Applications of Response Surface-Based Methods to Noise Analysis in the Conceptual Design of Revolutionary Aircraft

NASA Technical Reports Server (NTRS)

Hill, Geoffrey A.; Olson, Erik D.

2004-01-01

Due to the growing problem of noise in today's air transportation system, there have arisen needs to incorporate noise considerations in the conceptual design of revolutionary aircraft. Through the use of response surfaces, complex noise models may be converted into polynomial equations for rapid and simplified evaluation. This conversion allows many of the commonly used response surface-based trade space exploration methods to be applied to noise analysis. This methodology is demonstrated using a noise model of a notional 300 passenger Blended-Wing-Body (BWB) transport. Response surfaces are created relating source noise levels of the BWB vehicle to its corresponding FAR-36 certification noise levels and the resulting trade space is explored. Methods demonstrated include: single point analysis, parametric study, an optimization technique for inverse analysis, sensitivity studies, and probabilistic analysis. Extended applications of response surface-based methods in noise analysis are also discussed.

Linear and nonlinear response of a rotating tokamak plasma to a resonant error-field

NASA Astrophysics Data System (ADS)

Fitzpatrick, Richard

2014-09-01

An in-depth investigation of the effect of a resonant error-field on a rotating, quasi-cylindrical, tokamak plasma is preformed within the context of constant-ψ, resistive-magnetohydrodynamical theory. General expressions for the response of the plasma at the rational surface to the error-field are derived in both the linear and nonlinear regimes, and the extents of these regimes mapped out in parameter space. Torque-balance equations are also obtained in both regimes. These equations are used to determine the steady-state plasma rotation at the rational surface in the presence of the error-field. It is found that, provided the intrinsic plasma rotation is sufficiently large, the torque-balance equations possess dynamically stable low-rotation and high-rotation solution branches, separated by a forbidden band of dynamically unstable solutions. Moreover, bifurcations between the two stable solution branches are triggered as the amplitude of the error-field is varied. A low- to high-rotation bifurcation is invariably associated with a significant reduction in the width of the magnetic island chain driven at the rational surface, and vice versa. General expressions for the bifurcation thresholds are derived and their domains of validity mapped out in parameter space.

A regression technique for evaluation and quantification for water quality parameters from remote sensing data

NASA Technical Reports Server (NTRS)

Whitlock, C. H.; Kuo, C. Y.

1979-01-01

The objective of this paper is to define optical physics and/or environmental conditions under which the linear multiple-regression should be applicable. An investigation of the signal-response equations is conducted and the concept is tested by application to actual remote sensing data from a laboratory experiment performed under controlled conditions. Investigation of the signal-response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple-regression equation, even if nonlinear contributions from surface reflections, atmospheric constituents, or other water pollutants are included. Limitations on achieving this type of solution are defined.

Preparation of Curcumin Loaded Egg Albumin Nanoparticles Using Acetone and Optimization of Desolvation Process.

PubMed

Aniesrani Delfiya, D S; Thangavel, K; Amirtham, D

2016-04-01

In this study, acetone was used as a desolvating agent to prepare the curcumin-loaded egg albumin nanoparticles. Response surface methodology was employed to analyze the influence of process parameters namely concentration (5-15%w/v) and pH (5-7) of egg albumin solution on solubility, curcumin loading and entrapment efficiency, nanoparticles yield and particle size. Optimum processing conditions obtained from response surface analysis were found to be the egg albumin solution concentration of 8.85%w/v and pH of 5. At this optimum condition, the solubility of 33.57%, curcumin loading of 4.125%, curcumin entrapment efficiency of 55.23%, yield of 72.85% and particles size of 232.6 nm were obtained and these values were related to the values which are predicted using polynomial model equations. Thus, the model equations generated for each response was validated and it can be used to predict the response values at any concentration and pH.

The Chicken Problem.

ERIC Educational Resources Information Center

Reeves, Charles A.

2000-01-01

Uses the chicken problem for sixth grade students to scratch the surface of systems of equations using intuitive approaches. Provides students responses to the problem and suggests similar problems for extensions. (ASK)

An EBIC equation for solar cells. [Electron Beam Induced Current

NASA Technical Reports Server (NTRS)

Luke, K. L.; Von Roos, O.

1983-01-01

When an electron beam of a scanning electron microscope (SEM) impinges on an N-P junction, the generation of electron-hole pairs by impact ionization causes a characteristic short circuit current I(sc) to flow. The I(sc), i.e., EBIC (electron beam induced current) depends strongly on the configuration used to investigate the cell's response. In this paper the case where the plane of the junction is perpendicular to the surface is considered. An EBIC equation amenable to numerical computations is derived as a function of cell thickness, source depth, surface recombination velocity, diffusion length, and distance of the junction to the beam-cell interaction point for a cell with an ohmic contact at its back surface. It is shown that the EBIC equation presented here is more general and easier to use than those previously reported. The effects of source depth, ohmic contact, and diffusion length on the normalized EBIC characteristic are discussed.

Structure of a viscoplastic theory

NASA Technical Reports Server (NTRS)

Freed, Alan D.

1988-01-01

The general structure of a viscoplastic theory is developed from physical and thermodynamical considerations. The flow equation is of classical form. The dynamic recovery approach is shown to be superior to the hardening function approach for incorporating nonlinear strain hardening into the material response through the evolutionary equation for back stress. A novel approach for introducing isotropic strain hardening into the theory is presented, which results in a useful simplification. In particular, the limiting stress for the kinematic saturation of state (not the drag stress) is the chosen scalar-valued state variable. The resulting simplification is that there is no coupling between dynamic and thermal recovery terms in each evolutionary equation. The derived theory of viscoplasticity has the structure of a two-surface plasticity theory when the response is plasticlike, and the structure of a Bailey-Orowan creep theory when the response is creeplike.

MOM3D method of moments code theory manual

NASA Technical Reports Server (NTRS)

Shaeffer, John F.

1992-01-01

MOM3D is a FORTRAN algorithm that solves Maxwell's equations as expressed via the electric field integral equation for the electromagnetic response of open or closed three dimensional surfaces modeled with triangle patches. Two joined triangles (couples) form the vector current unknowns for the surface. Boundary conditions are for perfectly conducting or resistive surfaces. The impedance matrix represents the fundamental electromagnetic interaction of the body with itself. A variety of electromagnetic analysis options are possible once the impedance matrix is computed including backscatter radar cross section (RCS), bistatic RCS, antenna pattern prediction for user specified body voltage excitation ports, RCS image projection showing RCS scattering center locations, surface currents excited on the body as induced by specified plane wave excitation, and near field computation for the electric field on or near the body.

[Optimization for supercritical CO2 extraction with response surface methodology of Prunus armeniaca oil].

PubMed

Chen, Fei-Fei; Wu, Yan; Ge, Fa-Huan

2012-03-01

To optimize the extraction conditions of Prunus armeniaca oil by Supercritical CO2 extraction and identify its components by GC-MS. Optimized of SFE-CO extraction by response surface methodology and used GC-MS to analysis Prunus armeniaca oil compounds. Established the model of an equation for the extraction rate of Prunus armeniaca oil by supercritical CO2 extraction, and the optimal parameters for the supercritical CO2 extraction determined by the equation were: the extraction pressure was 27 MPa, temperature was 39 degrees C, the extraction rate of Prunus armeniaca oil was 44.5%. 16 main compounds of Prunus armeniaca oil extracted by supercritical CO2 were identified by GC-MS, unsaturated fatty acids were 92.6%. This process is simple, and can be used for the extraction of Prunus armeniaca oil.

Simulations of ecosystem hydrological processes using a unified multi-scale model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaofan; Liu, Chongxuan; Fang, Yilin

2015-01-01

This paper presents a unified multi-scale model (UMSM) that we developed to simulate hydrological processes in an ecosystem containing both surface water and groundwater. The UMSM approach modifies the Navier–Stokes equation by adding a Darcy force term to formulate a single set of equations to describe fluid momentum and uses a generalized equation to describe fluid mass balance. The advantage of the approach is that the single set of the equations can describe hydrological processes in both surface water and groundwater where different models are traditionally required to simulate fluid flow. This feature of the UMSM significantly facilitates modelling ofmore » hydrological processes in ecosystems, especially at locations where soil/sediment may be frequently inundated and drained in response to precipitation, regional hydrological and climate changes. In this paper, the UMSM was benchmarked using WASH123D, a model commonly used for simulating coupled surface water and groundwater flow. Disney Wilderness Preserve (DWP) site at the Kissimmee, Florida, where active field monitoring and measurements are ongoing to understand hydrological and biogeochemical processes, was then used as an example to illustrate the UMSM modelling approach. The simulations results demonstrated that the DWP site is subject to the frequent changes in soil saturation, the geometry and volume of surface water bodies, and groundwater and surface water exchange. All the hydrological phenomena in surface water and groundwater components including inundation and draining, river bank flow, groundwater table change, soil saturation, hydrological interactions between groundwater and surface water, and the migration of surface water and groundwater interfaces can be simultaneously simulated using the UMSM. Overall, the UMSM offers a cross-scale approach that is particularly suitable to simulate coupled surface and ground water flow in ecosystems with strong surface water and groundwater interactions.« less

Linear and Nonlinear Response of a Rotating Tokamak Plasma to a Resonant Error-Field

NASA Astrophysics Data System (ADS)

Fitzpatrick, Richard

2014-10-01

An in-depth investigation of the effect of a resonant error-field on a rotating, quasi-cylindrical, tokamak plasma is preformed within the context of resistive-MHD theory. General expressions for the response of the plasma at the rational surface to the error-field are derived in both the linear and nonlinear regimes, and the extents of these regimes mapped out in parameter space. Torque-balance equations are also obtained in both regimes. These equations are used to determine the steady-state plasma rotation at the rational surface in the presence of the error-field. It is found that, provided the intrinsic plasma rotation is sufficiently large, the torque-balance equations possess dynamically stable low-rotation and high-rotation solution branches, separated by a forbidden band of dynamically unstable solutions. Moreover, bifurcations between the two stable solution branches are triggered as the amplitude of the error-field is varied. A low- to high-rotation bifurcation is invariably associated with a significant reduction in the width of the magnetic island chain driven at the rational surface, and vice versa. General expressions for the bifurcation thresholds are derived, and their domains of validity mapped out in parameter space. This research was funded by the U.S. Department of Energy under Contract DE-FG02-04ER-54742.

Timescales of Land Surface Evapotranspiration Response

NASA Technical Reports Server (NTRS)

Scott, Russell; Entekhabi, Dara; Koster, Randal; Suarez, Max

1997-01-01

Soil and vegetation exert strong control over the evapotranspiration rate, which couples the land surface water and energy balances. A method is presented to quantify the timescale of this surface control using daily general circulation model (GCM) simulation values of evapotranspiration and precipitation. By equating the time history of evaporation efficiency (ratio of actual to potential evapotranspiration) to the convolution of precipitation and a unit kernel (temporal weighting function), response functions are generated that can be used to characterize the timescales of evapotranspiration response for the land surface model (LSM) component of GCMS. The technique is applied to the output of two multiyear simulations of a GCM, one using a Surface-Vegetation-Atmosphere-Transfer (SVAT) scheme and the other a Bucket LSM. The derived response functions show that the Bucket LSM's response is significantly slower than that of the SVAT across the globe. The analysis also shows how the timescales of interception reservoir evaporation, bare soil evaporation, and vegetation transpiration differ within the SVAT LSM.

Tidal Response of Europa's Subsurface Ocean

NASA Astrophysics Data System (ADS)

Karatekin, O.; Comblen, R.; Deleersnijder, E.; Dehant, V. M.

2010-12-01

Time-variable tides in the subsurface oceans of icy satellites cause large periodic surface displacements and tidal dissipation can become a major energy source that can affect long-term orbital and internal evolution. In the present study, we investigate the response of the subsurface ocean of Europa to a time-varibale tidal potential. Two-dimensional nonlinear shallow water equations are solved on a sphere by means of a finite element code. The resulting ocean tidal flow velocities,dissipation and surface displacements will be presented.

New technique for excitation of bulk and surface spin waves in ferromagnets

NASA Astrophysics Data System (ADS)

Bogacz, S. A.; Ketterson, J. B.

1985-09-01

A meander-line magnetic transducer is discussed in the context of bulk and surface spin-wave generation in ferromagnets. The magnetic field created by the transducer was calculated in closed analytic form for this model. The linear response of the ferromagnet to the inhomogenous surface disturbance of arbitrary ω and k was obtained as a self-consistent solution to the Bloch equation of motion and the Maxwell equations, subject to appropriate boundary condition. In particular, the energy flux through the boundary displays a sharp resonantlike absorption maximum concentrated at the frequency of the magnetostatic Damon-Eshbach (DE) surface mode; furthermore, the energy transfer spectrum is cut off abruptly below the threshold frequency of the bulk spin waves. The application of the meander line to the spin diffusion problem in NMR is also discussed.

Control of sound radiation from a wavepacket over a curved surface

NASA Technical Reports Server (NTRS)

Maestrello, Lucio; El Hady, Nabil M.

1989-01-01

Active control of acoustic pressure in the far field resulting from the growth and decay of a wavepacket convecting in a boundary layer over a concave-convex surface is investigated numerically using direct computations of the Navier-Stokes equations. The resulting sound radiation is computed using linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. The acoustic far field exhibits directivity type of behavior that points upstream to the flow direction. A fixed control algorithm is used where the attenuation signal is synthesized by a filter which actively adapt it to the amplitude-time response of the outgoing acoustic wave.

Summary of theoretical and experimental investigation of grating type, silicon photovoltaic cells. [using p-n junctions on light receiving surface of base crystal

NASA Technical Reports Server (NTRS)

Chen, L. Y.; Loferski, J. J.

1975-01-01

Theoretical and experimental aspects are summarized for single crystal, silicon photovoltaic devices made by forming a grating pattern of p/n junctions on the light receiving surface of the base crystal. Based on the general semiconductor equations, a mathematical description is presented for the photovoltaic properties of such grating-like structures in a two dimensional form. The resulting second order elliptical equation is solved by computer modeling to give solutions for various, reasonable, initial values of bulk resistivity, excess carrier concentration, and surface recombination velocity. The validity of the computer model is established by comparison with p/n devices produced by alloying an aluminum grating pattern into the surface of n-type silicon wafers. Current voltage characteristics and spectral response curves are presented for cells of this type constructed on wafers of different resistivities and orientations.

Overview of the CHarring Ablator Response (CHAR) Code

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Oliver, A. Brandon; Kirk, Benjamin S.; Salazar, Giovanni; Droba, Justin

2016-01-01

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation, surface-to-surface radiation exchange, and flowfield coupling. Finally, a discussion of ongoing development efforts is presented.

Numerical analysis of the transient response of an axisymmetric ablative char layer considering internal flow effects

NASA Technical Reports Server (NTRS)

Pittman, C. M.; Howser, L. M.

1972-01-01

The differential equations governing the transient response of the char layer of an ablating axisymmetric body, internal pyrolysis gas flow effects being considered, have been derived. These equations have been expanded into finite difference form and programed for numerical solution on a digital computer. Numerical results compare favorably with simplified exact solutions. The complete numerical analysis was used to obtain solutions for two representative body shapes subjected to a typical entry heating environment. Pronounced effects of the lateral flow of pyrolysis gases on the mass flow field within the char layer and the associated surface and pyrolysis interface recession rates are shown.

