Ain Ainsaar | Tallinn University (original) (raw)
Papers by Ain Ainsaar
Proceedings of the Estonian Academy of Sciences, 2000
Proceedings of the Estonian Academy of Sciences, 2004
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1979
A phenomenon present in many physical problems hodograph invariance of partial differential equat... more A phenomenon present in many physical problems hodograph invariance of partial differential equations is considered for two-dimensional submanifolds in three-and four-dimensional spaces. This means that the equation keeps its shape when interchanging the roles of any of the functions and arguments, i. e. under a hodograph transformation. For that purpose unified formulations for hodograph transformations are obtained. A method for the formation of hodograph invariant equations is shown. The well-known scalar Born-Infeld equation and its two-component generalization prove
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1986
A method of performing hodograph transformations of partial derivatives of any order lor arbitrar... more A method of performing hodograph transformations of partial derivatives of any order lor arbitrary dimensions is worked out. Hodograph transformation means a change of the roles of arguments and functions. The formulas obtained for first derivatives can easily be applied to any dimensions. Several explicit formulas for lower orders and dimensions are also given. Application to partial differential equations is discussed.
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1986
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1982
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1978
The action integral of a relativistic string is generalized to n-dimensional objects in m-dimensi... more The action integral of a relativistic string is generalized to n-dimensional objects in m-dimensional space. It can be brought to the action for m-n-component fields in ndimensional space. We call such object «sympleon». The corresponding equation is hodograph invariant via the equivalence of the initial coordinates. In the case of one-component field the scalar Born-Infeld equation is obtained. The action integral for a relativistic string, which is closely related to dual models [ l>2 ], is known to be
A group of transformations of four-fermion interaction lagrangians called the Pauli-Fierz group w... more A group of transformations of four-fermion interaction lagrangians called the Pauli-Fierz group was defined. It proves to be isomorphic to the group of space-time reflections. The interaction lagrangians are treated as eigenvec tors of the group operators. They are specified by the requirement that a certain kind of chirality should be assigne to one of the particles participating in the interaction. The lagrangians of the four-particle interaction are considered as vectors in a linear space, and their scalar products are defined. Relations between the coupling constants corresponding to the three types of lagrangians found (including the lagrangian of V--A type) are established by making use of the assumption that all the lagrangians have the same lengths. (auth)
Nukleonika, 2006
Experiments with plasma focus devices serve a special interest for investigations on the interact... more Experiments with plasma focus devices serve a special interest for investigations on the interaction of pulsed plasma streams with materials [21]. Among the various tasks of scientific activity in this field there is one of particular interest, namely, the elaboration of a phenomenological model of interaction between dense plasma beams and construction materials. Two sweeping generalization can be made about the processes between plasma and materials. They are intrinsically nonlinear and operate in noisy environment far from thermo-dynamic equilibrium. Within the past two decades the behavior of nonequilibrium systems depending on fluctuations (noise) has deserved considerable attention. Some phenomena recently discovered have brought about the idea that noise can induce order in nonlinear nonequilibrium systems. Stochastic resonance [3], noise-induced phase transitions in spatially extended systems [4], stochastic transport in ratchets [22], noise-induced spatial patterns [4], noi...
Proceeding from the Proca-Kemmer-Duffin equation and the fundamental properties of BETA -matrices... more Proceeding from the Proca-Kemmer-Duffin equation and the fundamental properties of BETA -matrices, transformational properties of expectation values for all independent products of BETA -matrices were obtained. It turns out that some basic matrices introduced by Umezawa have tensorical dimensionality. A new basis free from this defect was constructed. It is pointed out that there are no pseudoscalar matrices in the Kemmer-Duffin theory and the hamiltonians for the four-boson, three-boson, and twoboson-two-fermion interactions are given. (auth)
The influence of external and internal noises on the output signal of a fractional Langevin equat... more The influence of external and internal noises on the output signal of a fractional Langevin equation with the friction kernel of a viscoelastic type is considered. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise and by an additive noise with a zero mean. In the case of an external harmonic driving force it is shown that additive external and internal noises cause qualitatively different behaviors of the autocorrelation function for the output signal. Particularly, in the case of external noise it is established that at a sufficiently strong memory of the friction kernel the output signal corresponds to trapped dynamics in an effective potential well even if the system is subdiffusive in the case of internal noise.
The temporal behavior of the autocorrelation function for the output signal of a fractional oscil... more The temporal behavior of the autocorrelation function for the output signal of a fractional oscillator with fluctuating eigenfrequency subjected to a periodic force is considered. The influence of a fluctuating environment is modeled by a multiplicative white noise and by an additive noise with a zero mean. The viscoelastic type friction kernel with memory is assumed as a power-law function of time. On the basis of exact formulas it is demonstrated that the temporal behavior of the normalized autocorrelation function is qualitatively different for the cases of internal and external additive noise. This provides a simple criterion enabling one to analyse the output signal for alternative information about the physical nature of the additive noise.
