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At least 703 records · Page 39

An analytical treatment of discretely varying constraints and inertial properties in multi-body dynamics

A computerized procedure is presented for calculating instantaneous velocity changes due to discrete imposition of constraints, impact or discrete inertial changes. Such discrete changes are impulsive in nature, involve wave propagation and therefore usually require detailed modeling for accurate prediction. It is demonstrated that when modeling is coarse, physically unrealistic results can be produced. The present procedure, which concentrates on finite element analysis, reduces the need for detailed modeling by assuming that only those velocities in the neighborhood of grid points involved in the constraint or those rigidly connected to grid points involved in the constraint need be considered in calculating velocity changes. The procedure utilizes Newton's second law and as such conserves momentum where valid. Sample problems are provided.

Housner, J. M.↗

Development of an improved model for runback water on aircraft surfaces

A computer simulation for 'running wet' and evaporative aircraft anti-icing systems is developed. The model is based on the analysis of the liquid water film which forms in the regions of direct impingement and, then, breaks up near the impingement limits into rivulets. The wetness factor distribution resulting from the film breakup and the rivulet configuration on the surface are predicted using a stability analysis theory and the laws of mass energy conservation. The solid structure is modeled as a multiple layer wall. The anti-icing system modeled is of the thermal type utilizing hot air and/or electrical heating elements embedded within the wall layers. Experimental observations revealing some of the basic physics of the water flow on the surface are presented. Detailed qualitative documentation of the tests are given. Several numerical examples are considered, and the effect of some of the involved parameters on the system performance are investigated.

Al-Khalil, Kamel M.↗

Lorentz Symmetry Group, Retardation and Energy Transformations in a Relativistic Engine

In a previous paper, we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light in vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conservation was discussed in a pervious paper, while preliminary results regarding energy conservation where discussed in some additional papers. Here we give a complete analysis of the exchange of energy between the mechanical part of the relativistic engine and the field part, the energy radiated from the relativistic engine is also discussed. We show that the relativistic engine effect on the energy is 4th-order in 1c and no lower order relativistic engine effect on the energy exists.

42 ENGINEERING↗

Lorentz-covariant dissipative Lagrangian systems

The concept of dissipative Hamiltonian system is converted to Lorentz-covariant form, with evolution generated jointly by two scalar functionals, the Lagrangian action and the global entropy. A bracket formulation yields the local covariant laws of energy-momentum conservation and of entropy production. The formalism is illustrated by a derivation of the covariant Landau kinetic equation.

Kaufman, A. N.↗

Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, {PIML} models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, {PIML} models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of {PIML} is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in {PIML} for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of {PIML} models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

Nghiem, Truong↗

Development of prediction techniques for multi-jet thermal ground flow fields and fountain formation

Avoiding detrimental ground interaction is important for practical V/STOL aircraft. This paper reports recent developments in a numerical method for estimating thermal ground footprints. Upwash and fountain formation for arbitrarily oriented jet arrangements is predicted. Flow asymmetry due to roll, pitch, differential thrust or ground inclination is included. The prediction methodology uses simple inviscid relations for energy and momentum conservation along with an empirical entrainment law, applied in independent sectors of the wall jet and upwash. Asymmetrical stagnation line prediction is compared with experiment. Detailed flow measurements for a three-jet interaction are also presented.

Siclari, M. J.↗

Civil law enforcement missions

The user requirements for law enforcement, fire departments, paramedic, rescue, conservation and federal government agencies who use helicopters as a routine part of their operations are discussed.

Morrison, R. M.↗

Quasi-Static Probabilistic Structural Analyses Process and Criteria

Current deterministic structural methods are easily applied to substructures and components, and analysts have built great design insights and confidence in them over the years. However, deterministic methods cannot support systems risk analyses, and it was recently reported that deterministic treatment of statistical data is inconsistent with error propagation laws that can result in unevenly conservative structural predictions. Assuming non-nal distributions and using statistical data formats throughout prevailing stress deterministic processes lead to a safety factor in statistical format, which integrated into the safety index, provides a safety factor and first order reliability relationship. The embedded safety factor in the safety index expression allows a historically based risk to be determined and verified over a variety of quasi-static metallic substructures consistent with the traditional safety factor methods and NASA Std. 5001 criteria.