A Numerical Analysis of the Transient Response of an Ablation System Including Effects of Thermal Nonequilibrium, Mass Transfer and Chemical Kinetics. Ph.D Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Clark, R. K.

1972-01-01

The differential equations governing the transient response of a one-dimensional ablative thermal protection system undergoing stagnation ablation are derived. These equations are for thermal nonequilibrium effects between the pyrolysis gases and the char layer and kinetically controlled chemical reactions and mass transfer between the pyrolysis gases and the char layer. The boundary conditions are written for the particular case of stagnation heating with surface removal by oxidation or sublimation and pyrolysis of the uncharred layer occurring in a plane. The governing equations and boundary conditions are solved numerically using the modified implicit method (Crank-Nicolson method). Numerical results are compared with exact solutions for a number of simplified cases. The comparison is favorable in each instance.

Volterra Series Approach for Nonlinear Aeroelastic Response of 2-D Lifting Surfaces

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Marzocca, Piergiovanni; Librescu, Liviu

2001-01-01

The problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via Volterra series approach is addressed. The related aeroelastic governing equations are based upon the inclusion of structural nonlinearities, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of geometric nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Mixed oxidizer hybrid propulsion system optimization under uncertainty using applied response surface methodology and Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Whitehead, James Joshua

The analysis documented herein provides an integrated approach for the conduct of optimization under uncertainty (OUU) using Monte Carlo Simulation (MCS) techniques coupled with response surface-based methods for characterization of mixture-dependent variables. This novel methodology provides an innovative means of conducting optimization studies under uncertainty in propulsion system design. Analytic inputs are based upon empirical regression rate information obtained from design of experiments (DOE) mixture studies utilizing a mixed oxidizer hybrid rocket concept. Hybrid fuel regression rate was selected as the target response variable for optimization under uncertainty, with maximization of regression rate chosen as the driving objective. Characteristic operational conditions and propellant mixture compositions from experimental efforts conducted during previous foundational work were combined with elemental uncertainty estimates as input variables. Response surfaces for mixture-dependent variables and their associated uncertainty levels were developed using quadratic response equations incorporating single and two-factor interactions. These analysis inputs, response surface equations and associated uncertainty contributions were applied to a probabilistic MCS to develop dispersed regression rates as a function of operational and mixture input conditions within design space. Illustrative case scenarios were developed and assessed using this analytic approach including fully and partially constrained operational condition sets over all of design mixture space. In addition, optimization sets were performed across an operationally representative region in operational space and across all investigated mixture combinations. These scenarios were selected as representative examples relevant to propulsion system optimization, particularly for hybrid and solid rocket platforms. Ternary diagrams, including contour and surface plots, were developed and utilized to aid in visualization. The concept of Expanded-Durov diagrams was also adopted and adapted to this study to aid in visualization of uncertainty bounds. Regions of maximum regression rate and associated uncertainties were determined for each set of case scenarios. Application of response surface methodology coupled with probabilistic-based MCS allowed for flexible and comprehensive interrogation of mixture and operating design space during optimization cases. Analyses were also conducted to assess sensitivity of uncertainty to variations in key elemental uncertainty estimates. The methodology developed during this research provides an innovative optimization tool for future propulsion design efforts.

Study on the Optimization and Process Modeling of the Rotary Ultrasonic Machining of Zerodur Glass-Ceramic

NASA Astrophysics Data System (ADS)

Pitts, James Daniel

Rotary ultrasonic machining (RUM), a hybrid process combining ultrasonic machining and diamond grinding, was created to increase material removal rates for the fabrication of hard and brittle workpieces. The objective of this research was to experimentally derive empirical equations for the prediction of multiple machined surface roughness parameters for helically pocketed rotary ultrasonic machined Zerodur glass-ceramic workpieces by means of a systematic statistical experimental approach. A Taguchi parametric screening design of experiments was employed to systematically determine the RUM process parameters with the largest effect on mean surface roughness. Next empirically determined equations for the seven common surface quality metrics were developed via Box-Behnken surface response experimental trials. Validation trials were conducted resulting in predicted and experimental surface roughness in varying levels of agreement. The reductions in cutting force and tool wear associated with RUM, reported by previous researchers, was experimentally verified to also extended to helical pocketing of Zerodur glass-ceramic.

Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies.

PubMed

Olives, Juan

2010-03-03

The thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the temperature, the chemical potentials and the surface strain tensor (true thermodynamic variables, for a viscoelastic solid or a viscous fluid). A new definition of the surface stress is given and the corresponding surface thermodynamics equations are presented. The mechanical equilibrium equation at the surface is then obtained. It involves the surface stress and is similar to the Cauchy equation for the volume. Its normal component is a generalization of the Laplace equation. At a (body-fluid-fluid) triple contact line, two equations are obtained, which represent: (i) the equilibrium of the forces (surface stresses) for a triple line fixed on the body; (ii) the equilibrium relative to the motion of the line with respect to the body. This last equation leads to a strong modification of Young's classical capillary equation.

Effect of Configuration Pitching Motion on Twin Tail Buffet Response

NASA Technical Reports Server (NTRS)

Sheta, Essam F.; Kandil, Osama A.

1998-01-01

The effect of dynamic pitch-up motion of delta wing on twin-tail buffet response is investigated. The computational model consists of a delta wing-twin tail configuration. The computations are carried out on a dynamic multi-block grid structure. This multidisciplinary problem is solved using three sets of equations which consists of the unsteady Navier-Stokes equations, the aeroelastic equations, and the grid displacement equations. The configuration is pitched-up from zero up to 60 deg. angle of attack, and the freestream Mach number and Reynolds number are 0.3 and 1.25 million, respectively. With the twin tail fixed as rigid surfaces and with no-forced pitch-up motion, the problem is solved for the initial flow conditions. Next, the problem is solved for the twin-tail response for uncoupled bending and torsional vibrations due to the unsteady loads on the twin tail and due to the forced pitch-up motion. The dynamic pitch-up problem is also solved for the flow response with the twin tail kept rigid. The configuration is investigated for inboard position of the twin tail which corresponds to a separation distance between the twin tail of 33% wing chord. The computed results are compared with the available experimental data.

Multimedia and Understanding: Expert and Novice Responses To Different Representations of Chemical Phenomena.

ERIC Educational Resources Information Center

Kozma, Robert B.; Russell, Joel

1997-01-01

Examines how professional chemists and undergraduate chemistry students respond to chemistry-related video segments, graphs, animations, and equations. Discusses the role that surface features of representations play in the understanding of chemistry. Contains 36 references. (DDR)

Integrated Conceptual Design of Joined-Wing SensorCraft Using Response Surface Models

DTIC Science & Technology

2006-11-01

vi Acknowledgements I would like to express my sincere appreciation to my thesis advisor, Dr. Robert Canfield for his guidance and...55 Raymer Approximate and Group Weights Sizing Methods....................................... 57 Finite Element Model Structural Weight...Empty Weight Fraction Equation ............................... 54 Figure 29 Response of Refined Weight to T/W and W/S Inputs for Model (2) Raymer ASW

Nonlinear dynamic modeling of surface defects in rolling element bearing systems

NASA Astrophysics Data System (ADS)

Rafsanjani, Ahmad; Abbasion, Saeed; Farshidianfar, Anoushiravan; Moeenfard, Hamid

2009-01-01

In this paper an analytical model is proposed to study the nonlinear dynamic behavior of rolling element bearing systems including surface defects. Various surface defects due to local imperfections on raceways and rolling elements are introduced to the proposed model. The contact force of each rolling element described according to nonlinear Hertzian contact deformation and the effect of internal radial clearance has been taken into account. Mathematical expressions were derived for inner race, outer race and rolling element local defects. To overcome the strong nonlinearity of the governing equations of motion, a modified Newmark time integration technique was used to solve the equations of motion numerically. The results were obtained in the form of time series, frequency responses and phase trajectories. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The classical Floquet theory has been applied to the proposed model to investigate the linear stability of the defective bearing rotor systems as the parameters of the system changes. The peak-to-peak frequency response of the system for each case is obtained and the basic routes to periodic, quasi-periodic and chaotic motions for different internal radial clearances are determined. The current study provides a powerful tool for design and health monitoring of machine systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertucci, M.; Michelato, P.; Moretti, M.

X-ray fluorescence probe for detection of foreign material inclusions on the inner surface of superconducting cavities has been developed and tested. The setup detects trace element content such as a few micrograms of impurities responsible for thermal breakdown phenomena limiting the cavity performance. The setup has been customized for the geometry of 1.3 GHz TESLA-type niobium cavities and focuses on the surface of equator area at around 103 mm from the centre axis of the cavities with around 20 mm detection spot. More precise localization of inclusions can be reconstructed by means of angular or lateral displacement of the cavity.more » Preliminary tests confirmed a very low detection limit for elements laying in the high efficiency spectrum zone (from 5 to 10 keV), and a high angular resolution allowing an accurate localization of defects within the equator surface.« less

Effects of Nonequilibrium Chemistry and Darcy-Forchheimer Pyrolysis Flow for Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2013-01-01

The fully implicit ablation and thermal response code simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid.This work describes new modeling capabilities that are added to a special version of code. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Two groups of parametric studies of the phenolic impregnated carbon ablator are performed. In the first group, an Orion flight environment for a proposed lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results indicate that the presence of chemical nonequilibrium pyrolysis gas flow does not significantly alter the in-depth thermal response performance predicted using the chemical equilibrium gas model.

Implicit Coupling Approach for Simulation of Charring Carbon Ablators

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Gokcen, Tahir

2013-01-01

This study demonstrates that coupling of a material thermal response code and a flow solver with nonequilibrium gas/surface interaction for simulation of charring carbon ablators can be performed using an implicit approach. The material thermal response code used in this study is the three-dimensional version of Fully Implicit Ablation and Thermal response program, which predicts charring material thermal response and shape change on hypersonic space vehicles. The flow code solves the reacting Navier-Stokes equations using Data Parallel Line Relaxation method. Coupling between the material response and flow codes is performed by solving the surface mass balance in flow solver and the surface energy balance in material response code. Thus, the material surface recession is predicted in flow code, and the surface temperature and pyrolysis gas injection rate are computed in material response code. It is demonstrated that the time-lagged explicit approach is sufficient for simulations at low surface heating conditions, in which the surface ablation rate is not a strong function of the surface temperature. At elevated surface heating conditions, the implicit approach has to be taken, because the carbon ablation rate becomes a stiff function of the surface temperature, and thus the explicit approach appears to be inappropriate resulting in severe numerical oscillations of predicted surface temperature. Implicit coupling for simulation of arc-jet models is performed, and the predictions are compared with measured data. Implicit coupling for trajectory based simulation of Stardust fore-body heat shield is also conducted. The predicted stagnation point total recession is compared with that predicted using the chemical equilibrium surface assumption

New nonlinear evolution equations from surface theory

NASA Astrophysics Data System (ADS)

Gürses, Metin; Nutku, Yavuz

1981-07-01

We point out that the connection between surfaces in three-dimensional flat space and the inverse scattering problem provides a systematic way for constructing new nonlinear evolution equations. In particular we study the imbedding for Guichard surfaces which gives rise to the Calapso-Guichard equations generalizing the sine-Gordon (SG) equation. Further, we investigate the geometry of surfaces and their imbedding which results in the Korteweg-deVries (KdV) equation. Then by constructing a family of applicable surfaces we obtain a generalization of the KdV equation to a compressible fluid.

Utilization of a Response-Surface Technique in the Study of Plant Responses to Ozone and Sulfur Dioxide Mixtures 1

PubMed Central

Ormrod, Douglas P.; Tingey, David T.; Gumpertz, Marcia L.; Olszyk, David M.

1984-01-01

A second order rotatable design was used to obtain polynomial equations describing the effects of combinations of sulfur dioxide (SO2) and ozone (O3) on foliar injury and plant growth. The response surfaces derived from these equations were displayed as contour or isometric (3-dimensional) plots. The contour plots aided in the interpretation of the pollutant interactions and were judged easier to use than the isometric plots. Plants of `Grand Rapids' lettuce (Lactuca sativa L.), `Cherry Belle' radish (Raphanus sativus L.), and `Alsweet' pea (Pisum sativum L.) were grown in a controlled environment chamber and exposed to seven combinations of SO2 and O3. Injury was evaluated based on visible chlorosis and necrosis and growth was evaluated as leaf area and dry weight. Covariate measurements were used to increase precision. Radish and pea had greater injury, in general, that did lettuce; all three species were sensitive to O3, and pea was most sensitive and radish least sensitive to SO2. Leaf injury responses were relatively more affected by the pollutants than were plant growth responses in radish and pea but not in lettuce. In radish, hypocotyl growth was more sensitive to the pollutants than was leaf growth. PMID:16663598

Utilization of a response-surface technique in the study of plant responses to ozone and sulfur dioxide mixtures.

PubMed

Ormrod, D P; Tingey, D T; Gumpertz, M L; Olszyk, D M

1984-05-01

A second order rotatable design was used to obtain polynomial equations describing the effects of combinations of sulfur dioxide (SO(2)) and ozone (O(3)) on foliar injury and plant growth. The response surfaces derived from these equations were displayed as contour or isometric (3-dimensional) plots. The contour plots aided in the interpretation of the pollutant interactions and were judged easier to use than the isometric plots. Plants of ;Grand Rapids' lettuce (Lactuca sativa L.), ;Cherry Belle' radish (Raphanus sativus L.), and ;Alsweet' pea (Pisum sativum L.) were grown in a controlled environment chamber and exposed to seven combinations of SO(2) and O(3). Injury was evaluated based on visible chlorosis and necrosis and growth was evaluated as leaf area and dry weight. Covariate measurements were used to increase precision. Radish and pea had greater injury, in general, that did lettuce; all three species were sensitive to O(3), and pea was most sensitive and radish least sensitive to SO(2). Leaf injury responses were relatively more affected by the pollutants than were plant growth responses in radish and pea but not in lettuce. In radish, hypocotyl growth was more sensitive to the pollutants than was leaf growth.

Comparison of polynomial approximations and artificial neural nets for response surfaces in engineering optimization

NASA Technical Reports Server (NTRS)

Carpenter, William C.

1991-01-01

Engineering optimization problems involve minimizing some function subject to constraints. In areas such as aircraft optimization, the constraint equations may be from numerous disciplines such as transfer of information between these disciplines and the optimization algorithm. They are also suited to problems which may require numerous re-optimizations such as in multi-objective function optimization or to problems where the design space contains numerous local minima, thus requiring repeated optimizations from different initial designs. Their use has been limited, however, by the fact that development of response surfaces randomly selected or preselected points in the design space. Thus, they have been thought to be inefficient compared to algorithms to the optimum solution. A development has taken place in the last several years which may effect the desirability of using response surfaces. It may be possible that artificial neural nets are more efficient in developing response surfaces than polynomial approximations which have been used in the past. This development is the concern of the work.

Advanced control concepts. [trim solution for space shuttle

NASA Technical Reports Server (NTRS)

Hutton, M. F.; Friedland, B.

