The equation: ReF`(T,Z)ZF`(T,Z) = 1 for conformal maps f(t,z) is important in interfacial dynamic... more The equation: ReF`(T,Z)ZF`(T,Z) = 1 for conformal maps f(t,z) is important in interfacial dynamics. We extend the results by Gustafsson on existence and uniqueness of solutions of this equation from the case when f(t,z) is a rational function of z to the case when the spatial derivative f`(t,z) is rational.
Structure constants of the $su(N)$ ($N$ odd) Lie algebras converge when N goes to infinity to the... more Structure constants of the $su(N)$ ($N$ odd) Lie algebras converge when N goes to infinity to the structure constants of the Lie algebra {\it sdiff}$(T^2)$ of the group of area-preserving diffeomorphisms of a 2D torus. Thus Zeitlin and others hypothesized that solutions of the Euler equations associated with $su(N)$ algebras converge to solutions of the Euler equations of incompressible fluid dynamics on a 2D torus. In the paper we prove the hypothesis. Our numerical experiments show the Galerkin method applied to Euler equation of hydrodynamics is computationally more efficient in the range of time in which it is stable than that based on the SU(N) approximation. However, the latter is stable for much longer time. These numerical results agree with theoretical expectations.
Bulletin of the American Physical Society, Nov 12, 2007
implosion experiments, "mix" is commonly used to fix the simulation. If this fix is in any way as... more implosion experiments, "mix" is commonly used to fix the simulation. If this fix is in any way assumed to model reality, then we are assuming that the simulations calculate the effect of the mix on the implosion and yield correctly. To study whether this assumption is valid, we have done a series of experiments that purposely add a fixed amount of mix of varying atomic number and density. The experiments are very well characterized, measuring the proton and neutron yields, the ion and electron temperatures, the ρR and radius of the capsule, the radiation emission, and the x-ray spectra from the capsule. We find that,in general, the calculations have great difficulty matching this data. A summary of the measurements for various dopants and dopant levels and how well the calculations compare will be presented. Some possible reasons for the modeling difficulties will be discussed along with some preliminary efforts to address these problems.
This report was prepared as an account of work sponsored by an agency of the United States Govern... more This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, ~xprrss or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, ptoass, or service by trade name, trademark, manufacturer, or otherwise docs not necessarily constitute or imply its endorsement, mommendotion, or favoring by the United States Government or my agency thereof. The views and opinions of authors e x p d herein do not ncx#sarily state or reflect those of the United States Government o r m y agency thereof.
This report was prepared as an account of work sponsored by an agency of the United States Govern... more This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employm, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spccific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise docs not necessarily constitute or imply its endorsement, w mmendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
Il Nuovo cimento della Società italiana di fisica. B, May 1, 1994
Gl(n, R)-invariant n-bein theory of gravity, is generalized. This generalization is analogous to ... more Gl(n, R)-invariant n-bein theory of gravity, is generalized. This generalization is analogous to the generalization of the Palatini first-order approach to gravity presented in the paper by M. Ferraris, M. Francaviglia and I. Volovich in Nuovo Cimento B, 108, 1313 (1993). The models considered below are based on Lagrangians dependent on the metric g.~ and some ,,matter,, fields cA, built as a full contraction of the metric g.~" and a second-rank covariant tensor k~,,, which is of first order in fields CA. Special examples of field theories described by such Lagrangian as, e.g., bosonic membrane theories and ~awianowski's theory are pointed out. PACS 04.50-Unified field theories and other theories of gravitation. PACS 11.10-Field theory. PACS 11.17-Theories of strings and other extended objects.
A generalization of the results of Rasetti and Zanardi concerning avoiding errors in quantum comp... more A generalization of the results of Rasetti and Zanardi concerning avoiding errors in quantum computers by using states preserved by evolution is presented. The concept of dynamical symmetry is generalized from the level of classical Lie algebras and groups to the level of a dynamical symmetry based on quantum Lie algebras and quantum groups (in the sense of Woronowicz). A natural connection is proved between states preserved by representations of a quantum group and states preserved by evolution with dynamical symmetry of the appropriate universal enveloping algebra. Illustrative examples are discussed.
