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Results for “classical statistical mechanics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Lagrange thermodynamic potential and intrinsic variables for He-3 He-4 dilute solutions

For a two-fluid model of dilute solutions of He-3 in liquid He-4, a thermodynamic potential is constructed that provides a Lagrangian for deriving equations of motion by a variational procedure. This Lagrangian is defined for uniform velocity fields as a (negative) Legendre transform of total internal energy, and its primary independent variables, together with their thermodynamic conjugates, are identified. Here, similarities between relations in classical physics and quantum statistical mechanics serve as a guide for developing an alternate expression for this function that reveals its character as the difference between apparent kinetic energy and intrinsic internal energy. When the He-3 concentration in the mixtures tends to zero, this expression reduces to Zilsel's formula for the Lagrangian for pure liquid He-4. An investigation of properties of the intrinsic internal energy leads to the introduction of intrinsic chemical potentials along with other intrinsic variables for the mixtures. Explicit formulas for these variables are derived for a noninteracting elementary excitation model of the fluid. Using these formulas and others also derived from quantum statistical mechanics, another equivalent expression for the Lagrangian is generated.

Jackson, H. W.↗
NASA NTRS1990

Statistical mechanics models for motion and force planning

The models of statistical mechanics provide an alternative to the methods of classical mechanics more traditionally used in robotics. They have a potential to: improve analysis of object collisions; handle kinematic and dynamic contact interactions within the same frmework; and reduce the need for perfect deterministic world model information. The statistical mechanics models characterize the state of the system as a probability density function (p.d.f.) whose time evolution is governed by a partial differential equation subject to boundary and initial conditions. The boundary conditions when rigid objects collide reflect the conservation of momentum. The models are being developed to embedd in remote semi-autonomous systems with a need to reason and interact with a multiobject environment.

Rodriguez, G.↗
NASA NTRS1976

Thermodynamics and statistical mechanics

The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.

Source record↗
NASA NTRS1981

Calculations of the surface tensions of liquid metals

The understanding of the surface tension of liquid metals and alloys from as close to first principles as possible is discussed. The two ingredients which are combined in these calculations are: the electron theory of metals, and the classical theory of liquids, as worked out within the framework of statistical mechanics. The results are a new theory of surface tensions and surface density profiles from knowledge purely of the bulk properties of the coexisting liquid and vapor phases. It is found that the method works well for the pure liquid metals on which it was tested; work is extended to mixtures of liquid metals, interfaces between immiscible liquid metals, and to the temperature derivative of the surface tension.

Stroud, D. G.↗
NASA NTRS2010

Fiber Breakage Model for Carbon Composite Stress Rupture Phenomenon: Theoretical Development and Applications

Stress rupture failure of Carbon Composite Overwrapped Pressure Vessels (COPVs) is of serious concern to Science Mission and Constellation programs since there are a number of COPVs on board space vehicles with stored gases under high pressure for long durations of time. It has become customary to establish the reliability of these vessels using the so called classic models. The classical models are based on Weibull statistics fitted to observed stress rupture data. These stochastic models cannot account for any additional damage due to the complex pressure-time histories characteristic of COPVs being supplied for NASA missions. In particular, it is suspected that the effects of proof test could significantly reduce the stress rupture lifetime of COPVs. The focus of this paper is to present an analytical appraisal of a model that incorporates damage due to proof test. The model examined in the current paper is based on physical mechanisms such as micromechanics based load sharing concepts coupled with creep rupture and Weibull statistics. For example, the classic model cannot accommodate for damage due to proof testing which every flight vessel undergoes. The paper compares current model to the classic model with a number of examples. In addition, several applications of the model to current ISS and Constellation program issues are also examined.