1973-01-01

The selection of a trim solution that provides the space shuttle with the highest level of performance and dynamic control in the presense of wind disturbances and bias torques due to misalignment of rocket engines is described. It was determined that engine gimballing is insufficient to provide control to trim the vehicle for headwind and sidewind disturbances, and that it is necessary to use aerodynamic surfaces in conjunction with engine gimballing to achieve trim. The algebraic equations for computing the trim solution were derived from the differential equations describing the motion of the vehicle by substituting the desired trim conditions. The general problem of showing how the trim equations are derived from the equations of motion and the mathematical forms of the performance criterion is discussed in detail, along with the general equations for studying the dynamic response of the trim solution.

Response to "No Evidence for Iris"

NASA Technical Reports Server (NTRS)

Chou, Ming-Dah; Lindzen, Richard S.; Hou, Arthur Y.; Lau, William K. M. (Technical Monitor)

2001-01-01

Hartmann and Michelsen claimed that there was no evidence for the negative relation between the high-level clouds and the sea surface temperature as suggested by Lindzen et al. The assertion made by Hartmann and Michelsen that there is a need for clouds thousands of kilometers away from the equator to be connected to convection at the equator does not seem to have any validity. Nor does their suggestion that the causes of the observational relations shown in Lindzen et al. do not involve detrainment.

Analysis of control system responses for aircraft stability and efficient numerical techniques for real-time simulations

NASA Astrophysics Data System (ADS)

Stroe, Gabriela; Andrei, Irina-Carmen; Frunzulica, Florin

2017-01-01

The objectives of this paper are the study and the implementation of both aerodynamic and propulsion models, as linear interpolations using look-up tables in a database. The aerodynamic and propulsion dependencies on state and control variable have been described by analytic polynomial models. Some simplifying hypotheses were made in the development of the nonlinear aircraft simulations. The choice of a certain technique to use depends on the desired accuracy of the solution and the computational effort to be expended. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. The engine power dynamic response was modeled with an additional state equation as first order lag in the actual power level response to commanded power level was computed as a function of throttle position. The number of control inputs and engine power states varied depending on the number of control surfaces and aircraft engines. The set of coupled, nonlinear, first-order ordinary differential equations that comprise the simulation model can be represented by the vector differential equation. A linear time-invariant (LTI) system representing aircraft dynamics for small perturbations about a reference trim condition is given by the state and output equations present. The gradients are obtained numerically by perturbing each state and control input independently and recording the changes in the trimmed state and output equations. This is done using the numerical technique of central finite differences, including the perturbations of the state and control variables. For a reference trim condition of straight and level flight, linearization results in two decoupled sets of linear, constant-coefficient differential equations for longitudinal and lateral / directional motion. The linearization is valid for small perturbations about the reference trim condition. Experimental aerodynamic and thrust data are used to model the applied aerodynamic and propulsion forces and moments for arbitrary states and controls. There is no closed form solution to such problems, so the equations must be solved using numerical integration. Techniques for solving this initial value problem for ordinary differential equations are employed to obtain approximate solutions at discrete points along the aircraft state trajectory.

Roughness topographical effects on mean momentum and stress budgets in developed turbulent channel flows

NASA Astrophysics Data System (ADS)

Aghaei Jouybari, Mostafa; Yuan, Junlin

2017-11-01

Direct numerical simulations of turbulent channel flows are carried out over two surfaces: a synthesized sand-grain surface and a realistic turbine roughness that is characterized by more prominent large-scale surface features. To separate the effects of wall-normal variation of the roughness area fraction from the (true) variation of flow statistics, the governing equations are area-averaged using intrinsic averaging, contrary to the usually practice based on the total area (i.e., superficial averaging). Additional terms appear in the mean-momentum equation resulted from the wall-normal variation of the solid fraction and play a role in the near-wall balance. Results from surfaces with a step solidity function (e.g., cubes) will also be discussed. Compared to the sand grains, the turbine surface generates stronger form-induced fluctuations, despite weaker dispersive shear stress. This is associated with more significant form-induced productions (comparable to shear production) in Reynolds stress budgets, weaker pressure work, and, consequently, more anisotropic redistribution of turbulent kinetic energy in the roughness sublayer, which potentially leads to different turbulent responses between the two surfaces in non-equilibrium flows.

General eigenstates of Maxwell's equations in a two-constituent composite medium

NASA Astrophysics Data System (ADS)

Bergman, David J.; Farhi, Asaf

2016-11-01

Eigenstates of Maxwell's equations in the quasistatic regime were used recently to calculate the response of a Veselago Lens1 to the field produced by a time dependent point electric charge.2, 3 More recently, this approach was extended to calculate the non-quasistatic response of such a lens. This necessitated a calculation of the eigenstates of the full Maxwell equations in a flat slab structure where the electric permittivity ɛ1 of the slab differs from the electric permittivity ɛ2 of its surroundings while the magnetic permeability is equal to 1 everywhere.4 These eigenstates were used to calculate the response of a Veselago Lens to an oscillating point electric dipole source of electromagnetic (EM) waves. A result of these calculations was that, although images with subwavelength resolution are achievable, as first predicted by John Pendry,5 those images appear not at the points predicted by geometric optics. They appear, instead, at points which lie upon the slab surfaces. This is strongly connected to the fact that when ɛ1/ɛ2 = -1 a strong singularity occurs in Maxwell's equations: This value of ɛ1/ɛ2 is a mathemetical accumulation point for the EM eigenvalues.6 Unfortunately, many physicists are unaware of this crucial mathematical property of Maxwell's equations. In this article we describe how the non-quasistatic eigenstates of Maxwell's equations in a composite microstructure can be calculated for general two-constituent microstructures, where both ɛ and μ have different values in the two constituents.

[Optimization for supercritical CO2 extraction with response surface methodology and component analysis of Sapindus mukorossi oil].

PubMed

Wu, Yan; Xiao, Xin-yu; Ge, Fa-huan

2012-02-01

To study the extraction conditions of Sapindus mukorossi oil by Supercritical CO2 Extraction and identify its components. Optimized SFE-CO2 Extraction by response surface methodology and used GC-MS to analysie Sapindus mukorossi oil compounds. Established the model of an equation for the extraction rate of Sapindus mukorossi oil by Supercritical CO2 Extraction, and the optimal parameters for the Supercritical CO2 Extraction determined by the equation were: the extraction pressure was 30 MPa, temperature was 40 degrees C; The separation I pressure was 14 MPa, temperature was 45 degrees C; The separation II pressure was 6 MPa, temperature was 40 degrees C; The extraction time was 60 min and the extraction rate of Sapindus mukorossi oil of 17.58%. 22 main compounds of Sapindus mukorossi oil extracted by supercritical CO2 were identified by GC-MS, unsaturated fatty acids were 86.59%. This process is reliable, safe and with simple operation, and can be used for the extraction of Sapindus mukorossi oil.

An experimental and computational investigation of the flow field about a transonic airfoil in supercritical flow with turbulent boundary-layer separation

NASA Technical Reports Server (NTRS)

Rubesin, M. W.; Okuno, A. F.; Levy, L. L., Jr.; Mcdevitt, J. B.; Seegmiller, H. L.

1976-01-01

A combined experimental and computational research program is described for testing and guiding turbulence modeling within regions of separation induced by shock waves incident in turbulent boundary layers. Specifically, studies are made of the separated flow the rear portion of an 18%-thick circular-arc airfoil at zero angle of attack in high Reynolds number supercritical flow. The measurements include distributions of surface static pressure and local skin friction. The instruments employed include highfrequency response pressure cells and a large array of surface hot-wire skin-friction gages. Computations at the experimental flow conditions are made using time-dependent solutions of ensemble-averaged Navier-Stokes equations, plus additional equations for the turbulence modeling.

Modeling the Benchmark Active Control Technology Wind-Tunnel Model for Application to Flutter Suppression

NASA Technical Reports Server (NTRS)

Waszak, Martin R.

1996-01-01

This paper describes the formulation of a model of the dynamic behavior of the Benchmark Active Controls Technology (BACT) wind-tunnel model for application to design and analysis of flutter suppression controllers. The model is formed by combining the equations of motion for the BACT wind-tunnel model with actuator models and a model of wind-tunnel turbulence. The primary focus of this paper is the development of the equations of motion from first principles using Lagrange's equations and the principle of virtual work. A numerical form of the model is generated using values for parameters obtained from both experiment and analysis. A unique aspect of the BACT wind-tunnel model is that it has upper- and lower-surface spoilers for active control. Comparisons with experimental frequency responses and other data show excellent agreement and suggest that simple coefficient-based aerodynamics are sufficient to accurately characterize the aeroelastic response of the BACT wind-tunnel model. The equations of motion developed herein have been used to assist the design and analysis of a number of flutter suppression controllers that have been successfully implemented.

Assessing the Combined Antibacterial Effect of Isoniazid and Rifampin on Four Mycobacterium tuberculosis Strains Using In Vitro Experiments and Response-Surface Modeling

PubMed Central

2017-01-01

ABSTRACT While isoniazid and rifampin have been the cornerstone of tuberculosis therapy caused by drug-susceptible Mycobacterium tuberculosis for more than 40 years, their combined action has never been thoroughly assessed by modern quantitative pharmacology approaches. The aims of this work were to perform in vitro experiments and mathematical modeling of the antibacterial effect of isoniazid and rifampin alone and in combination against various strains of Mycobacterium tuberculosis. After MIC determination of H37Rv and three strains belonging to the Beijing, Euro-American, and Indo-Oceanic lineages, the antibacterial effects of isoniazid and rifampin alone and in combination were studied in static time-kill experiments. A sigmoidal maximum effect model (Hill equation) and a response-surface model were used to describe the effect of the drugs alone and in combination, respectively. The killing effect of isoniazid and rifampin alone were well described by the Hill equation. Rifampin displayed a more concentration-dependent effect than isoniazid around the MIC. The pharmacodynamics parameters of each drug (maximal effect, median effect concentration, and coefficient of sigmoidicity) were quite similar between the four strains. The response-surface model from Minto et al. fit data of combined effect very well with low bias and imprecision (C. F. Minto, T. W. Schnider, T. G. Short, K. M. Gregg, A. Gentilini, Anesthesiology 92:1603–1616, 2000, https://doi.org/10.1097/00000542-200006000-00017). Response-surface modeling showed that the combined action of isoniazid and rifampin was synergistic for the H37Rv, Beijing, and Euro-American strains but only additive for the Indo-Oceanic strain. This study can serve as a motivating example for preclinical evaluation of combined action of antituberculous drugs. PMID:29061753

Determining animal drug combinations based on efficacy and safety.

PubMed

Kratzer, D D; Geng, S

1986-08-01

A procedure for deriving drug combinations for animal health is used to derive an optimal combination of 200 mg of novobiocin and 650,000 IU of penicillin for nonlactating cow mastitis treatment. The procedure starts with an estimated second order polynomial response surface equation. That surface is translated into a probability surface with contours called isoprobs. The isoprobs show drug amounts that have equal probability to produce maximal efficacy. Safety factors are incorporated into the probability surface via a noncentrality parameter that causes the isoprobs to expand as safety decreases, resulting in lower amounts of drug being used.

A method for the analysis of nonlinearities in aircraft dynamic response to atmospheric turbulence

NASA Technical Reports Server (NTRS)

Sidwell, K.

1976-01-01

An analytical method is developed which combines the equivalent linearization technique for the analysis of the response of nonlinear dynamic systems with the amplitude modulated random process (Press model) for atmospheric turbulence. The method is initially applied to a bilinear spring system. The analysis of the response shows good agreement with exact results obtained by the Fokker-Planck equation. The method is then applied to an example of control-surface displacement limiting in an aircraft with a pitch-hold autopilot.

Effects of surface roughness, MHD and couple stress on squeeze film characteristics between curved circular plates

NASA Astrophysics Data System (ADS)

Hanumagowda, B. N.; Salma, A.; Nagarajappa, C. S.

2018-04-01

The theoretical discussion is carried out for understanding the combined study of MHD, rough surface and couple-stress in the presence of applied magnetic field between two curved circular plates is present analysis. Modified Reynolds Equations accounting for rough surface using stochastic model of Christensen are mathematically formulated. The close form derivations for pressure, load-supporting capacity and response-film time are obtained. Our results shows that, there is an significant increase (decrease) for pressure, load-supporting capacity and squeeze film time due to the effect of azimuthal (radial) roughness parameter when compared to the Hanumagowda.et.al [14] and numerical data of load supporting capacity and response time are given in Table for engineering applications.

Effects of Non-Equilibrium Chemistry and Darcy-Forchheimer Flow of Pyrolysis Gas for a Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2011-01-01

The Fully Implicit Ablation and Thermal Response code, FIAT, simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid. This work describes new modeling capabilities that are added to a special version of FIAT. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite-rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Parametric studies are performed using this enhanced version of FIAT. Two groups of analyses of Phenolic Impregnated Carbon Ablator (PICA) are presented. In the first group, an Orion flight environment for a proposed Lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on PICA material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results are presented, discussed, and compared with those predicted by the baseline PICA/FIAT ablation and thermal response model developed by the Orion Thermal Protection System Advanced Development Project.

Nonlinear optical response in narrow graphene nanoribbons

NASA Astrophysics Data System (ADS)

Karimi, Farhad; Knezevic, Irena

We present an iterative method to calculate the nonlinear optical response of armchair graphene nanoribbons (aGNRs) and zigzag graphene nanoribbons (zGNRs) while including the effects of dissipation. In contrast to methods that calculate the nonlinear response in the ballistic (dissipation-free) regime, here we obtain the nonlinear response of an electronic system to an external electromagnetic field while interacting with a dissipative environment (to second order). We use a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations, and we solve the master equation iteratively to obtain the higher-order response functions. We employ the SCF-MMEF to calculate the nonlinear conductance and susceptibility, as well as to calculate the dependence of the plasmon dispersion and plasmon propagation length on the intensity of the electromagnetic field in GNRs. The electron scattering mechanisms included in this work are scattering with intrinsic phonons, ionized impurities, surface optical phonons, and line-edge roughness. Unlike in wide GNRs, where ionized-impurity scattering dominates dissipation, in ultra-narrow nanoribbons on polar substrates optical-phonon scattering and ionized-impurity scattering are equally prominent. Support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0008712.

Response surface methodology modeling to improve degradation of Chlorpyrifos in agriculture runoff using TiO2 solar photocatalytic in a raceway pond reactor.

PubMed

Amiri, Hoda; Nabizadeh, Ramin; Silva Martinez, Susana; Jamaleddin Shahtaheri, Seyed; Yaghmaeian, Kamyar; Badiei, Alireza; Nazmara, Shahrokh; Naddafi, Kazem

2018-01-01

This paper deals with the use of a raceway pond reactor (RPR) as an alternative photoreactor for solar photocatalytic applications. Raceway pond reactors are common low-cost reactors which can treat large volumes of water. The experiments were carried out with TiO 2 in the agriculture effluent spiked with Chlorpyrifos (CPF) at circumneutral pH. The Response Surface Methodology (RSM) was used to find the optimum process parameters to maximize CPF oxidation from the mathematical model equations developed in this study using R software. By ANOVA, p-value of lack of fit > 0.05 indicated that, the equation was well-fitted. The theoretical efficiency of CPF removal, under the optimum oxidation conditions with UV solar energy of around 697 ± 5.33 lux, was 84.01%, which is in close agreement with the mean experimental value (80 ± 1.42%) confirming that the response model was suitable for the optimization. As far as the authors know, this is the first study of CPF removal using RPR in agriculture runoff at circumneutral pH. Copyright © 2017. Published by Elsevier Inc.