12/21/2020 | 2 Los Alamos National Laboratory Astronomical observations, unusual medical cases, p... more 12/21/2020 | 2 Los Alamos National Laboratory Astronomical observations, unusual medical cases, physics experiments too costly to repeat, natural events like earthquakes, hurricanesall of them are impossible to repeat yet produce important scientific information not achievable in other way. This data should not be treated as qualitative, anecdotal evidence only. It should be analyzed in a mathematically rigorous way to produce quantitative experimental data. Analysis method for one-of-a-kind event data differs from analysis of a repeated experiment data. For a repeated experiments the experimental error includes a range of true values generated by repetitions of the experiment, and measurement uncertainty caused by detectors. They are independent. Repetitions of any experiment, as similar as achievable, always have built-in differences resulting in a range of the true values rather than in a single true experimental value. Measurement uncertainty depends on the measurement system only. Modern digital measurements have very small uncertainty, frequently smaller than the range of true experimental values resulting from built-in differences in the experiment repetitions. When data from one-of-a-kind experiment are analyzed, only the measurement uncertainty can be reported.
Journal of Knot Theory and Its Ramifications, Jun 1, 2018
The most popular theories of everything are various versions of the superstring theory. The theor... more The most popular theories of everything are various versions of the superstring theory. The theories require existence of additional space dimensions, vibrations of which create the material particles in [Formula: see text] space. The additional space dimensions are understood as being currently smaller than the Planck Length and due to this not directly observable. We search for multidimensional models of the Universe (one time dimension; three isotropic, flat external dimensions, and [Formula: see text]-internal dimensions), which satisfy the multidimensional Einstein equations and which started from the same radius of all of the internal and external dimensions, with an anisotropic energy–momentum tensor. Analytical solution of [Formula: see text]-dimensional Einstein equation in a reparameterized time is reminded and discussed. The energy–momentum tensor is solely responsible for expansion of the external dimensions and shrinking of the internal ones; and to obtain this behavior of the space the tensor needs to fulfill some conditions i.e. the energy–momentum tensor cannot include only radiation, vacuum and baryonic matter. For the behavior of the physical space consistent with the one observed in our Universe, the dark energy and/or dark matter have to exist.
Journal of Knot Theory and Its Ramifications, Mar 1, 2017
Quantum computers by their nature are many particle quantum systems. Both the many-particle arran... more Quantum computers by their nature are many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.
Deuterium-tritium (D-T) and deuterium-deuterium (D-D) fusion reaction rates are observable using ... more Deuterium-tritium (D-T) and deuterium-deuterium (D-D) fusion reaction rates are observable using leakage gamma flux. A direct measurement of γ-rays with equipment that exhibits fast temporal response could be used to infer temperature, if the detector signal is amenable for taking the logarithmic time-derivative, alpha. We consider the temperature dependence for fusion cross section reactivity.
International Journal of Theoretical Physics, May 1, 1995
Given Einstein's theory of gravitation, the relaxation-time approximation for a general-rela... more Given Einstein's theory of gravitation, the relaxation-time approximation for a general-relativistic Boltzmann equation is studied with a view to demonstrating its usefulness in the context of Robertson-Walker universe models. Solutions of the full nonlinear equations for the metric and the distribution function are examined, together with their relation to linearized perturbations. Emphasis is placed on finding analogs of the exact results on strong or weak convergence to equilibrium employed in special-relativistic kinetic theory. At the late stages of cosmic expansion, an explicit choice of the empirical collision frequency is made to fit optimally the relaxation-time model to the “actual” Einstein-Boltzmann system. Finally, perspectives for some future generalizations are outlined.
