws of heat and diffusion transmission are derived. By the C0-semigroup theory, the well-posedness of the proposed equations is shown.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51579040,51379033,and 51522902)the National Basic Research Program of China(Grant No.2013CB036101)Liaoning Natural Science Foundation,China(Grant No.201602172)
文摘We construct the Hirota bilinear form of the nonlocal Boussinesq（nlBq） equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.
基金This work is supported in part by the National Key Research and Development Program of China under Grant No. 2017YFB0802000, the National Natural Science Foundation of China under Grant Nos. 61472084 and U1536205, the Shanghai Innovation Action Project under Grant No. 16DZ1100200, the Shanghai Science and Technology Development Funds under Grant No. 6JC1400801, and the Shandong Provincial Key Research and Development Program of China under Grant No. 2017CXG0701.
文摘Bitcoin has gained its popularity for almost 10 years as a ＂secure and anonymous digital currency＂. However, according to several recent researches, we know that it can only provide pseudonymity rather than real anonymity, and privacy has been one of the main concerns in the system similar to Bitcoin. Ring signature is a good method for those users who need better anonymity in cryptocurrency. It was first proposed by Rivest et al. based upon the discrete logarithm problem （DLP） assumption in 2006, which allows a user to sign a message anonymously on behalf of a group of users even without their coordination. The size of ring signature is one of the dominating parameters, and constant-size ring signature （where signature size is independent of the ring size） is much desirable. Otherwise, when the ring size is large, the resultant ring signature becomes unbearable for power limited devices or leads to heavy burden over the communication network. Though being extensively studied, currently there are only two approaches for constant-size ring signature. Achieving practical constant-size ring signature is a long-standing open problem since its introduction. In this work, we solve this open question. We present a new constant-size ring signature scheme based on bilinear pairing and accumulator, which is provably secure under the random oracle （RO） model. To the best of our knowledge, it stands for the most practical ring signature up to now.
基金Supported by the National Natural Science Foundation of China (Grant No. 10704012)NSC (Taiwan), Academia Sinica, and the Natural Science Foundation of Liaoning Province (Grant No. 2006Z064)
文摘The importance of anharmonic effect in dissociation of molecular systems especially clusters has been noted. In this paper, we shall study the effect of coupled anharmonic oscillator of the standard bilinear form (SBF) Morse oscillator (MO) potential on unimolecular reaction. We shall use the systematic theoretical approach, YL method, proposed by Yao and Lin (YAO L, et. al. J Phys Chem A, 2007, 111(29): 6722-6729), which can evaluate anharmonic effects on the rate constants based on the transition state theory. In treating the anharmonic effect with the Morse oscillator potential on unimolecular reactions under collision-free conditions by using the RRKM (Rice-Ramsperger-Kassel-Marcus) theory, the in-verse Laplace transformation of the partition functions was used to obtain the total amount of state and density of state by using the first-order and the second-order approximations of the saddle-point method. To demonstrate the anharmonic effect of the SBF Morse model, we choose some model systems and a real reaction as examples.