Magnetohydrodynamic simulation study of plasma jets and plasma-surface contact in coaxial plasma accelerators

DOE PAGES

Subramaniam, Vivek; Raja, Laxminarayan L.

2017-06-13

Recent experiments by Loebner et al. [IEEE Trans. Plasma Sci. 44, 1534 (2016)] studied the effect of a hypervelocity jet emanating from a coaxial plasma accelerator incident on target surfaces in an effort to mimic the transient loading created during edge localized mode disruption events in fusion plasmas. In this study, we present a magnetohydrodynamic (MHD) numerical model to simulate plasma jet formation and plasma-surface contact in this coaxial plasma accelerator experiment. The MHD system of equations is spatially discretized using a cell-centered finite volume formulation. The temporal discretization is performed using a fully implicit backward Euler scheme and themore » resultant stiff system of nonlinear equations is solved using the Newton method. The numerical model is employed to obtain some key insights into the physical processes responsible for the generation of extreme stagnation conditions on the target surfaces. Simulations of the plume (without the target plate) are performed to isolate and study phenomena such as the magnetic pinch effect that is responsible for launching pressure pulses into the jet free stream. The simulations also yield insights into the incipient conditions responsible for producing the pinch, such as the formation of conductive channels. The jet-target impact studies indicate the existence of two distinct stages involved in the plasma-surface interaction. A fast transient stage characterized by a thin normal shock transitions into a pseudo-steady stage that exhibits an extended oblique shock structure. A quadratic scaling of the pinch and stagnation conditions with the total current discharged between the electrodes is in qualitative agreement with the results obtained in the experiments. Finally, this also illustrates the dominant contribution of the magnetic pressure term in determining the magnitude of the quantities of interest.« less

Magnetohydrodynamic simulation study of plasma jets and plasma-surface contact in coaxial plasma accelerators

NASA Astrophysics Data System (ADS)

Subramaniam, Vivek; Raja, Laxminarayan L.

2017-06-01

Recent experiments by Loebner et al. [IEEE Trans. Plasma Sci. 44, 1534 (2016)] studied the effect of a hypervelocity jet emanating from a coaxial plasma accelerator incident on target surfaces in an effort to mimic the transient loading created during edge localized mode disruption events in fusion plasmas. In this paper, we present a magnetohydrodynamic (MHD) numerical model to simulate plasma jet formation and plasma-surface contact in this coaxial plasma accelerator experiment. The MHD system of equations is spatially discretized using a cell-centered finite volume formulation. The temporal discretization is performed using a fully implicit backward Euler scheme and the resultant stiff system of nonlinear equations is solved using the Newton method. The numerical model is employed to obtain some key insights into the physical processes responsible for the generation of extreme stagnation conditions on the target surfaces. Simulations of the plume (without the target plate) are performed to isolate and study phenomena such as the magnetic pinch effect that is responsible for launching pressure pulses into the jet free stream. The simulations also yield insights into the incipient conditions responsible for producing the pinch, such as the formation of conductive channels. The jet-target impact studies indicate the existence of two distinct stages involved in the plasma-surface interaction. A fast transient stage characterized by a thin normal shock transitions into a pseudo-steady stage that exhibits an extended oblique shock structure. A quadratic scaling of the pinch and stagnation conditions with the total current discharged between the electrodes is in qualitative agreement with the results obtained in the experiments. This also illustrates the dominant contribution of the magnetic pressure term in determining the magnitude of the quantities of interest.

Magnetohydrodynamic simulation study of plasma jets and plasma-surface contact in coaxial plasma accelerators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Subramaniam, Vivek; Raja, Laxminarayan L.

Recent experiments by Loebner et al. [IEEE Trans. Plasma Sci. 44, 1534 (2016)] studied the effect of a hypervelocity jet emanating from a coaxial plasma accelerator incident on target surfaces in an effort to mimic the transient loading created during edge localized mode disruption events in fusion plasmas. In this study, we present a magnetohydrodynamic (MHD) numerical model to simulate plasma jet formation and plasma-surface contact in this coaxial plasma accelerator experiment. The MHD system of equations is spatially discretized using a cell-centered finite volume formulation. The temporal discretization is performed using a fully implicit backward Euler scheme and themore » resultant stiff system of nonlinear equations is solved using the Newton method. The numerical model is employed to obtain some key insights into the physical processes responsible for the generation of extreme stagnation conditions on the target surfaces. Simulations of the plume (without the target plate) are performed to isolate and study phenomena such as the magnetic pinch effect that is responsible for launching pressure pulses into the jet free stream. The simulations also yield insights into the incipient conditions responsible for producing the pinch, such as the formation of conductive channels. The jet-target impact studies indicate the existence of two distinct stages involved in the plasma-surface interaction. A fast transient stage characterized by a thin normal shock transitions into a pseudo-steady stage that exhibits an extended oblique shock structure. A quadratic scaling of the pinch and stagnation conditions with the total current discharged between the electrodes is in qualitative agreement with the results obtained in the experiments. Finally, this also illustrates the dominant contribution of the magnetic pressure term in determining the magnitude of the quantities of interest.« less

The differential equation of an arbitrary reflecting surface

NASA Astrophysics Data System (ADS)

Melka, Richard F.; Berrettini, Vincent D.; Yousif, Hashim A.

2018-05-01

A differential equation describing the reflection of a light ray incident upon an arbitrary reflecting surface is obtained using the law of reflection. The derived equation is written in terms of a parameter and the value of this parameter determines the nature of the reflecting surface. Under various parametric constraints, the solution of the differential equation leads to the various conic surfaces but is not generally solvable. In addition, the dynamics of the light reflections from the conic surfaces are executed in the Mathematica software. Our derivation is the converse of the traditional approach and our analysis assumes a relation between the object distance and the image distance. This leads to the differential equation of the reflecting surface.

[Optimization of one-step pelletization technology of Biqiu granules by Plackett-Burman design and Box-Behnken response surface methodology].

PubMed

Zhang, Yan-jun; Liu, Li-li; Hu, Jun-hua; Wu, Yun; Chao, En-xiang; Xiao, Wei

2015-11-01

First with the qualified rate of granules as the evaluation index, significant influencing factors were firstly screened by Plackett-Burman design. Then, with the qualified rate and moisture content as the evaluation indexes, significant factors that affect one-step pelletization technology were further optimized by Box-Behnken design; experimental data were imitated by multiple regression and second-order polynomial equation; and response surface method was used for predictive analysis of optimal technology. The best conditions were as follows: inlet air temperature of 85 degrees C, sample introduction speed of 33 r x min(-1), density of concrete 1. 10. One-step pelletization technology of Biqiu granules by Plackett-Burman design and Box-Behnken response surface methodology was stable and feasible with good predictability, which provided reliable basis for the industrialized production of Biqiu granules.

Application of response surface methodology to optimise supercritical carbon dioxide extraction of essential oil from Cyperus rotundus Linn.

PubMed

Wang, Hongwu; Liu, Yanqing; Wei, Shoulian; Yan, Zijun

2012-05-01

Supercritical fluid extraction with carbon dioxide (SC-CO2 extraction) was performed to isolate essential oils from the rhizomes of Cyperus rotundus Linn. Effects of temperature, pressure, extraction time, and CO2 flow rate on the yield of essential oils were investigated by response surface methodology (RSM). The oil yield was represented by a second-order polynomial model using central composite rotatable design (CCRD). The oil yield increased significantly with pressure (p<0.0001) and CO2 flow rate (p<0.01). The maximum oil yield from the response surface equation was predicted to be 1.82% using an extraction temperature of 37.6°C, pressure of 294.4bar, extraction time of 119.8 min, and CO2 flow rate of 20.9L/h. Copyright © 2011 Elsevier Ltd. All rights reserved.

RF tumour ablation: computer simulation and mathematical modelling of the effects of electrical and thermal conductivity.

PubMed

Lobo, S M; Liu, Z-J; Yu, N C; Humphries, S; Ahmed, M; Cosman, E R; Lenkinski, R E; Goldberg, W; Goldberg, S N

2005-05-01

This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07-12 S m-1) and 'tumour' radius (5-30 mm) at a given background electrical conductivity (0.12 S m-1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3-2 W m-1 degrees C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n=425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T=a+bRc exp(dR) s(f) exp(g)(s)) for RF generator-energy dependent situations and (T=h+k exp(mR)+n?exp(p)(s)) for RF generator-current limited situations, where T is the temperature (degrees C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97-0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2=0.96-0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result, the non-linear temperature response of RF induced heating can be adequately expressed mathematically as a function of electrical conductivity, radius and thermal conductivity. Hence, thermal conductivity accounts for some of the previously unexplained variance. Furthermore, the addition of this variable into the mathematical model substantially simplifies the equations and, as such, it is expected that this will permit improved prediction of RF ablation induced temperatures in clinical practice.

Non-uniform Erosion and Surface Evolution of Plasma-Facing Materials for Electric Propulsion

NASA Astrophysics Data System (ADS)

Matthes, Christopher Stanley Rutter

A study regarding the surface evolution of plasma-facing materials is presented. Experimental efforts were performed in the UCLA Pi Facility, designed to explore the physics of plasma-surface interactions. The influence of micro-architectured surfaces on the effects of plasma sputtering is compared with the response of planar samples. Ballistic deposition of sputtered atoms as a result of geometric re-trapping is observed. This provides a self-healing mechanism of micro-architectured surfaces during plasma exposure. This result is quantified using a QCM to demonstrate the evolution of surface features and the corresponding influence on the instantaneous sputtering yield. The sputtering yield of textured molybdenum samples exposed to 300 eV Ar plasma is found to be roughly 1 of the 2 corresponding value of flat samples, and increases with ion fluence. Mo samples exhibited a sputtering yield initially as low as 0.22+/-8%, converging to 0.4+/-8% at high fluence. Although the yield is dependent on the initial surface structure, it is shown to be transient, reaching a steady-state value that is independent of initial surface conditions. A continuum model of surface evolution resulting from sputtering, deposition and surface diffusion is also derived to resemble the damped Kuramoto-Sivashinsky (KS) equation of non-linear dynamics. Linear stability analysis of the evolution equation provides an estimate of the selected wavelength, and its dependence on the ion energy and angle of incidence. The analytical results are confirmed by numerical simulations of the equation with a Fast Fourier Transform method. It is shown that for an initially flat surface, small perturbations lead to the evolution of a selected surface pattern that has nano- scale wavelength. When the surface is initially patterned by other means, the final resulting pattern is a competition between the "templated" pattern and the "self-organized" structure. Potential future routes of research are also discussed, corresponding to a design analysis of the current experimental study.

Structural vibration-based damage classification of delaminated smart composite laminates

NASA Astrophysics Data System (ADS)

Khan, Asif; Kim, Heung Soo; Sohn, Jung Woo

2018-03-01

Separation along the interfaces of layers (delamination) is a principal mode of failure in laminated composites and its detection is of prime importance for structural integrity of composite materials. In this work, structural vibration response is employed to detect and classify delaminations in piezo-bonded laminated composites. Improved layerwise theory and finite element method are adopted to develop the electromechanically coupled governing equation of a smart composite laminate with and without delaminations. Transient responses of the healthy and damaged structures are obtained through a surface bonded piezoelectric sensor by solving the governing equation in the time domain. Wavelet packet transform (WPT) and linear discriminant analysis (LDA) are employed to extract discriminative features from the structural vibration response of the healthy and delaminated structures. Dendrogram-based support vector machine (DSVM) is used to classify the discriminative features. The confusion matrix of the classification algorithm provided physically consistent results.

Evaluation of Finite-Rate Gas/Surface Interaction Models for a Carbon Based Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Goekcen, Tahir

2015-01-01

Two sets of finite-rate gas-surface interaction model between air and the carbon surface are studied. The first set is an engineering model with one-way chemical reactions, and the second set is a more detailed model with two-way chemical reactions. These two proposed models intend to cover the carbon surface ablation conditions including the low temperature rate-controlled oxidation, the mid-temperature diffusion-controlled oxidation, and the high temperature sublimation. The prediction of carbon surface recession is achieved by coupling a material thermal response code and a Navier-Stokes flow code. The material thermal response code used in this study is the Two-dimensional Implicit Thermal-response and Ablation Program, which predicts charring material thermal response and shape change on hypersonic space vehicles. The flow code solves the reacting full Navier-Stokes equations using Data Parallel Line Relaxation method. Recession analyses of stagnation tests conducted in NASA Ames Research Center arc-jet facilities with heat fluxes ranging from 45 to 1100 wcm2 are performed and compared with data for model validation. The ablating material used in these arc-jet tests is Phenolic Impregnated Carbon Ablator. Additionally, computational predictions of surface recession and shape change are in good agreement with measurement for arc-jet conditions of Small Probe Reentry Investigation for Thermal Protection System Engineering.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David M.

1999-01-01

The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are derived. These equations are then modified to allow the plate reference surface to be located a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described. The terms of the plate stiffness matrix using both classical plate theory (CPT) and first-order shear-deformation plate theory (SDPT) are presented. The effects of in-plane transverse and in-plane shear loads are included in the in-plane stability equations. Numerical results for several example problems with different loading states are presented. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPT are made. The computational effort required by the new analysis is compared to that of the analysis currently in the VICONOPT program. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.

Machinability Study on Milling Kenaf Fiber Reinforced Plastic Composite Materials using Design of Experiments

NASA Astrophysics Data System (ADS)

Azmi, H.; Haron, C. H. C.; Ghani, J. A.; Suhaily, M.; Yuzairi, A. R.

2018-04-01

The surface roughness (Ra) and delamination factor (Fd) of a milled kenaf reinforced plastic composite materials are depending on the milling parameters (spindle speed, feed rate and depth of cut). Therefore, a study was carried out to investigate the relationship between the milling parameters and their effects on a kenaf reinforced plastic composite materials. The composite panels were fabricated using vacuum assisted resin transfer moulding (VARTM) method. A full factorial design of experiments was use as an initial step to screen the significance of the parameters on the defects using Analysis of Variance (ANOVA). If the curvature of the collected data shows significant, Response Surface Methodology (RSM) is then applied for obtaining a quadratic modelling equation that has more reliable in expressing the optimization. Thus, the objective of this research is obtaining an optimum setting of milling parameters and modelling equations to minimize the surface roughness (Ra) and delamination factor (Fd) of milled kenaf reinforced plastic composite materials. The spindle speed and feed rate contributed the most in affecting the surface roughness and the delamination factor of the kenaf composite materials.

Soil temperature investigations using satellite acquired thermal-infrared data in semi-arid regions. Thesis. Final Report; [Utah

NASA Technical Reports Server (NTRS)

Day, R. L.; Petersen, G. W.

1983-01-01

Thermal-infrared data from the Heat Capacity Mapping Mission satellite were used to map the spatial distribution of diurnal surface temperatures and to estimate mean annual soil temperatures (MAST) and annual surface temperature amplitudes (AMP) in semi-arid east central Utah. Diurnal data with minimal snow and cloud cover were selected for five dates throughout a yearly period and geometrically co-registered. Rubber-sheet stretching was aided by the WARP program which allowed preview of image transformations. Daytime maximum and nighttime minimum temperatures were averaged to generation average daily temperature (ADT) data set for each of the five dates. Five ADT values for each pixel were used to fit a sine curve describing the theoretical annual surface temperature response as defined by a solution of a one-dimensinal heat flow equation. Linearization of the equation produced estimates of MAST and AMP plus associated confidence statistics. MAST values were grouped into classes and displayed on a color video screen. Diurnal surface temperatures and MAST were primarily correlated with elevation.