A golden standard in science is to repeat an experiment a statistically significant number of tim... more A golden standard in science is to repeat an experiment a statistically significant number of times, recording data using the same set of detectors and the same data analysis methodology. In such case experimental error includes both the range of true values generated by repetitions of the experiment, and measurement uncertainty caused by the detector. They are independent. It is a huge and too frequently used simplification, to assume that one can measure multiple repetitions of an identical experiment, resulting in identical true experimental value. Repetitions, as similar is it is experimentally achievable, have unavoidable built-in differences resulting in a range of the true values rather than in a single value. When modern, very sensitive and well calibrated measurement systems are used, this range is not negligible, and sometimes dominates over the measurement uncertainty. Range of true values depends on built-in differences in physics of the experiment. Stochastic physical processes result typically in a broader range of true values than non-stochastic processes do. Measurement uncertainty depends on a measurement method (properties of the detector not of the experiment). Modern measurement methods, including digital ones, frequently make the measurement uncertainty very small. When data from one-of-a kind experiment are analyzed, only the measurement uncertainty is reported. It provides no information about the range of true experimental values, neither about reliability of a reported data point. Reliability of a data point is in general independent from its measurement uncertainty. However, in practice reliable measurement methods frequently have high measurement uncertainty, while low reliability methods are applied to limit measurement uncertainty. Comparison of reliable data with high measurement uncertainty to not so reliable data measured with low uncertainty is discussed-in different scenarios different data analysis methods are applicable. Methods for data analysis from an experiment repeated statistically significant number of times are very well developed. They do not require a detailed expertise in physics of an experiment, nor in the properties of the measurement system used, and meaning of the reported uncertainty is well understood in any scientific community. It all changes when data from one-of-a-kind experiment is analyzed. Analyst's expertise is required both in the physics of the experiment and in all aspects of the measurement system, all possible malfunctions. Data users must remember that only measurement uncertainty is reported from any one-of-a-kind experiment. Theory with simulations may provide estimation of expected built-in differences in the experiment, and by this of expected range of true values for a given experiment; yet measurement uncertainty can never be used in place of the range of true experimental values.
The equation: ReF`(T,Z)ZF`(T,Z) = 1 for conformal maps f(t,z) is important in interfacial dynamic... more The equation: ReF`(T,Z)ZF`(T,Z) = 1 for conformal maps f(t,z) is important in interfacial dynamics. We extend the results by Gustafsson on existence and uniqueness of solutions of this equation from the case when f(t,z) is a rational function of z to the case when the spatial derivative f`(t,z) is rational.
Structure constants of the $su(N)$ ($N$ odd) Lie algebras converge when N goes to infinity to the... more Structure constants of the $su(N)$ ($N$ odd) Lie algebras converge when N goes to infinity to the structure constants of the Lie algebra {\it sdiff}$(T^2)$ of the group of area-preserving diffeomorphisms of a 2D torus. Thus Zeitlin and others hypothesized that solutions of the Euler equations associated with $su(N)$ algebras converge to solutions of the Euler equations of incompressible fluid dynamics on a 2D torus. In the paper we prove the hypothesis. Our numerical experiments show the Galerkin method applied to Euler equation of hydrodynamics is computationally more efficient in the range of time in which it is stable than that based on the SU(N) approximation. However, the latter is stable for much longer time. These numerical results agree with theoretical expectations.
Bulletin of the American Physical Society, Nov 12, 2007
implosion experiments, "mix" is commonly used to fix the simulation. If this fix is in any way as... more implosion experiments, "mix" is commonly used to fix the simulation. If this fix is in any way assumed to model reality, then we are assuming that the simulations calculate the effect of the mix on the implosion and yield correctly. To study whether this assumption is valid, we have done a series of experiments that purposely add a fixed amount of mix of varying atomic number and density. The experiments are very well characterized, measuring the proton and neutron yields, the ion and electron temperatures, the ρR and radius of the capsule, the radiation emission, and the x-ray spectra from the capsule. We find that,in general, the calculations have great difficulty matching this data. A summary of the measurements for various dopants and dopant levels and how well the calculations compare will be presented. Some possible reasons for the modeling difficulties will be discussed along with some preliminary efforts to address these problems.