Murthy, Pappu L. N.↗
NASA NTRS2010

Physics of Life: A Model for Non-Newtonian Properties of Living Systems

This innovation proposes the reconciliation of the evolution of life with the second law of thermodynamics via the introduction of the First Principle for modeling behavior of living systems. The structure of the model is quantum-inspired: it acquires the topology of the Madelung equation in which the quantum potential is replaced with the information potential. As a result, the model captures the most fundamental property of life: the progressive evolution; i.e. the ability to evolve from disorder to order without any external interference. The mathematical structure of the model can be obtained from the Newtonian equations of motion (representing the motor dynamics) coupled with the corresponding Liouville equation (representing the mental dynamics) via information forces. All these specific non-Newtonian properties equip the model with the levels of complexity that matches the complexity of life, and that makes the model applicable for description of behaviors of ecological, social, and economical systems. Rather than addressing the six aspects of life (organization, metabolism, growth, adaptation, response to stimuli, and reproduction), this work focuses only on biosignature ; i.e. the mechanical invariants of life, and in particular, the geometry and kinematics of behavior of living things. Living things obey the First Principles of Newtonian mechanics. One main objective of this model is to extend the First Principles of classical physics to include phenomenological behavior on living systems; to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems such as formation of the collective mind based upon abstract images of the selves and non-selves; exploitation of this collective mind for communications and predictions of future expected characteristics of evolution; and for making decisions and implementing the corresponding corrections if the expected scenario is different from the originally planned one. This approach postulates that even a primitive living species possesses additional, non-Newtonian properties that are not included in the laws of Newtonian or statistical mechanics. These properties follow from a privileged ability of living systems to possess a self-image (a concept introduced in psychology) and to interact with it. The proposed mathematical system is based on the coupling of the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. The coupling is implemented by the information-based supervising forces that can be associated with self-awareness. These forces fundamentally change the pattern of the probability evolution, and therefore, lead to a major departure of the behavior of living systems from the patterns of both Newtonian and statistical mechanics. This innovation is meant to capture the signature of life based only on observable behavior, not on any biochemistry. This will not prevent the use of this model for developing artificial living systems, as well as for studying some general properties of behavior of natural, living systems.

Zak, Michail↗
NASA NTRS1972

Strongly magnetized classical plasma models

The class of plasma processes for which the so-called Vlasov approximation is inadequate is investigated. Results from the equilibrium statistical mechanics of two-dimensional plasmas are derived. These results are independent of the presence of an external dc magnetic field. The nonequilibrium statistical mechanics of the electrostatic guiding-center plasma, a two-dimensional plasma model, is discussed. This model is then generalized to three dimensions. The guiding-center model is relaxed to include finite Larmor radius effects for a two-dimensional plasma.

Montgomery, D. C.↗
NASA NTRS1976

Nonclassical acoustics

A statistical approach to sound propagation is considered in situations where, due to the presence of large gradients of properties of the medium, the classical (deterministic) treatment of wave motion is inadequate. Mathematical methods for wave motions not restricted to small wavelengths (analogous to known methods of quantum mechanics) are used to formulate a wave theory of sound in nonuniform flows. Nonlinear transport equations for field probabilities are derived for the limiting case of noninteracting sound waves and it is postulated that such transport equations, appropriately generalized, may be used to predict the statistical behavior of sound in arbitrary flows.

Kentzer, C. P.↗
NASA NTRS1986

Investigation of advanced fault insertion and simulator methods

The cooperative agreement partly supported research leading to the open-literature publication cited. Additional efforts under the agreement included research into fault modeling of semiconductor devices. Results of this research are presented in this report which is summarized in the following paragraphs. As a result of the cited research, it appears that semiconductor failure mechanism data is abundant but of little use in developing pin-level device models. Failure mode data on the other hand does exist but is too sparse to be of any statistical use in developing fault models. What is significant in the failure mode data is that, unlike classical logic, MSI and LSI devices do exhibit more than 'stuck-at' and open/short failure modes. Specifically they are dominated by parametric failures and functional anomalies that can include intermittent faults and multiple-pin failures. The report discusses methods of developing composite pin-level models based on extrapolation of semiconductor device failure mechanisms, failure modes, results of temperature stress testing and functional modeling. Limitations of this model particularly with regard to determination of fault detection coverage and latency time measurement are discussed. Indicated research directions are presented.