A contact mechanics model for ankle implants with inclusion of surface roughness effects

NASA Astrophysics Data System (ADS)

Hodaei, M.; Farhang, K.; Maani, N.

2014-02-01

Total ankle replacement is recognized as one of the best procedures to treat painful arthritic ankles. Even though this method can relieve patients from pain and reproduce the physiological functions of the ankle, an improper design can cause an excessive amount of metal debris due to wear, causing toxicity in implant recipient. This paper develops a contact model to treat the interaction of tibia and talus implants in an ankle joint. The contact model describes the interaction of implant rough surfaces including both elastic and plastic deformations. In the model, the tibia and the talus surfaces are viewed as macroscopically conforming cylinders or conforming multi-cylinders containing micrometre-scale roughness. The derived equations relate contact force on the implant and the minimum mean surface separation of the rough surfaces. The force is expressed as a statistical integral function of asperity heights over the possible region of interaction of the roughness of the tibia and the talus implant surfaces. A closed-form approximate equation relating contact force and minimum separation is used to obtain energy loss per cycle in a load-unload sequence applied to the implant. In this way implant surface statistics are related to energy loss in the implant that is responsible for internal void formation and subsequent wear and its harmful toxicity to the implant recipient.

Analyzing the vibrational response of an AFM cantilever in liquid with the consideration of tip mass by comparing the hydrodynamic and contact repulsive force models in higher modes

NASA Astrophysics Data System (ADS)

Korayem, Moharam Habibnejad; Nahavandi, Amir

2017-04-01

This paper investigates the vibration of a tapping-mode Atomic Force Microscope (AFM) cantilever covered with two whole piezoelectric layers in a liquid medium. The authors of this article have already modeled the vibration of a cantilever immersed in liquid over rough surfaces. Five new ideas have been considered for improving the results of the previous work. Mass and damping of a cantilever probe tip have been considered. Since the probe tip of an AFM cantilever has a mass, which can itself affect the natural frequency of vibration, the significance of this mass has been explored. Also, two hydrodynamic force models for analyzing the mass and damping added to a cantilever in liquid medium have been evaluated. In modeling the vibration of a cantilever in liquid, simplifications are made to the theoretical equations used in the modeling, which may make the obtained results different from those in the real case. So, two hydrodynamic force models are introduced and compared with each other. In addition to the already introduced DMT model, the JKR model has been proposed. The forces acting on a probe tip have attractive and repulsive effects. The attractive Van der Waals force can vary depending on the surface smoothness or roughness, and the repulsive contact force, which is independent of the type of surface roughness and usually varies with the hardness or softness of a surface. When the first mode is used in the vibration of an AFM cantilever, the changes of the existing physical parameters in the simulation do not usually produce a significant difference in the response. Thus, three cantilever vibration modes have been investigated. Finally, an analytical approach for obtaining the response of equations is presented which solves the resulting motion equation by the Laplace method and, thus, a time function is obtained for cantilever deflection is determined. Also, using the COMSOL software to model a cantilever in a liquid medium, the computed natural frequencies have been compared.

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

NASA Astrophysics Data System (ADS)

Huang, Rui; Hu, Haiyan; Zhao, Yonghui

2013-10-01

In this paper, the effects of structural nonlinearity due to free-play in both leading-edge and trailing-edge outboard control surfaces on the linear flutter control system are analyzed for an aeroelastic model of three-dimensional multiple-actuated-wing. The free-play nonlinearities in the control surfaces are modeled theoretically by using the fictitious mass approach. The nonlinear aeroelastic equations of the presented model can be divided into nine sub-linear modal-based aeroelastic equations according to the different combinations of deflections of the leading-edge and trailing-edge outboard control surfaces. The nonlinear aeroelastic responses can be computed based on these sub-linear aeroelastic systems. To demonstrate the effects of nonlinearity on the linear flutter control system, a single-input and single-output controller and a multi-input and multi-output controller are designed based on the unconstrained optimization techniques. The numerical results indicate that the free-play nonlinearity can lead to either limit cycle oscillations or divergent motions when the linear control system is implemented.

Response function of a moving contact line

NASA Astrophysics Data System (ADS)

Perrin, H.; Belardinelli, D.; Sbragaglia, M.; Andreotti, B.

2018-04-01

The hydrodynamics of a liquid-vapor interface in contact with a heterogeneous surface is largely impacted by the presence of defects at the smaller scales. Such defects introduce morphological disturbances on the contact line and ultimately determine the force exerted on the wedge of liquid in contact with the surface. From the mathematical point of view, defects introduce perturbation modes, whose space-time evolution is governed by the interfacial hydrodynamic equations of the contact line. In this paper we derive the response function of the contact line to such generic perturbations. The contact line response may be used to design simplified one-dimensional time-dependent models accounting for the complexity of interfacial flows coupled to nanoscale defects, yet offering a more tractable mathematical framework to explore contact line motion through a disordered energy landscape.

A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; Lee, Henry

2014-01-01

The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no indication in Ref. II that the gaps are explicitly modeled as in Ref. 6. Computations using overset grids are reported in Ref. 12 for a case by adding moving control surface to an existing blade but with no validation either with an experiment or another computation.

Transport of inertial anisotropic particles under surface gravity waves

NASA Astrophysics Data System (ADS)

Dibenedetto, Michelle; Koseff, Jeffrey; Ouellette, Nicholas

2016-11-01

The motion of neutrally and almost-neutrally buoyant particles under surface gravity waves is relevant to the transport of microplastic debris and other small particulates in the ocean. Consequently, a number of studies have looked at the transport of spherical particles or mobile plankton in these conditions. However, the effects of particle-shape anisotropy on the trajectories and behavior of irregularly shaped particles in this type of oscillatory flow are still relatively unknown. To better understand these issues, we created an idealized numerical model which simulates the three-dimensional behavior of anisotropic spheroids in flow described by Airy wave theory. The particle's response is calculated using a simplified Maxey-Riley equation coupled with Jeffery's equation for particle rotation. We show that the particle dynamics are strongly dependent on their initial conditions and shape, with some some additional dependence on Stokes number.

Global fields of soil moisture and land surface evapotranspiration derived from observed precipitation and surface air temperature

NASA Technical Reports Server (NTRS)

Mintz, Y.; Walker, G. K.

1993-01-01

The global fields of normal monthly soil moisture and land surface evapotranspiration are derived with a simple water budget model that has precipitation and potential evapotranspiration as inputs. The precipitation is observed and the potential evapotranspiration is derived from the observed surface air temperature with the empirical regression equation of Thornthwaite (1954). It is shown that at locations where the net surface radiation flux has been measured, the potential evapotranspiration given by the Thornthwaite equation is in good agreement with those obtained with the radiation-based formulations of Priestley and Taylor (1972), Penman (1948), and Budyko (1956-1974), and this provides the justification for the use of the Thornthwaite equation. After deriving the global fields of soil moisture and evapotranspiration, the assumption is made that the potential evapotranspiration given by the Thornthwaite equation and by the Priestley-Taylor equation will everywhere be about the same; the inverse of the Priestley-Taylor equation is used to obtain the normal monthly global fields of net surface radiation flux minus ground heat storage. This and the derived evapotranspiration are then used in the equation for energy conservation at the surface of the earth to obtain the global fields of normal monthly sensible heat flux from the land surface to the atmosphere.

Analytical description of concentration dependence of surface tension in multicomponent systems

NASA Astrophysics Data System (ADS)

R, Dadashev; R, Kutuev; D, Elimkhanov

2008-02-01

From the basic fundamental thermodynamic expressions the equation of isotherms of the surface tension of a ternary system is received. Various assumptions concerning the concentration dependence of molar areas are usually made when the equation is derived. The dependence of the molar areas is calculated as an additive function of the structure of a volumetric phase or the structure of a surface layer. To define the concentration dependence of the molar areas we used a stricter thermodynamic expression offered by Butler. In the received equation the dependence of molar areas on the structure of the solution is taken into account. Therefore, the equation can be applied for the calculation of surface tension over a wide concentration range of the components. Unlike the known expressions, the equation includes the surface tension properties of lateral binary systems, which makes the accuracy of the calculated values considerably higher. Thus, among the advantages of the offered equation we can point out the mathematical simplicity of the received equation and the fact that the equation includes physical parameters the experimental definition of which does not present any special difficulties.

Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

NASA Astrophysics Data System (ADS)

Zhao, Hai-Sheng; Zhang, Yao; Lie, Seng-Tjhen

2018-02-01

Considerations of nonlocal elasticity and surface effects in micro- and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions: hinged-hinged, clamped-clamped and clamped-hinged ends. For a hinged-hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped-clamped and clamped-hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short, explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.

Detection of macrophages in atherosclerotic tissue using magnetic nanoparticles and differential phase optical coherence tomography.

PubMed

Oh, Junghwan; Feldman, Marc D; Kim, Jihoon; Sanghi, Pramod; Do, Dat; Mancuso, J Jacob; Kemp, Nate; Cilingiroglu, Mehmet; Milner, Thomas E

2008-01-01

We demonstrate the detection of iron oxide nanoparticles taken up by macrophages in atherosclerotic plaque with differential phase optical coherence tomography (DP-OCT). Magneto mechanical detection of nanoparticles is demonstrated in hyperlipidemic Watanabe and balloon-injured fat-fed New Zealand white rabbits injected with monocrystalline iron oxide nanoparticles (MIONs) of < 40 nm diam. MIONs taken up by macrophages was excited by an oscillating magnetic flux density and resulting nanometer tissue surface displacement was detected by DP-OCT. Frequency response of tissue surface displacement in response to an externally applied magnetic flux density was twice the stimulus frequency as expected from the equations of motion for the nanoparticle cluster.

Barometric fluctuations in wells tapping deep unconfined aquifers

USGS Publications Warehouse

Weeks, Edwin P.

1979-01-01

Water levels in wells screened only below the water table in unconfined aquifers fluctuate in response to atmospheric pressure changes. These fluctuations occur because the materials composing the unsaturated zone resist air movement and have capacity to store air with a change in pressure. Consequently, the translation of any pressure change at land surface is slowed as it moves through the unsaturated zone to the water table, but it reaches the water surface in the well instantaneously. Thus a pressure imbalance is created that results in a water level fluctuation. Barometric effects on water levels in unconfined aquifers can be computed by solution of the differential equation governing the flow of gas in the unsaturated zone subject to the appropriate boundary conditions. Solutions to this equation for two sets of boundary conditions were applied to compute water level response in a well tapping the Ogallala Formation near Lubbock, Texas from simultaneous microbarograph records. One set of computations, based on the step function unit response solution and convolution, resulted in a very good match between computed and measured water levels. A second set of computations, based on analysis of the amplitude ratios of simultaneous cyclic microbarograph and water level fluctuations, gave inconsistent results in terms of the unsaturated zone pneumatic properties but provided useful insights on the nature of unconfined-aquifer water level fluctuations.

Reconstruction of vibroacoustic responses of a highly nonspherical structure using Helmholtz equation least-squares method.

PubMed

Lu, Huancai; Wu, Sean F

2009-03-01

The vibroacoustic responses of a highly nonspherical vibrating object are reconstructed using Helmholtz equation least-squares (HELS) method. The objectives of this study are to examine the accuracy of reconstruction and the impacts of various parameters involved in reconstruction using HELS. The test object is a simply supported and baffled thin plate. The reason for selecting this object is that it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are taken as the basis functions in the HELS formulation, yet the analytic solutions to vibroacoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked accurately. The input field acoustic pressures for reconstruction are generated by the Rayleigh integral. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply supported plate. The impacts of various parameters such as number of measurement points, measurement distance, location of the origin of the coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined.

Stable Algorithm For Estimating Airdata From Flush Surface Pressure Measurements

NASA Technical Reports Server (NTRS)

Whitmore, Stephen, A. (Inventor); Cobleigh, Brent R. (Inventor); Haering, Edward A., Jr. (Inventor)

2001-01-01

An airdata estimation and evaluation system and method, including a stable algorithm for estimating airdata from nonintrusive surface pressure measurements. The airdata estimation and evaluation system is preferably implemented in a flush airdata sensing (FADS) system. The system and method of the present invention take a flow model equation and transform it into a triples formulation equation. The triples formulation equation eliminates the pressure related states from the flow model equation by strategically taking the differences of three surface pressures, known as triples. This triples formulation equation is then used to accurately estimate and compute vital airdata from nonintrusive surface pressure measurements.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David M.; Anderson, Melvin S.

1998-01-01

The analytical formulation of curved-plate non-linear equilibrium equations that include transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Using several simplifying assumptions, linearized, stability equations are derived that describe the response of the plate just after bifurcation buckling occurs. These equations are then modified to allow the plate reference surface to be located a distance z(c), from the centroid surface which is convenient for modeling stiffened-plate assemblies. The implementation of the new theory into the VICONOPT buckling and vibration analysis and optimum design program code is described. Either classical plate theory (CPT) or first-order shear-deformation plate theory (SDPT) may be selected in VICONOPT. Comparisons of numerical results for several example problems with different loading states are made. Results from the new curved-plate analysis compare well with closed-form solution results and with results from known example problems in the literature. Finally, a design-optimization study of two different cylindrical shells subject to uniform axial compression is presented.