Erosion of divertor and first-wall armour material of ITER is still a problem not resolved. Tungs... more Erosion of divertor and first-wall armour material of ITER is still a problem not resolved. Tungsten as a candidate for the divertor material of ITER or other fusion devices is very brittle and has a high DBTT. The main damage in lower temperatures is a mesh of cracks. At higher temperatures sputters and splashes appear. It is suggested that addition of different materials (La2O3, Y2O3, TiC etc) may lower the DBTT and increase the ductility of tungsten [1-5].
Physical Review E, 2000
The colored three-level Markovian noise-driven nonequilibrium dynamics of overdamped Brownian par... more The colored three-level Markovian noise-driven nonequilibrium dynamics of overdamped Brownian particles in a spatially periodic asymmetric potential ͑ratchet͒ is investigated. An explicit second-order linear ordinary differential equation for the stationary probability density distribution is obtained for the process. In the case of a piecewise linear potential with an additive three-level ͑trichotomous͒ noise the exact formula for the stationary current is presented. The dependence of the current reversals on the noise parameters is investigated in detail and illustrated by a phase diagram. Asymptotic formulas for the current for various limits of the noise parameters are found and compared with the results of other authors. Applications to the fluctuationinduced separation of particles are also discussed.
The dynamics of a population growth model with generalized Verhulst self-regulation driven by a m... more The dynamics of a population growth model with generalized Verhulst self-regulation driven by a multiplicative three-level Markovian noise (trichotomous noise) as well as by a time-dependent deterministic stimulus is considered. In the white noise limit, the exact formulae for the conditional probability density of the population size and for the first passage time distribution are derived separately for both the reflecting and absorbing boundary conditions at the carrying capacity. In the case of multiplicative trichotomous noise, using the reflecting boundary condition, an exact analytical solution for the stationary probability distribution is found. It is established that a variation of noise parameters, such as correlation time, amplitude, and kurtosis, can cause noise-induced phase transitions. The dependence of the critical noise characteristic, which marks a transition between different phases, on other system parameters is analysed.
Proceedings of the Estonian Academy of Sciences, 2000
Proceedings of the Estonian Academy of Sciences, 2004
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1979
A phenomenon present in many physical problems hodograph invariance of partial differential equat... more A phenomenon present in many physical problems hodograph invariance of partial differential equations is considered for two-dimensional submanifolds in three-and four-dimensional spaces. This means that the equation keeps its shape when interchanging the roles of any of the functions and arguments, i. e. under a hodograph transformation. For that purpose unified formulations for hodograph transformations are obtained. A method for the formation of hodograph invariant equations is shown. The well-known scalar Born-Infeld equation and its two-component generalization prove
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1986
A method of performing hodograph transformations of partial derivatives of any order lor arbitrar... more A method of performing hodograph transformations of partial derivatives of any order lor arbitrary dimensions is worked out. Hodograph transformation means a change of the roles of arguments and functions. The formulas obtained for first derivatives can easily be applied to any dimensions. Several explicit formulas for lower orders and dimensions are also given. Application to partial differential equations is discussed.
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1986
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1982
Proceedings of the Academy of Sciences of the Estonian SSR. Physics. Mathematics, 1978
The action integral of a relativistic string is generalized to n-dimensional objects in m-dimensi... more The action integral of a relativistic string is generalized to n-dimensional objects in m-dimensional space. It can be brought to the action for m-n-component fields in ndimensional space. We call such object «sympleon». The corresponding equation is hodograph invariant via the equivalence of the initial coordinates. In the case of one-component field the scalar Born-Infeld equation is obtained. The action integral for a relativistic string, which is closely related to dual models [ l>2 ], is known to be
A group of transformations of four-fermion interaction lagrangians called the Pauli-Fierz group w... more A group of transformations of four-fermion interaction lagrangians called the Pauli-Fierz group was defined. It proves to be isomorphic to the group of space-time reflections. The interaction lagrangians are treated as eigenvec tors of the group operators. They are specified by the requirement that a certain kind of chirality should be assigne to one of the particles participating in the interaction. The lagrangians of the four-particle interaction are considered as vectors in a linear space, and their scalar products are defined. Relations between the coupling constants corresponding to the three types of lagrangians found (including the lagrangian of V--A type) are established by making use of the assumption that all the lagrangians have the same lengths. (auth)
Nukleonika, 2006
Experiments with plasma focus devices serve a special interest for investigations on the interact... more Experiments with plasma focus devices serve a special interest for investigations on the interaction of pulsed plasma streams with materials [21]. Among the various tasks of scientific activity in this field there is one of particular interest, namely, the elaboration of a phenomenological model of interaction between dense plasma beams and construction materials. Two sweeping generalization can be made about the processes between plasma and materials. They are intrinsically nonlinear and operate in noisy environment far from thermo-dynamic equilibrium. Within the past two decades the behavior of nonequilibrium systems depending on fluctuations (noise) has deserved considerable attention. Some phenomena recently discovered have brought about the idea that noise can induce order in nonlinear nonequilibrium systems. Stochastic resonance [3], noise-induced phase transitions in spatially extended systems [4], stochastic transport in ratchets [22], noise-induced spatial patterns [4], noi...