Dunn, W. R.↗
NASA NTRS2010

Hidden Statistics Approach to Quantum Simulations

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the transitional potential is to provide a jump from a deterministic state to a random state with prescribed probability density. This jump is triggered by blowup instability due to violation of Lipschitz condition generated by the quantum potential. As a result, the dynamics attains quantum properties on a classical scale. The model can be implemented physically as an analog VLSI-based (very-large-scale integration-based) computer, or numerically on a digital computer. This work opens a way of developing fundamentally new algorithms for quantum simulations of exponentially complex problems that expand NASA capabilities in conducting space activities. It has been illustrated that the complexity of simulations of particle interaction can be reduced from an exponential one to a polynomial one.

Zak, Michail↗
NASA NTRS1972

Study of optimum methods of optical communication

Optimum methods of optical communication accounting for the effects of the turbulent atmosphere and quantum mechanics, both by the semi-classical method and the full-fledged quantum theoretical model are described. A concerted effort to apply the techniques of communication theory to the novel problems of optical communication by a careful study of realistic models and their statistical descriptions, the finding of appropriate optimum structures and the calculation of their performance and, insofar as possible, comparing them to conventional and other suboptimal systems are discussed. In this unified way the bounds on performance and the structure of optimum communication systems for transmission of information, imaging, tracking, and estimation can be determined for optical channels.

Harger, R. O.↗
NASA NTRS1974

Strongly magnetized classical plasma models

Discrete particle processes in the presence of a strong external magnetic field were investigated. These processes include equations of state and other equilibrium thermodynamic relations, thermal relaxation phenomena, transport properties, and microscopic statistical fluctuations in such quantities as the electric field and the charge density. Results from the equilibrium statistical mechanics of two-dimensional plasmas are discussed, along with nonequilibrium statistical mechanics of the electrostatic guiding-center plasma (a two-dimensional plasma model).

Montgomery, D.↗
NASA NTRS1994

Applications of squeezed states: Bogoliubov transformations and wavelets to the statistical mechanics of water and its bubbles

The squeezed states or Bogoliubov transformations and wavelets are applied to two problems in nonrelativistic statistical mechanics: the dielectric response of liquid water, epsilon(q-vector,w), and the bubble formation in water during insonnification. The wavelets are special phase-space windows which cover the domain and range of L(exp 1) intersection of L(exp 2) of classical causal, finite energy solutions. The multiresolution of discrete wavelets in phase space gives a decomposition into regions of time and scales of frequency thereby allowing the renormalization group to be applied to new systems in addition to the tired 'usual suspects' of the Ising models and lattice gasses. The Bogoliubov transformation: squeeze transformation is applied to the dipolaron collective mode in water and to the gas produced by the explosive cavitation process in bubble formation.

Defacio, Brian↗
NASA NTRS1977

Quantum statistical theory of semiconductor junctions in thermal equilibrium

Free carrier and electric field distributions of one-dimensional semiconductor junctions are evaluated using a quantum mechanical phase-space distribution and its corresponding Boltzmann equation. Attention is given to quantum and exchange corrections in cases of high doping concentrations when carrier densities become degenerate. Quantitative differences between degenerate and classical junction characteristics, e.g., maximum electric field and built-in voltage and carrier concentration within the transition region, are evaluated numerically.

Von Roos, O.↗
NASA NTRS2010

The Prediction Properties of Inverse and Reverse Regression for the Simple Linear Calibration Problem

The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions.

Parker, Peter A.↗
NASA NTRS2011

Hidden Statistics of Schroedinger Equation

Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

Zak, Michail↗
NASA NTRS1981

Design and control strategies for CELSS - Integrating mechanistic paradigms and biological complexities

Systems analysis and control theory consideration are given to simulations of both individual components and total systems, in order to develop a reliable control strategy for a Controlled Ecological Life Support System (CELSS) which includes complex biological components. Because of the numerous nonlinearities and tight coupling within the biological component, classical control theory may be inadequate and the statistical analysis of factorial experiments more useful. The range in control characteristics of particular species may simplify the overall task by providing an appropriate balance of stability and controllability to match species function in the overall design. The ultimate goal of this research is the coordination of biological and mechanical subsystems in order to achieve a self-supporting environment.

Moore, B., III↗