Goldberg, B.↗

Dynamics of Aqueous Foam Drops

We develop a model for the nonlinear oscillations of spherical drops composed of aqueous foam. Beginning with a simple mixture law, and utilizing a mass-conserving bubble-in-cell scheme, we obtain a Rayleigh-Plesset-like equation for the dynamics of bubbles in a foam mixture. The dispersion relation for sound waves in a bubbly liquid is then coupled with a normal modes expansion to derive expressions for the frequencies of eigenmodal oscillations. These eigenmodal (breathing plus higher-order shape modes) frequencies are elicited as a function of the void fraction of the foam. A Mathieu-like equation is obtained for the dynamics of the higher-order shape modes and their parametric coupling to the breathing mode. The proposed model is used to explain recently obtained experimental data.

Akhatov, Iskander↗

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗

Electromagnetic fluctuations for anisotropic media and the generalized Kirchhoff's law

In this paper the polarimetric emission parameters for anisotropic media are derived using the generalized Kirchhoff's law for media with a uniform temperature and the fluctuation-dissipation theory for media with a temperature profile. Both finite-size objects and half-space media are considered. When the object has a uniform temperature across its body, the Kirchhoff's law, based on the condition of energy conservation in thermal equilibrium is generalized to obtain the emission parameters of an anisotropic medium, which can be interpreted as the absorptivity or the absorption cross section of the complementary object with a permittivity that is the transpose of the original object. When the medium has a nonuniform temperature distribution, the fluctuation-dissipation theory is applied for deriving the covariances between vector components of the thermal currents and, consequently, the covariances of the polarizations of electric fields radiated by the thermal currents. To verify the formulas derived from the fluctuation-dissipation theory, we let the temperature of the object be a constant and show that the results reduce to those obtained from the generalized Kirchhoff's law.

Yueh, Simon H.↗

Finite amplitude Alfven waves in a multi-ion plasma - Propagation, acceleration, and heating

An expression is derived for the wave action flux of finite-amplitude Alfven waves in a multi-ion plasma. The expression is valid in the presence of dissipative forces and permits an arbitrary angle between the average magnetic field and the wave vector. Applying the conservation of wave action and the first law of thermodynamics yields, for a multi-ion plasma, an expression for the spatial evolution of Alfven wave amplitude in the absence of dissipation. It also gives the relationship between the wave amplitude and the dissipative heating, as well as an expression for the acceleration of an ion species by finite-amplitude Alfven waves. It is pointed out that the acceleration comprises a nondissipative wave pressure that is identical to that derived previously under more restrictive conditions and a new term giving the acceleration that must accompany dissipative heating. The results are discussed in the context of the observations of heavy ions in the solar wind.

Isenberg, P. A.↗

On-orbit cryogenic fluid transfer research at NASA Lewis Research Center

A summary of research into on-orbit cryogenic fluid transfer at the NASA Lewis Research Center (LRC) is presented. Variable test parameters and liquid injection configurations elucidated the conditions necessary for a successful transfer of liquid hydrogen by the no-vent fill method. The model is based on conservation of mass and a first-law energy balance for a control volume. The ullage, the bulk liquid, and the tank wall are each represented by a single node. The magnitude of the maximum receiver tank pressure was found to be dependent on the liquid inlet temperature, the inlet mass flow rate, and the initial temperature. A comparison of the test data and the analytical results for a no-vent fill test with a small receiver tank is presented.

Taylor, W. J.↗

Physical Laws for Mechanobiology

Higher-level physical laws applicable to biological tissues are presented that will permit the modeling of metabolic activity at the cellular level, including variations in the mass of a tissue. Here the tissue is represented as a fluid/solid mixture, wherein molecular solutes transport within the fluid, and cells can migrate throughout the porous solid. Variations in mass can arise via exchanges in mass between the constituent phases within a control volume such that mass is conserved in the tissue overall. The governing balance laws for mass, momentum, energy, and entropy are a special case of those describing a chemically reacting mixture with diffusion. Thermodynamic constraints on the constitutive structure are addressed. Biophysics; Biomechanics; Brownian motion; Cell migration; Mixture theory; Thermodynamic laws; Tissue mechanics