Experimental Design for a Sponge-Wipe Study to Relate the Recovery Efficiency and False Negative Rate to the Concentration of a Bacillus anthracis Surrogate for Six Surface Materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piepel, Gregory F.; Amidan, Brett G.; Krauter, Paula

2011-05-01

Two concerns were raised by the Government Accountability Office following the 2001 building contaminations via letters containing Bacillus anthracis (BA). These included the: 1) lack of validated sampling methods, and 2) need to use statistical sampling to quantify the confidence of no contamination when all samples have negative results. Critical to addressing these concerns is quantifying the false negative rate (FNR). The FNR may depend on the 1) method of contaminant deposition, 2) surface concentration of the contaminant, 3) surface material being sampled, 4) sample collection method, 5) sample storage/transportation conditions, 6) sample processing method, and 7) sample analytical method.more » A review of the literature found 17 laboratory studies that focused on swab, wipe, or vacuum samples collected from a variety of surface materials contaminated by BA or a surrogate, and used culture methods to determine the surface contaminant concentration. These studies quantified performance of the sampling and analysis methods in terms of recovery efficiency (RE) and not FNR (which left a major gap in available information). Quantifying the FNR under a variety of conditions is a key aspect of validating sample and analysis methods, and also for calculating the confidence in characterization or clearance decisions based on a statistical sampling plan. A laboratory study was planned to partially fill the gap in FNR results. This report documents the experimental design developed by Pacific Northwest National Laboratory and Sandia National Laboratories (SNL) for a sponge-wipe method. The testing was performed by SNL and is now completed. The study investigated the effects on key response variables from six surface materials contaminated with eight surface concentrations of a BA surrogate (Bacillus atrophaeus). The key response variables include measures of the contamination on test coupons of surface materials tested, contamination recovered from coupons by sponge-wipe samples, RE, and FNR. The experimental design involves 16 test runs, performed in two blocks of eight runs. Three surface materials (stainless steel, vinyl tile, and ceramic tile) were tested in the first block, while three other surface materials (plastic, painted wood paneling, and faux leather) were tested in the second block. The eight surface concentrations of the surrogate were randomly assigned to test runs within each block. Some of the concentrations were very low and presented challenges for deposition, sampling, and analysis. However, such tests are needed to investigate RE and FNR over the full range of concentrations of interest. In each run, there were 10 test coupons of each of the three surface materials. A positive control sample was generated at the same time as each test sample. The positive control results will be used to 1) calculate RE values for the wipe sampling and analysis method, and 2) fit RE- and FNR-concentration equations, for each of the six surface materials. Data analyses will support 1) estimating the FNR for each combination of contaminant concentration and surface material, 2) estimating the surface concentrations and their uncertainties of the contaminant for each combination of concentration and surface material, 3) estimating RE (%) and their uncertainties for each combination of contaminant concentration and surface material, 4) fitting FNR-concentration and RE-concentration equations for each of the six surface materials, 5) assessing goodness-of-fit of the equations, and 6) quantifying the uncertainty in FNR and RE predictions made with the fitted equations.« less

Experimental Design for a Sponge-Wipe Study to Relate the Recovery Efficiency and False Negative Rate to the Concentration of a Bacillus anthracis Surrogate for Six Surface Materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piepel, Gregory F.; Amidan, Brett G.; Krauter, Paula

2010-12-16

Two concerns were raised by the Government Accountability Office following the 2001 building contaminations via letters containing Bacillus anthracis (BA). These included the: 1) lack of validated sampling methods, and 2) need to use statistical sampling to quantify the confidence of no contamination when all samples have negative results. Critical to addressing these concerns is quantifying the probability of correct detection (PCD) (or equivalently the false negative rate FNR = 1 - PCD). The PCD/FNR may depend on the 1) method of contaminant deposition, 2) surface concentration of the contaminant, 3) surface material being sampled, 4) sample collection method, 5)more » sample storage/transportation conditions, 6) sample processing method, and 7) sample analytical method. A review of the literature found 17 laboratory studies that focused on swab, wipe, or vacuum samples collected from a variety of surface materials contaminated by BA or a surrogate, and used culture methods to determine the surface contaminant concentration. These studies quantified performance of the sampling and analysis methods in terms of recovery efficiency (RE) and not PCD/FNR (which left a major gap in available information). Quantifying the PCD/FNR under a variety of conditions is a key aspect of validating sample and analysis methods, and also for calculating the confidence in characterization or clearance decisions based on a statistical sampling plan. A laboratory study was planned to partially fill the gap in PCD/FNR results. This report documents the experimental design developed by Pacific Northwest National Laboratory and Sandia National Laboratories (SNL) for a sponge-wipe method. The study will investigate the effects on key response variables from six surface materials contaminated with eight surface concentrations of a BA surrogate (Bacillus atrophaeus). The key response variables include measures of the contamination on test coupons of surface materials tested, contamination recovered from coupons by sponge-wipe samples, RE, and PCD/FNR. The experimental design involves 16 test runs, to be performed in two blocks of eight runs. Three surface materials (stainless steel, vinyl tile, and ceramic tile) were tested in the first block, while three other surface materials (plastic, painted wood paneling, and faux leather) will be tested in the second block. The eight surface concentrations of the surrogate were randomly assigned to test runs within each block. Some of the concentrations will be very low and may present challenges for deposition, sampling, and analysis. However, such tests are needed to investigate RE and PCD/FNR over the full range of concentrations of interest. In each run, there will be 10 test coupons of each of the three surface materials. A positive control sample will be generated prior to each test sample. The positive control results will be used to 1) calculate RE values for the wipe sampling and analysis method, and 2) fit RE- and PCD-concentration equations, for each of the six surface materials. Data analyses will support 1) estimating the PCD for each combination of contaminant concentration and surface material, 2) estimating the surface concentrations and their uncertainties of the contaminant for each combination of concentration and surface material, 3) estimating RE (%) and their uncertainties for each combination of contaminant concentration and surface material, 4) fitting PCD-concentration and RE-concentration equations for each of the six surface materials, 5) assessing goodness-of-fit of the equations, and 6) quantifying the uncertainty in PCD and RE predictions made with the fitted equations.« less

Calculation of the flow field including boundary layer effects for supersonic mixed compression inlets at angles of attack

NASA Technical Reports Server (NTRS)

Vadyak, J.; Hoffman, J. D.

1982-01-01

The flow field in supersonic mixed compression aircraft inlets at angle of attack is calculated. A zonal modeling technique is employed to obtain the solution which divides the flow field into different computational regions. The computational regions consist of a supersonic core flow, boundary layer flows adjacent to both the forebody/centerbody and cowl contours, and flow in the shock wave boundary layer interaction regions. The zonal modeling analysis is described and some computational results are presented. The governing equations for the supersonic core flow form a hyperbolic system of partial differential equations. The equations for the characteristic surfaces and the compatibility equations applicable along these surfaces are derived. The characteristic surfaces are the stream surfaces, which are surfaces composed of streamlines, and the wave surfaces, which are surfaces tangent to a Mach conoid. The compatibility equations are expressed as directional derivatives along streamlines and bicharacteristics, which are the lines of tangency between a wave surface and a Mach conoid.

Diffraction efficiency calculations of polarization diffraction gratings with surface relief

NASA Astrophysics Data System (ADS)

Nazarova, D.; Sharlandjiev, P.; Berberova, N.; Blagoeva, B.; Stoykova, E.; Nedelchev, L.

2018-03-01

In this paper, we evaluate the optical response of a stack of two diffraction gratings of equal one-dimensional periodicity. The first one is a surface-relief grating structure; the second, a volume polarization grating. This model is based on our experimental results from polarization holographic recordings in azopolymer films. We used films of commercially available azopolymer (poly[1-[4-(3-carboxy-4-hydroxyphenylazo) benzenesulfonamido]-1,2-ethanediyl, sodium salt]), shortly denoted as PAZO. During the recording process, a polarization grating in the volume of the material and a relief grating on the film surface are formed simultaneously. In order to evaluate numerically the optical response of this “hybrid” diffraction structure, we used the rigorous coupled-wave approach (RCWA). It yields stable numerical solutions of Maxwell’s vector equations using the algebraic eigenvalue method.

Sensitivity analysis of eigenvalues for an electro-hydraulic servomechanism

NASA Astrophysics Data System (ADS)

Stoia-Djeska, M.; Safta, C. A.; Halanay, A.; Petrescu, C.

2012-11-01

Electro-hydraulic servomechanisms (EHSM) are important components of flight control systems and their role is to control the movement of the flying control surfaces in response to the movement of the cockpit controls. As flight-control systems, the EHSMs have a fast dynamic response, a high power to inertia ratio and high control accuracy. The paper is devoted to the study of the sensitivity for an electro-hydraulic servomechanism used for an aircraft aileron action. The mathematical model of the EHSM used in this paper includes a large number of parameters whose actual values may vary within some ranges of uncertainty. It consists in a nonlinear ordinary differential equation system composed by the mass and energy conservation equations, the actuator movement equations and the controller equation. In this work the focus is on the sensitivities of the eigenvalues of the linearized homogeneous system, which are the partial derivatives of the eigenvalues of the state-space system with respect the parameters. These are obtained using a modal approach based on the eigenvectors of the state-space direct and adjoint systems. To calculate the eigenvalues and their sensitivity the system's Jacobian and its partial derivatives with respect the parameters are determined. The calculation of the derivative of the Jacobian matrix with respect to the parameters is not a simple task and for many situations it must be done numerically. The system stability is studied in relation with three parameters: m, the equivalent inertial load of primary control surface reduced to the actuator rod; B, the bulk modulus of oil and p a pressure supply proportionality coefficient. All the sensitivities calculated in this work are in good agreement with those obtained through recalculations.

Multidimensional effects in the thermal response of fuel rod simulators. [PWR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dabbs, R.D.; Ott, L.J.

1980-01-01

One of the primary objectives of the Oak Ridge National Laboratory Pressurized-Water Reactor Blowdown Heat Transfer Separate-Effects Program is the determination of the transient surface temperature and surface heat flux of fuel pin simulators (FPSs) from internal thermocouple signals obtained during a loss-of-coolant experiment (LOCE) in the Thermal-Hydraulics Test Facility. This analysis requires the solution of the classical inverse heat conduction problem. The assumptions that allow the governing differential equation to be reduced to one dimension can introduce significant errors in the computed surface heat flux and surface temperature. The degree to which these computed variables are perturbed is addressedmore » and quantified.« less

ANTS-anchored Zn-Al-CO{sub 3}-LDH particles as fluorescent probe for sensing of folic acid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Pengfei; Liu, Dan; Liu, Yanhuan

2016-09-15

A novel fluorescent nanosensor for detecting folic acid (FA) in aqueous media has been developed based on 8-aminonaphthalene-1,3,6-trisulfonate (ANTS) anchored to the surface of Zn-Al-CO{sub 3}-layered double hydroxides (LDH) particles. The nanosensor showed high fluorescence intensity and good photostability due to a strong coordination interaction between surface Zn{sup 2+} ions of Zn-Al-CO{sub 3}-LDH and N atoms of ANTS, which were verified by result of X-ray photoelectron spectroscopy (XPS). ANTS-anchored on the surface of Zn-Al-CO{sub 3}-LDH restricted the intra-molecular rotation leading to ANTS-anchored J-type aggregation emission enhancement. ANTS-anchored Zn-Al-CO{sub 3}-LDH particles exhibited highly sensitive and selective response to FA over othermore » common metal ions and saccharides present in biological fluids. The proposed mechanism was that oxygen atoms of -SO{sub 3} groups in ANTS-anchored on the surface of Zn-Al-CO{sub 3}-LDH were easily collided by FA molecules to form potential hydrogen bonds between ANTS-anchored and FA molecules, which could effectively quench the ANTS-anchored fluorescence. Under the simulated physiological conditions (pH of 7.4), the fluorescence quenching was fitted to Stern-Volmer equation with a linear response in the concentration range of 1 μM to 200 μM with a limit of detection of 0.1 μM. The results indicate that ANTS-anchored Zn-Al-CO{sub 3}-LDH particles can afford a very sensitive system for the sensing FA in aqueous solution. - Highlights: • A novel fluorescent nanosensor has been developed. • The sensor exhibited highly sensitive and selective response to FA. • The fluorescence quenching was fitted to Stern–Volmer equation. • The linear response range was 1–200 μM with a limit of detection of 0.1 μM.« less

Seismic reflection imaging, accounting for primary and multiple reflections

NASA Astrophysics Data System (ADS)

Wapenaar, Kees; van der Neut, Joost; Thorbecke, Jan; Broggini, Filippo; Slob, Evert; Snieder, Roel

2015-04-01

Imaging of seismic reflection data is usually based on the assumption that the seismic response consists of primary reflections only. Multiple reflections, i.e. waves that have reflected more than once, are treated as primaries and are imaged at wrong positions. There are two classes of multiple reflections, which we will call surface-related multiples and internal multiples. Surface-related multiples are those multiples that contain at least one reflection at the earth's surface, whereas internal multiples consist of waves that have reflected only at subsurface interfaces. Surface-related multiples are the strongest, but also relatively easy to deal with because the reflecting boundary (the earth's surface) is known. Internal multiples constitute a much more difficult problem for seismic imaging, because the positions and properties of the reflecting interfaces are not known. We are developing reflection imaging methodology which deals with internal multiples. Starting with the Marchenko equation for 1D inverse scattering problems, we derived 3D Marchenko-type equations, which relate reflection data at the surface to Green's functions between virtual sources anywhere in the subsurface and receivers at the surface. Based on these equations, we derived an iterative scheme by which these Green's functions can be retrieved from the reflection data at the surface. This iterative scheme requires an estimate of the direct wave of the Green's functions in a background medium. Note that this is precisely the same information that is also required by standard reflection imaging schemes. However, unlike in standard imaging, our iterative Marchenko scheme retrieves the multiple reflections of the Green's functions from the reflection data at the surface. For this, no knowledge of the positions and properties of the reflecting interfaces is required. Once the full Green's functions are retrieved, reflection imaging can be carried out by which the primaries and multiples are mapped to their correct positions, with correct reflection amplitudes. In the presentation we will illustrate this new methodology with numerical examples and discuss its potential and limitations.

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

Response surface modeling for hot, humid air decontamination of materials contaminated with Bacillus anthracis ∆Sterne and Bacillus thuringiensis Al Hakam spores

PubMed Central

2014-01-01

Response surface methodology using a face-centered cube design was used to describe and predict spore inactivation of Bacillus anthracis ∆Sterne and Bacillus thuringiensis Al Hakam spores after exposure of six spore-contaminated materials to hot, humid air. For each strain/material pair, an attempt was made to fit a first or second order model. All three independent predictor variables (temperature, relative humidity, and time) were significant in the models except that time was not significant for B. thuringiensis Al Hakam on nylon. Modeling was unsuccessful for wiring insulation and wet spores because there was complete spore inactivation in the majority of the experimental space. In cases where a predictive equation could be fit, response surface plots with time set to four days were generated. The survival of highly purified Bacillus spores can be predicted for most materials tested when given the settings for temperature, relative humidity, and time. These predictions were cross-checked with spore inactivation measurements. PMID:24949256

A Study of Supersonic Surface Sources: The Ffowcs Williams-Hawkings Equation and the Kirchhoff Formula

NASA Technical Reports Server (NTRS)

Farassat, F.; Brentner, Kenneth S.; Dunn, M. H.

2004-01-01

In this paper we address the mathematical problem of noise generation from high speed moving surfaces. The problem we are solving is the linear wave equation with sources on a moving surface. The Ffowcs Williams-Hawkings (FW-H) equation as well as the govern- ing equation for deriving the Kirchhoff formula for moving surfaces are both this type of partial differential equation. We give a new exact solution of this problem here in closed form which is valid for subsonic and supersonic motion of the surface but it is particularly suitable for supersonically moving surfaces. This new solution is the simplest of all high speed formulations of Langley and is denoted formulation 4 following the tradition of numbering of our major results for the prediction of the noise of rotating blades. We show that for a smooth surface moving at supersonic speed, our solution has only removable singularities. Thus it can be used for numerical work.

Effect of random surface inhomogeneities on spectral properties of dielectric-disk microresonators: theory and modeling at millimeter wave range.

PubMed

Ganapolskii, E M; Eremenko, Z E; Tarasov, Yu V

2009-04-01

The influence of random axially homogeneous surface roughness on spectral properties of dielectric resonators of circular disk form is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields, the method of eigenmode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering that is highly responsible for nondissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object, we use a dielectric disk resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigenfrequencies and the Q factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.