This report was prepared as an account of work sponsored by an agency of the United States Govern... more This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, ~xprrss or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, ptoass, or service by trade name, trademark, manufacturer, or otherwise docs not necessarily constitute or imply its endorsement, mommendotion, or favoring by the United States Government or my agency thereof. The views and opinions of authors e x p d herein do not ncx#sarily state or reflect those of the United States Government o r m y agency thereof.
This report was prepared as an account of work sponsored by an agency of the United States Govern... more This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employm, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spccific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise docs not necessarily constitute or imply its endorsement, w mmendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
Il Nuovo cimento della Società italiana di fisica. B, May 1, 1994
Gl(n, R)-invariant n-bein theory of gravity, is generalized. This generalization is analogous to ... more Gl(n, R)-invariant n-bein theory of gravity, is generalized. This generalization is analogous to the generalization of the Palatini first-order approach to gravity presented in the paper by M. Ferraris, M. Francaviglia and I. Volovich in Nuovo Cimento B, 108, 1313 (1993). The models considered below are based on Lagrangians dependent on the metric g.~ and some ,,matter,, fields cA, built as a full contraction of the metric g.~" and a second-rank covariant tensor k~,,, which is of first order in fields CA. Special examples of field theories described by such Lagrangian as, e.g., bosonic membrane theories and ~awianowski's theory are pointed out. PACS 04.50-Unified field theories and other theories of gravitation. PACS 11.10-Field theory. PACS 11.17-Theories of strings and other extended objects.
A generalization of the results of Rasetti and Zanardi concerning avoiding errors in quantum comp... more A generalization of the results of Rasetti and Zanardi concerning avoiding errors in quantum computers by using states preserved by evolution is presented. The concept of dynamical symmetry is generalized from the level of classical Lie algebras and groups to the level of a dynamical symmetry based on quantum Lie algebras and quantum groups (in the sense of Woronowicz). A natural connection is proved between states preserved by representations of a quantum group and states preserved by evolution with dynamical symmetry of the appropriate universal enveloping algebra. Illustrative examples are discussed.
12/21/2020 | 2 Los Alamos National Laboratory Astronomical observations, unusual medical cases, p... more 12/21/2020 | 2 Los Alamos National Laboratory Astronomical observations, unusual medical cases, physics experiments too costly to repeat, natural events like earthquakes, hurricanesall of them are impossible to repeat yet produce important scientific information not achievable in other way. This data should not be treated as qualitative, anecdotal evidence only. It should be analyzed in a mathematically rigorous way to produce quantitative experimental data. Analysis method for one-of-a-kind event data differs from analysis of a repeated experiment data. For a repeated experiments the experimental error includes a range of true values generated by repetitions of the experiment, and measurement uncertainty caused by detectors. They are independent. Repetitions of any experiment, as similar as achievable, always have built-in differences resulting in a range of the true values rather than in a single true experimental value. Measurement uncertainty depends on the measurement system only. Modern digital measurements have very small uncertainty, frequently smaller than the range of true experimental values resulting from built-in differences in the experiment repetitions. When data from one-of-a-kind experiment are analyzed, only the measurement uncertainty can be reported.
Journal of Knot Theory and Its Ramifications, Jun 1, 2018
The most popular theories of everything are various versions of the superstring theory. The theor... more The most popular theories of everything are various versions of the superstring theory. The theories require existence of additional space dimensions, vibrations of which create the material particles in [Formula: see text] space. The additional space dimensions are understood as being currently smaller than the Planck Length and due to this not directly observable. We search for multidimensional models of the Universe (one time dimension; three isotropic, flat external dimensions, and [Formula: see text]-internal dimensions), which satisfy the multidimensional Einstein equations and which started from the same radius of all of the internal and external dimensions, with an anisotropic energy–momentum tensor. Analytical solution of [Formula: see text]-dimensional Einstein equation in a reparameterized time is reminded and discussed. The energy–momentum tensor is solely responsible for expansion of the external dimensions and shrinking of the internal ones; and to obtain this behavior of the space the tensor needs to fulfill some conditions i.e. the energy–momentum tensor cannot include only radiation, vacuum and baryonic matter. For the behavior of the physical space consistent with the one observed in our Universe, the dark energy and/or dark matter have to exist.