Freed, Alan D.↗

Sondheimer oscillations as a probe of non-ohmic flow in WP 2 crystals

As conductors in electronic applications shrink, microscopic conduction processes lead to strong deviations from Ohm’s law. Depending on the length scales of momentum conserving (l MC ) and relaxing (l MR ) electron scattering, and the device size (d), current flows may shift from ohmic to ballistic to hydrodynamic regimes. So far, an in situ methodology to obtain these parameters within a micro/nanodevice is critically lacking. In this context, we exploit Sondheimer oscillations, semi-classical magnetoresistance oscillations due to helical electronic motion, as a method to obtain l MR even when l MR $\gg$ d. We extract l MR from the Sondheimer amplitude in WP 2 , at temperatures up to T ~ 40 K, a range most relevant for hydrodynamic transport phenomena. Our data on μm-sized devices are in excellent agreement with experimental reports of the bulk l MR and confirm that WP 2 can be microfabricated without degradation. These results conclusively establish Sondheimer oscillations as a quantitative probe of l MR in micro-devices.

36 MATERIALS SCIENCE↗

Physically-Derived Dynamical Cores in Atmospheric General Circulation Models

The algorithm chosen to represent the advection in atmospheric models is often used as the primary attribute to classify the model. Meteorological models are generally classified as spectral or grid point, with the term grid point implying discretization using finite differences. These traditional approaches have a number of shortcomings that render them non-physical. That is, they provide approximate solutions to the conservation equations that do not obey the fundamental laws of physics. The most commonly discussed shortcomings are overshoots and undershoots which manifest themselves most overtly in the constituent continuity equation. For this reason many climate models have special algorithms to model water vapor advection. This talk focuses on the development of an atmospheric general circulation model which uses a consistent physically-based advection algorithm in all aspects of the model formulation. The shallow-water model is generalized to three dimensions and combined with the physics parameterizations of NCAR's Community Climate Model. The scientific motivation for the development is to increase the integrity of the underlying fluid dynamics so that the physics terms can be more effectively isolated, examined, and improved. The expected benefits of the new model are discussed and results from the initial integrations will be presented.

Rood, Richard B.↗

Physically-Derived Dynamical Cores in Atmospheric General Circulation Models

The algorithm chosen to represent the advection in atmospheric models is often used as the primary attribute to classify the model. Meteorological models are generally classified as spectral or grid point, with the term grid point implying discretization using finite differences. These traditional approaches have a number of shortcomings that render them non-physical. That is, they provide approximate solutions to the conservation equations that do not obey the fundamental laws of physics. The most commonly discussed shortcomings are overshoots and undershoots which manifest themselves most overtly in the constituent continuity equation. For this reason many climate models have special algorithms to model water vapor advection. This talk focuses on the development of an atmospheric general circulation model which uses a consistent physically-based advection algorithm in all aspects of the model formulation. The shallow-water model of Lin and Rood (QJRMS, 1997) is generalized to three dimensions and combined with the physics parameterizations of NCAR's Community Climate Model. The scientific motivation for the development is to increase the integrity of the underlying fluid dynamics so that the physics terms can be more effectively isolated, examined, and improved. The expected benefits of the new model are discussed and results from the initial integrations will be presented.

Rood, Richard B.↗

Comparison of Non-Parabolic Hydrodynamic Simulations for Semiconductor Devices

Parabolic drift-diffusion simulators are common engineering level design tools for semiconductor devices. Hydrodynamic simulators, based on the parabolic band approximation, are becoming more prevalent as device dimensions shrink and energy transport effects begin to dominate device characteristic. However, band structure effects present in state-of-the-art devices necessitate relaxing the parabolic band approximation. This paper presents simulations of ballistic diodes, a benchmark device, of Si and GaAs using two different non-parabolic hydrodynamic formulations. The first formulation uses the Kane dispersion relationship in the derivation of the conservation equations. The second model uses a power law dispersion relation {(hk)(exp 2)/2m = xW(exp Y)}. Current-voltage relations show that for the ballistic diodes considered. the non-parabolic formulations predict less current than the parabolic case. Explanations of this will be provided by examination of velocity and energy profiles. At low bias, the simulations based on the Kane formulation predict greater current flow than the power law formulation. As the bias is increased this trend changes and the power law predicts greater current than the Kane formulation. It will be shown that the non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation are limited due to the binomial approximation which was utilized in the derivation.

Smith, A. W.↗