Integrated Thermal Response Tool for Earth Entry Vehicles

NASA Technical Reports Server (NTRS)

Chen, Y.-K.; Milos, F. S.; Partridge, Harry (Technical Monitor)

2001-01-01

A system is presented for multi-dimensional, fully-coupled thermal response modeling of hypersonic entry vehicles. The system consists of a two-dimensional implicit thermal response, pyrolysis and ablation program (TITAN), a commercial finite-element thermal and mechanical analysis code (MARC), and a high fidelity Navier-Stokes equation solver (GIANTS). The simulations performed by this integrated system include hypersonic flow-field, fluid and solid interaction, ablation, shape change, pyrolysis gas generation and flow, and thermal response of heatshield and structure. The thermal response of the ablating and charring heatshield material is simulated using TITAN, and that of the underlying structural is simulated using MARC. The ablating heatshield is treated as an outer boundary condition of the structure, and continuity conditions of temperature and heat flux are imposed at the interface between TITAN and MARC. Aerothermal environments with fluid and solid interaction are predicted by coupling TITAN and GIANTS through surface energy balance equations. With this integrated system, the aerothermal environments for an entry vehicle and the thermal response of both the heatshield and the structure can be obtained simultaneously. Representative computations for a proposed blunt body earth entry vehicle are presented and discussed in detail.

Thermal Response Modeling System for a Mars Sample Return Vehicle

NASA Technical Reports Server (NTRS)

Chen, Y.-K.; Miles, Frank S.; Arnold, Jim (Technical Monitor)

2001-01-01

A multi-dimensional, coupled thermal response modeling system for analysis of hypersonic entry vehicles is presented. The system consists of a high fidelity Navier-Stokes equation solver (GIANTS), a two-dimensional implicit thermal response, pyrolysis and ablation program (TITAN), and a commercial finite-element thermal and mechanical analysis code (MARC). The simulations performed by this integrated system include hypersonic flowfield, fluid and solid interaction, ablation, shape change, pyrolysis gas eneration and flow, and thermal response of heatshield and structure. The thermal response of the heatshield is simulated using TITAN, and that of the underlying structural is simulated using MARC. The ablating heatshield is treated as an outer boundary condition of the structure, and continuity conditions of temperature and heat flux are imposed at the interface between TITAN and MARC. Aerothermal environments with fluid and solid interaction are predicted by coupling TITAN and GIANTS through surface energy balance equations. With this integrated system, the aerothermal environments for an entry vehicle and the thermal response of the entire vehicle can be obtained simultaneously. Representative computations for a flat-faced arc-jet test model and a proposed Mars sample return capsule are presented and discussed.

Thermal Response Modeling System for a Mars Sample Return Vehicle

NASA Technical Reports Server (NTRS)

Chen, Y.-K.; Milos, F. S.

2002-01-01

A multi-dimensional, coupled thermal response modeling system for analysis of hypersonic entry vehicles is presented. The system consists of a high fidelity Navier-Stokes equation solver (GIANTS), a two-dimensional implicit thermal response, pyrolysis and ablation program (TITAN), and a commercial finite element thermal and mechanical analysis code (MARC). The simulations performed by this integrated system include hypersonic flowfield, fluid and solid interaction, ablation, shape change, pyrolysis gas generation and flow, and thermal response of heatshield and structure. The thermal response of the heatshield is simulated using TITAN, and that of the underlying structural is simulated using MARC. The ablating heatshield is treated as an outer boundary condition of the structure, and continuity conditions of temperature and heat flux are imposed at the interface between TITAN and MARC. Aerothermal environments with fluid and solid interaction are predicted by coupling TITAN and GIANTS through surface energy balance equations. With this integrated system, the aerothermal environments for an entry vehicle and the thermal response of the entire vehicle can be obtained simultaneously. Representative computations for a flat-faced arc-jet test model and a proposed Mars sample return capsule are presented and discussed.

Ablation, Thermal Response, and Chemistry Program for Analysis of Thermal Protection Systems

NASA Technical Reports Server (NTRS)

Milos, Frank S.; Chen, Yih-Kanq

2010-01-01

In previous work, the authors documented the Multicomponent Ablation Thermochemistry (MAT) and Fully Implicit Ablation and Thermal response (FIAT) programs. In this work, key features from MAT and FIAT were combined to create the new Fully Implicit Ablation, Thermal response, and Chemistry (FIATC) program. FIATC is fully compatible with FIAT (version 2.5) but has expanded capabilities to compute the multispecies surface chemistry and ablation rate as part of the surface energy balance. This new methodology eliminates B' tables, provides blown species fractions as a function of time, and enables calculations that would otherwise be impractical (e.g. 4+ dimensional tables) such as pyrolysis and ablation with kinetic rates or unequal diffusion coefficients. Equations and solution procedures are presented, then representative calculations of equilibrium and finite-rate ablation in flight and ground-test environments are discussed.

Influence of foundation mass and surface roughness on dynamic response of beam on dynamic foundation subjected to the moving load

NASA Astrophysics Data System (ADS)

Tran Quoc, Tinh; Khong Trong, Toan; Luong Van, Hai

2018-04-01

In this paper, Improved Moving Element Method (IMEM) is used to analyze the dynamic response of Euler-Bernoulli beam structures on the dynamic foundation model subjected to the moving load. The effects of characteristic foundation model parameters such as Winkler stiffness, shear layer based on the Pasternak model, viscoelastic dashpot and characteristic parameter of mass on foundation. Beams are modeled by moving elements while the load is fixed. Based on the principle of the publicly virtual balancing and the theory of moving element method, the motion differential equation of the system is established and solved by means of the numerical integration based on the Newmark algorithm. The influence of mass on foundation and the roughness of the beam surface on the dynamic response of beam are examined in details.

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

1997-01-01

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Analysis and Sizing for Transient Thermal Heating of Insulated Aerospace Vehicle Structures

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An analytical solution was derived for the transient response of an insulated structure subjected to a simplified heat pulse. The solution is solely a function of two nondimensional parameters. Simpler functions of these two parameters were developed to approximate the maximum structural temperature over a wide range of parameter values. Techniques were developed to choose constant, effective thermal properties to represent the relevant temperature and pressure-dependent properties for the insulator and structure. A technique was also developed to map a time-varying surface temperature history to an equivalent square heat pulse. Equations were also developed for the minimum mass required to maintain the inner, unheated surface below a specified temperature. In the course of the derivation, two figures of merit were identified. Required insulation masses calculated using the approximate equation were shown to typically agree with finite element results within 10%-20% over the relevant range of parameters studied.

Iterative discrete ordinates solution of the equation for surface-reflected radiance

NASA Astrophysics Data System (ADS)

Radkevich, Alexander

2017-11-01

This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

Application of mathematical model methods for optimization tasks in construction materials technology

NASA Astrophysics Data System (ADS)

Fomina, E. V.; Kozhukhova, N. I.; Sverguzova, S. V.; Fomin, A. E.

2018-05-01

In this paper, the regression equations method for design of construction material was studied. Regression and polynomial equations representing the correlation between the studied parameters were proposed. The logic design and software interface of the regression equations method focused on parameter optimization to provide the energy saving effect at the stage of autoclave aerated concrete design considering the replacement of traditionally used quartz sand by coal mining by-product such as argillite. The mathematical model represented by a quadric polynomial for the design of experiment was obtained using calculated and experimental data. This allowed the estimation of relationship between the composition and final properties of the aerated concrete. The surface response graphically presented in a nomogram allowed the estimation of concrete properties in response to variation of composition within the x-space. The optimal range of argillite content was obtained leading to a reduction of raw materials demand, development of target plastic strength of aerated concrete as well as a reduction of curing time before autoclave treatment. Generally, this method allows the design of autoclave aerated concrete with required performance without additional resource and time costs.

Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

NASA Technical Reports Server (NTRS)

Wang, Chi R.

2005-01-01

This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation turbulence model is an effective approach for turbulence modeling in the near solid wall surface region of flow over a concave wall.

A Hybrid Method of Moment Equations and Rate Equations to Modeling Gas-Grain Chemistry

NASA Astrophysics Data System (ADS)

Pei, Y.; Herbst, E.

2011-05-01

Grain surfaces play a crucial role in catalyzing many important chemical reactions in the interstellar medium (ISM). The deterministic rate equation (RE) method has often been used to simulate the surface chemistry. But this method becomes inaccurate when the number of reacting particles per grain is typically less than one, which can occur in the ISM. In this condition, stochastic approaches such as the master equations are adopted. However, these methods have mostly been constrained to small chemical networks due to the large amounts of processor time and computer power required. In this study, we present a hybrid method consisting of the moment equation approximation to the stochastic master equation approach and deterministic rate equations to treat a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In this model, we use the standard OSU gas phase network (version OSU2006V3) which involves 458 gas phase species and more than 4000 reactions, and treat it by deterministic rate equations. A medium-sized surface reaction network which consists of 21 species and 19 reactions accounts for the productions of stable molecules such as H_2O, CO, CO_2, H_2CO, CH_3OH, NH_3 and CH_4. These surface reactions are treated by a hybrid method of moment equations (Barzel & Biham 2007) and rate equations: when the abundance of a surface species is lower than a specific threshold, say one per grain, we use the ``stochastic" moment equations to simulate the evolution; when its abundance goes above this threshold, we use the rate equations. A continuity technique is utilized to secure a smooth transition between these two methods. We have run chemical simulations for a time up to 10^8 yr at three temperatures: 10 K, 15 K, and 20 K. The results will be compared with those generated from (1) a completely deterministic model that uses rate equations for both gas phase and grain surface chemistry, (2) the method of modified rate equations (Garrod 2008), which partially takes into account the stochastic effect for surface reactions, and (3) the master equation approach solved using a Monte Carlo technique. At 10 K and standard grain sizes, our model results agree well with the above three methods, while discrepancies appear at higher temperatures and smaller grain sizes.

The effect of glycerin solution density and viscosity on vibration amplitude of oblique different piezoelectric MC near the surface in 3D modeling

NASA Astrophysics Data System (ADS)

Korayem, A. H.; Abdi, M.; Korayem, M. H.

2018-06-01

The surface topography in nanoscale is one of the most important applications of AFM. The analysis of piezoelectric microcantilevers vibration behavior is essential to improve the AFM performance. To this end, one of the appropriate methods to simulate the dynamic behavior of microcantilever (MC) is a numerical solution with FEM in the 3D modeling using COMSOL software. The present study aims to simulate different geometries of the four-layered AFM piezoelectric MCs in 2D and 3D modeling in a liquid medium using COMSOL software. The 3D simulation was done in a spherical container using FSI domain in COMSOL. In 2D modeling by applying Hamilton's Principle based on Euler-Bernoulli Beam theory, the governing motion equation was derived and discretized with FEM. In this mode, the hydrodynamic force was assumed with a string of spheres. The effect of this force along with the squeezed-film force was considered on MC equations. The effect of fluid density and viscosity on the MC vibrations that immersed in different glycerin solutions was investigated in 2D and 3D modes and the results were compared with the experimental results. The frequencies and time responses of MC close to the surface were obtained considering tip-sample forces. The surface topography of MCs different geometries were compared in the liquid medium and the comparison was done in both tapping and non-contact mode. Various types of surface roughness were considered in the topography for MC different geometries. Also, the effect of geometric dimensions on the surface topography was investigated. In liquid medium, MC is installed at an oblique position to avoid damaging the MC due to the squeezed-film force in the vicinity of MC surface. Finally, the effect of MC's angle on surface topography and time response of the system was investigated.

Solution of the surface Euler equations for accurate three-dimensional boundary-layer analysis of aerodynamic configurations

NASA Technical Reports Server (NTRS)

Iyer, V.; Harris, J. E.

1987-01-01

The three-dimensional boundary-layer equations in the limit as the normal coordinate tends to infinity are called the surface Euler equations. The present paper describes an accurate method for generating edge conditions for three-dimensional boundary-layer codes using these equations. The inviscid pressure distribution is first interpolated to the boundary-layer grid. The surface Euler equations are then solved with this pressure field and a prescribed set of initial and boundary conditions to yield the velocities along the two surface coordinate directions. Results for typical wing and fuselage geometries are presented. The smoothness and accuracy of the edge conditions obtained are found to be superior to the conventional interpolation procedures.

Response of near-surface currents in the Indian Ocean to the anomalous atmospheric condition in 2015

NASA Astrophysics Data System (ADS)

Utari, P. A.; Nurkhakim, M. Y.; Setiabudidaya, D.; Iskandar, I.

2018-05-01

Anomalous ocean-atmosphere conditions were detected in the tropical Indian Ocean during boreal spring to boreal winter 2015. It was suggested that the anomalous conditions were characteristics of the positive Indian Ocean Dipole (pIOD) event. The purpose of this investigation was to investigate the response of near-surface currents in the tropical Indian Ocean to the anomalous atmospheric condition in 2015. Near-surface current from OSCAR (Ocean Surface Current Analyses Real Time) reanalysis data combined with the sea surface temperature (SST) data from OISST – NOAA, sea surface height (SSH) and surface winds from the ECMWF were used in this investigation. The analysis showed that the evolution of 2015 pIOD started in June/July, peaked in the September and terminated in late November 2015. Correlated with the evolution of the pIOD, easterly winds anomalies were detected along the equator. As the oceanic response to these easterly wind anomalies, the surface currents anomalously westward during the peak of the pIOD. It was interesting to note that the evolution of 2015 pIOD event was closely related to the ocean wave dynamics as revealed by the SSH data. Downwelling westward propagating Rossby waves were detected in the southwestern tropical Indian Ocean. Once reached the western boundary of the Indian Ocean, they were redirected back into interior Indian Ocean and propagating eastward as the downwelling Kelvin waves.

On the Monge-Ampere equivalent of the sine-Gordon equation

NASA Astrophysics Data System (ADS)

Ferapontov, E. V.; Nutku, Y.

1994-12-01

Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampere equation for the graph of the surface. We present the explicit form of the correspondence between these two integrable non-linear partial differential equations using their well-known properties in differential geometry. We find that the cotangent of the angle between asymptotic directions is directly related to the mean curvature of the surface. This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere equations.

Response to 'Comment on 'Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks' '[Phys. Plasmas 19, 064701 (2012)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lakhin, V. P.; Ilgisonis, V. I.; Peoples' Friendship University, 3 Ordzhonikidze St., Moscow 117198

2012-06-15

The equations for the continuous spectra derived in our paper [V. P. Lakhin and V. I. Ilgisonis, Phys. Plasmas 18, 092103 (2011)] can be reduced to the matrix form used by Goedbloed et al.[Phys. Plasmas 11, 28 (2004)]. It is shown that the assumptions made in our paper provide the elliptic flow regime and guarantee the existence of plasma equilibrium with nested magnetic surfaces of circular cross-section. The new results on magnetohydrodynamic instabilities of such tokamak equilibria obtained in our paper but absent in the paper by Goedbloed et al. are emphasized.

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

Wintertime Phytoplankton Blooms in the Western Equatorial Indian Ocean Associated With the Madden-Julian Oscillation

NASA Astrophysics Data System (ADS)

Liao, Xiaomei; Du, Yan; Zhan, Haigang; Wang, Tianyu; Feng, Ming

2017-12-01

This study investigated boreal wintertime phytoplankton blooms in the western equatorial Indian Ocean (WEIO) and the underlying physical mechanisms. The Sea viewing Wide field of View sensor (SeaWiFS) chlorophyll-a (Chla) concentrations show that phytoplankton blooms occur in the WEIO during December-March. The development of these blooms is not only a seasonal process but also consists of 2-3 intraseasonal events induced by the Madden-Julian Oscillation (MJO). During a typical intraseasonal event, enhanced cross-equatorial wind induces strong upwelling and ocean mixing, thus increasing the supply of nutrients to the surface in equatorial regions. Argo profiles clearly show various responses to the intraseasonal wind bursts, including shoaling of the thermocline and deepening of the mixed layer. Further analysis reveals that the former is the dominant mechanism for the blooms along the equator, while the latter controls the high Chla concentrations off the coast of Somalia. Surface ocean circulations not only account for the blooms south of the equator but also modulate the thermocline depth in the WEIO. The shallower thermocline during the early period of the northeast monsoon season provides favorable conditions for a stronger Chla response to intraseasonal forcing.