Proceeding from the Proca-Kemmer-Duffin equation and the fundamental properties of BETA -matrices... more Proceeding from the Proca-Kemmer-Duffin equation and the fundamental properties of BETA -matrices, transformational properties of expectation values for all independent products of BETA -matrices were obtained. It turns out that some basic matrices introduced by Umezawa have tensorical dimensionality. A new basis free from this defect was constructed. It is pointed out that there are no pseudoscalar matrices in the Kemmer-Duffin theory and the hamiltonians for the four-boson, three-boson, and twoboson-two-fermion interactions are given. (auth)
The influence of external and internal noises on the output signal of a fractional Langevin equat... more The influence of external and internal noises on the output signal of a fractional Langevin equation with the friction kernel of a viscoelastic type is considered. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise and by an additive noise with a zero mean. In the case of an external harmonic driving force it is shown that additive external and internal noises cause qualitatively different behaviors of the autocorrelation function for the output signal. Particularly, in the case of external noise it is established that at a sufficiently strong memory of the friction kernel the output signal corresponds to trapped dynamics in an effective potential well even if the system is subdiffusive in the case of internal noise.
The temporal behavior of the autocorrelation function for the output signal of a fractional oscil... more The temporal behavior of the autocorrelation function for the output signal of a fractional oscillator with fluctuating eigenfrequency subjected to a periodic force is considered. The influence of a fluctuating environment is modeled by a multiplicative white noise and by an additive noise with a zero mean. The viscoelastic type friction kernel with memory is assumed as a power-law function of time. On the basis of exact formulas it is demonstrated that the temporal behavior of the normalized autocorrelation function is qualitatively different for the cases of internal and external additive noise. This provides a simple criterion enabling one to analyse the output signal for alternative information about the physical nature of the additive noise.
Erosion of divertor and first-wall armour material of ITER is still a problem not resolved. Tungs... more Erosion of divertor and first-wall armour material of ITER is still a problem not resolved. Tungsten as a candidate for the divertor material of ITER or other fusion devices is very brittle and has a high DBTT. The main damage in lower temperatures is a mesh of cracks. At higher temperatures sputters and splashes appear. It is suggested that addition of different materials (La2O3, Y2O3, TiC etc) may lower the DBTT and increase the ductility of tungsten [1-5].
Physical Review E, 2000
The colored three-level Markovian noise-driven nonequilibrium dynamics of overdamped Brownian par... more The colored three-level Markovian noise-driven nonequilibrium dynamics of overdamped Brownian particles in a spatially periodic asymmetric potential ͑ratchet͒ is investigated. An explicit second-order linear ordinary differential equation for the stationary probability density distribution is obtained for the process. In the case of a piecewise linear potential with an additive three-level ͑trichotomous͒ noise the exact formula for the stationary current is presented. The dependence of the current reversals on the noise parameters is investigated in detail and illustrated by a phase diagram. Asymptotic formulas for the current for various limits of the noise parameters are found and compared with the results of other authors. Applications to the fluctuationinduced separation of particles are also discussed.
The dynamics of a population growth model with generalized Verhulst self-regulation driven by a m... more The dynamics of a population growth model with generalized Verhulst self-regulation driven by a multiplicative three-level Markovian noise (trichotomous noise) as well as by a time-dependent deterministic stimulus is considered. In the white noise limit, the exact formulae for the conditional probability density of the population size and for the first passage time distribution are derived separately for both the reflecting and absorbing boundary conditions at the carrying capacity. In the case of multiplicative trichotomous noise, using the reflecting boundary condition, an exact analytical solution for the stationary probability distribution is found. It is established that a variation of noise parameters, such as correlation time, amplitude, and kurtosis, can cause noise-induced phase transitions. The dependence of the critical noise characteristic, which marks a transition between different phases, on other system parameters is analysed.