Journal of Knot Theory and Its Ramifications, Mar 1, 2017
Quantum computers by their nature are many particle quantum systems. Both the many-particle arran... more Quantum computers by their nature are many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.
Deuterium-tritium (D-T) and deuterium-deuterium (D-D) fusion reaction rates are observable using ... more Deuterium-tritium (D-T) and deuterium-deuterium (D-D) fusion reaction rates are observable using leakage gamma flux. A direct measurement of γ-rays with equipment that exhibits fast temporal response could be used to infer temperature, if the detector signal is amenable for taking the logarithmic time-derivative, alpha. We consider the temperature dependence for fusion cross section reactivity.
International Journal of Theoretical Physics, May 1, 1995
Given Einstein's theory of gravitation, the relaxation-time approximation for a general-rela... more Given Einstein's theory of gravitation, the relaxation-time approximation for a general-relativistic Boltzmann equation is studied with a view to demonstrating its usefulness in the context of Robertson-Walker universe models. Solutions of the full nonlinear equations for the metric and the distribution function are examined, together with their relation to linearized perturbations. Emphasis is placed on finding analogs of the exact results on strong or weak convergence to equilibrium employed in special-relativistic kinetic theory. At the late stages of cosmic expansion, an explicit choice of the empirical collision frequency is made to fit optimally the relaxation-time model to the “actual” Einstein-Boltzmann system. Finally, perspectives for some future generalizations are outlined.
A golden standard in science is to repeat an experiment a statistically significant number of tim... more A golden standard in science is to repeat an experiment a statistically significant number of times, recording data using the same set of detectors and the same data analysis methodology. In such case experimental error includes both the range of true values generated by repetitions of the experiment, and measurement uncertainty caused by the detector. They are independent. It is a huge and too frequently used simplification, to assume that one can measure multiple repetitions of an identical experiment, resulting in identical true experimental value. Repetitions, as similar is it is experimentally achievable, have unavoidable built-in differences resulting in a range of the true values rather than in a single value. When modern, very sensitive and well calibrated measurement systems are used, this range is not negligible, and sometimes dominates over the measurement uncertainty. Range of true values depends on built-in differences in physics of the experiment. Stochastic physical processes result typically in a broader range of true values than non-stochastic processes do. Measurement uncertainty depends on a measurement method (properties of the detector not of the experiment). Modern measurement methods, including digital ones, frequently make the measurement uncertainty very small. When data from one-of-a kind experiment are analyzed, only the measurement uncertainty is reported. It provides no information about the range of true experimental values, neither about reliability of a reported data point. Reliability of a data point is in general independent from its measurement uncertainty. However, in practice reliable measurement methods frequently have high measurement uncertainty, while low reliability methods are applied to limit measurement uncertainty. Comparison of reliable data with high measurement uncertainty to not so reliable data measured with low uncertainty is discussed-in different scenarios different data analysis methods are applicable. Methods for data analysis from an experiment repeated statistically significant number of times are very well developed. They do not require a detailed expertise in physics of an experiment, nor in the properties of the measurement system used, and meaning of the reported uncertainty is well understood in any scientific community. It all changes when data from one-of-a-kind experiment is analyzed. Analyst's expertise is required both in the physics of the experiment and in all aspects of the measurement system, all possible malfunctions. Data users must remember that only measurement uncertainty is reported from any one-of-a-kind experiment. Theory with simulations may provide estimation of expected built-in differences in the experiment, and by this of expected range of true values for a given experiment; yet measurement uncertainty can never be used in place of the range of true experimental values.
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