Formulation of topical bioadhesive gel of aceclofenac using 3-level factorial design.

PubMed

Singh, Sanjay; Parhi, Rabinarayan; Garg, Anuj

2011-01-01

The objective of this work was to develop bioadhesive topical gel of Aceclofenac with the help of response-surface approach. Experiments were performed according to a 3-level factorial design to evaluate the effects of two independent variables [amount of Poloxamer 407 (PL-407 = X1) and hydroxypropylmethyl cellulose K100 M (HPMC = X2)] on the bioadhesive character of gel, rheological property of gel (consistency index), and in-vitro drug release. The best model was selected to fit the data. Mathematical equation was generated by Design Expert® software for the model which assists in determining the effect of independent variables. Response surface plots were also generated by the software for analyzing effect of the independent variables on the response. Quadratic model was found to be the best for all the responses. Both independent variable (X1 and X2) were found to have synergistic effect on bioadhesion (Y1) but the effect of HPMC was more pronounced than PL-407. Consistency index was enhanced by increasing the level of both independent variables. An antagonistic effect of both independent variables was found on cumulative percentage release of drug in 2 (Y3) and 8 h (Y4). Both independent variables approximately equally contributed the antagonistic effect on Y3 whereas antagonistic effect of HPMC was more pronounced than PL-407. The effect of formulation variables on the product characteristics can be easily predicted and precisely interpreted by using a 3-level factorial experimental design and generated quadratic mathematical equations.

A Numerical Method for Predicting Rayleigh Surface Wave Velocity in Anisotropic Crystals (Postprint)

DTIC Science & Technology

2017-09-05

generalized version of the equations are very difficult to derive, even in symbolic math languages such as Mathematica. As a result, the equations are...formalism, Math . Mech. Solids 9 (1) (2004) 5–15. [8] M. Destrade, The explicit secular equation for surface acoustic waves in monoclinic elastic crystals...Q. J. Mech. Appl. Math . 55 (2) (2002) 297–311. [10] D. Taylor, Surface waves in anisotropic media: the secular equation and its numerical solution

Surface-slip equations for multicomponent nonequilibrium air flow

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Scott, C. D.; Moss, J. N.

1985-01-01

Equations are presented for the surface-slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds number, high-altitude flight regime of a space vehicle. The equations are obtained from closed form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities were obtained in a form which can be employed in flowfield computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate, species-concentration boundary condition for a multicomponent mixture in absence of slip.

Broad-Band Pump-Probe Spectroscopy Quantifies Ultrafast Solvation Dynamics of Proteins and Molecules.

PubMed

Jumper, Chanelle C; Arpin, Paul C; Turner, Daniel B; McClure, Scott D; Rafiq, Shahnawaz; Dean, Jacob C; Cina, Jeffrey A; Kovac, Philip A; Mirkovic, Tihana; Scholes, Gregory D

2016-11-17

In this work, we demonstrate the use of broad-band pump-probe spectroscopy to measure femtosecond solvation dynamics. We report studies of a rhodamine dye in methanol and cryptophyte algae light-harvesting proteins in aqueous suspension. Broad-band impulsive excitation generates a vibrational wavepacket that oscillates on the excited-state potential energy surface, destructively interfering with itself at the minimum of the surface. This destructive interference gives rise to a node at a certain probe wavelength that varies with time. This reveals the Gibbs free-energy changes of the excited-state potential energy surface, which equates to the solvation time correlation function. This method captures the inertial solvent response of water (∼40 fs) and the bimodal inertial response of methanol (∼40 and ∼150 fs) and reveals how protein-buried chromophores are sensitive to the solvent dynamics inside and outside of the protein environment.

Magnetohydrodynamics Carreau nanofluid flow over an inclined convective heated stretching cylinder with Joule heating

NASA Astrophysics Data System (ADS)

Khan, Imad; Shafquatullah; Malik, M. Y.; Hussain, Arif; Khan, Mair

Current work highlights the computational aspects of MHD Carreau nanofluid flow over an inclined stretching cylinder with convective boundary conditions and Joule heating. The mathematical modeling of physical problem yields nonlinear set of partial differential equations. A suitable scaling group of variables is employed on modeled equations to convert them into non-dimensional form. The integration scheme Runge-Kutta-Fehlberg on the behalf of shooting technique is utilized to solve attained set of equations. The interesting aspects of physical problem (linear momentum, energy and nanoparticles concentration) are elaborated under the different parametric conditions through graphical and tabular manners. Additionally, the quantities (local skin friction coefficient, local Nusselt number and local Sherwood number) which are responsible to dig out the physical phenomena in the vicinity of stretched surface are computed and delineated by varying controlling flow parameters.

Theoretical Foundation of Zisman's Empirical Equation for Wetting of Liquids on Solid Surfaces

ERIC Educational Resources Information Center

Zhu, Ruzeng; Cui, Shuwen; Wang, Xiaosong

2010-01-01

Theories of wetting of liquids on solid surfaces under the condition that van der Waals force is dominant are briefly reviewed. We show theoretically that Zisman's empirical equation for wetting of liquids on solid surfaces is a linear approximation of the Young-van der Waals equation in the wetting region, and we express the two parameters in…

The dynamics of oceanic fronts. I - The Gulf Stream

NASA Technical Reports Server (NTRS)

Kao, T. W.

1980-01-01

The establishment and maintenance of the mean hydrographic properties of large-scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near-surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density; full time dependent diffusion and Navier-Stokes equations are then used with constant eddy diffusion and viscosity coefficients, together with a constant Coriolis parameter. Scaling analysis reveals three independent scales of the problem including the radius of deformation of the inertial length, buoyancy length, and diffusive length scales. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on the Ekman number alone for problems of oceanic interest. It is concluded that the mean Gulf Stream dynamics can be interpreted in terms of a solution of the Navier-Stokes and diffusion equations, with the cross-stream circulation responsible for the maintenance of the front; this mechanism is suggested for the maintenance of the Gulf Stream dynamics.

Exact solutions for postbuckling of a graded porous beam

NASA Astrophysics Data System (ADS)

Ma, L. S.; Ou, Z. Y.

2018-06-01

An exact, closed-form solution for the postbuckling responses of graded porous beams subjected to axially loading is obtained. It was assumed that the properties of the graded porous materials vary continuously through thickness of the beams, the equations governing the axial and transverse deformations are derived based on the classical beam theory and the physical neutral surface concept. The two equations are reduced to a single nonlinear fourth-order integral-differential equation governing the transverse deformations. The nonlinear equation is directly solved without any use of approximation and a closed-form solution for postbuckled deformation is obtained as a function of the applied load. The exact solutions explicitly describe the nonlinear equilibrium paths of the buckled beam and thus are able to provide insight into deformation problems. Based on the exact solutions obtained herein, the effects of various factors such as porosity distribution pattern, porosity coefficient and boundary conditions on postbuckling behavior of graded porous beams have been investigated.

The rotational feedback on linear-momentum balance in glacial isostatic adjustment

NASA Astrophysics Data System (ADS)

Martinec, Zdenek; Hagedoorn, Jan

2015-04-01

The influence of changes in surface ice-mass redistribution and associated viscoelastic response of the Earth, known as glacial-isostatic adjustment (GIA), on the Earth's rotational dynamics has long been known. Equally important is the effect of the changes in the rotational dynamics on the viscoelastic deformation of the Earth. This signal, known as the rotational feedback, or more precisely, the rotational feedback on the sea-level equation, has been mathematically described by the sea-level equation extended for the term that is proportional to perturbation in the centrifugal potential and the second-degree tidal Love number. The perturbation in the centrifugal force due to changes in the Earth's rotational dynamics enters not only into the sea-level equation, but also into the conservation law of linear momentum such that the internal viscoelastic force, the perturbation in the gravitational force and the perturbation in the centrifugal force are in balance. Adding the centrifugal-force perturbation to the linear-momentum balance creates an additional rotational feedback on the viscoelastic deformations of the Earth. We term this feedback mechanism as the rotational feedback on the linear-momentum balance. We extend both the time-domain method for modelling the GIA response of laterally heterogeneous earth models and the traditional Laplace-domain method for modelling the GIA-induced rotational response to surface loading by considering the rotational feedback on linear-momentum balance. The correctness of the mathematical extensions of the methods is validated numerically by comparing the polar motion response to the GIA process and the rotationally-induced degree 2 and order 1 spherical harmonic component of the surface vertical displacement and gravity field. We present the difference between the case where the rotational feedback on linear-momentum balance is considered against that where it is not. Numerical simulations show that the resulting difference in radial displacement and sea-level change between these situations since the Last Glacial Maximum reaches values of ± 25 m and ± 1.8 m, respectively. Furthermore, the surface deformation pattern is modified by up to 10% in areas of former or ongoing glaciation, but by up to 50% at the bottom of the southern Indian ocean. This also results in the movement of coastlines during the last deglaciation to differ between the two cases due to the difference in the ocean loading, which is seen for instance in the area around Hudson Bay, Canada, and along the Chinese, Australian, or Argentinian coastlines.

The rotational feedback on linear-momentum balance in glacial isostatic adjustment

NASA Astrophysics Data System (ADS)

Martinec, Zdeněk; Hagedoorn, Jan

2014-12-01

The influence of changes in surface ice-mass redistribution and associated viscoelastic response of the Earth, known as glacial isostatic adjustment (GIA), on the Earth's rotational dynamics has long been known. Equally important is the effect of the changes in the rotational dynamics on the viscoelastic deformation of the Earth. This signal, known as the rotational feedback, or more precisely, the rotational feedback on the sea level equation, has been mathematically described by the sea level equation extended for the term that is proportional to perturbation in the centrifugal potential and the second-degree tidal Love number. The perturbation in the centrifugal force due to changes in the Earth's rotational dynamics enters not only into the sea level equation, but also into the conservation law of linear momentum such that the internal viscoelastic force, the perturbation in the gravitational force and the perturbation in the centrifugal force are in balance. Adding the centrifugal-force perturbation to the linear-momentum balance creates an additional rotational feedback on the viscoelastic deformations of the Earth. We term this feedback mechanism, which is studied in this paper, as the rotational feedback on the linear-momentum balance. We extend both the time-domain method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec and the traditional Laplace-domain method for modelling the GIA-induced rotational response to surface loading by considering the rotational feedback on linear-momentum balance. The correctness of the mathematical extensions of the methods is validated numerically by comparing the polar-motion response to the GIA process and the rotationally induced degree 2 and order 1 spherical harmonic component of the surface vertical displacement and gravity field. We present the difference between the case where the rotational feedback on linear-momentum balance is considered against that where it is not. Numerical simulations show that the resulting difference in radial displacement and sea level change between these situations since the Last Glacial Maximum reaches values of ±25 and ±1.8 m, respectively. Furthermore, the surface deformation pattern is modified by up to 10 per cent in areas of former or ongoing glaciation, but by up to 50 per cent at the bottom of the southern Indian ocean. This also results in the movement of coastlines during the last deglaciation to differ between the two cases due to the difference in the ocean loading, which is seen for instance in the area around Hudson Bay, Canada and along the Chinese, Australian or Argentinian coastlines.

Computational modeling of mediator oxidation by oxygen in an amperometric glucose biosensor.

PubMed

Simelevičius, Dainius; Petrauskas, Karolis; Baronas, Romas; Razumienė, Julija

2014-02-07

In this paper, an amperometric glucose biosensor is modeled numerically. The model is based on non-stationary reaction-diffusion type equations. The model consists of four layers. An enzyme layer lies directly on a working electrode surface. The enzyme layer is attached to an electrode by a polyvinyl alcohol (PVA) coated terylene membrane. This membrane is modeled as a PVA layer and a terylene layer, which have different diffusivities. The fourth layer of the model is the diffusion layer, which is modeled using the Nernst approach. The system of partial differential equations is solved numerically using the finite difference technique. The operation of the biosensor was analyzed computationally with special emphasis on the biosensor response sensitivity to oxygen when the experiment was carried out in aerobic conditions. Particularly, numerical experiments show that the overall biosensor response sensitivity to oxygen is insignificant. The simulation results qualitatively explain and confirm the experimentally observed biosensor behavior.

Computational Modeling of Mediator Oxidation by Oxygen in an Amperometric Glucose Biosensor

PubMed Central

Šimelevičius, Dainius; Petrauskas, Karolis; Baronas, Romas; Julija, Razumienė

2014-01-01

In this paper, an amperometric glucose biosensor is modeled numerically. The model is based on non-stationary reaction-diffusion type equations. The model consists of four layers. An enzyme layer lies directly on a working electrode surface. The enzyme layer is attached to an electrode by a polyvinyl alcohol (PVA) coated terylene membrane. This membrane is modeled as a PVA layer and a terylene layer, which have different diffusivities. The fourth layer of the model is the diffusion layer, which is modeled using the Nernst approach. The system of partial differential equations is solved numerically using the finite difference technique. The operation of the biosensor was analyzed computationally with special emphasis on the biosensor response sensitivity to oxygen when the experiment was carried out in aerobic conditions. Particularly, numerical experiments show that the overall biosensor response sensitivity to oxygen is insignificant. The simulation results qualitatively explain and confirm the experimentally observed biosensor behavior. PMID:24514882

Advanced computational simulations of water waves interacting with wave energy converters

NASA Astrophysics Data System (ADS)

Pathak, Ashish; Freniere, Cole; Raessi, Mehdi

2017-03-01

Wave energy converter (WEC) devices harness the renewable ocean wave energy and convert it into useful forms of energy, e.g. mechanical or electrical. This paper presents an advanced 3D computational framework to study the interaction between water waves and WEC devices. The computational tool solves the full Navier-Stokes equations and considers all important effects impacting the device performance. To enable large-scale simulations in fast turnaround times, the computational solver was developed in an MPI parallel framework. A fast multigrid preconditioned solver is introduced to solve the computationally expensive pressure Poisson equation. The computational solver was applied to two surface-piercing WEC geometries: bottom-hinged cylinder and flap. Their numerically simulated response was validated against experimental data. Additional simulations were conducted to investigate the applicability of Froude scaling in predicting full-scale WEC response from the model experiments.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David Michael

1997-01-01

The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. The formulation uses the principle of virtual work. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are then derived after the application of several simplifying assumptions. These equations are then modified to allow the reference surface of the plate to be located at a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described as well. The terms of the plate stiffness matrix using both Classical Plate Theory (CPT) and first-order Shear-Deformation Plate Theory (SDPT) are presented. The necessary steps to include the effects of in-plane transverse and in-plane shear loads in the in-plane stability equations are also outlined. Numerical results are presented using the newly implemented capability. Comparisons of results for several example problems with different loading states are made. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPF are also made. Results comparing the computational effort required by the new analysis to that of the analysis currently in the VICONOPT program are presented. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.

A study of the effect of a boundary layer profile on the dynamic response and acoustic radiation of flat panels. Ph.D. Thesis - Virginia Univ.

NASA Technical Reports Server (NTRS)

Mixson, J. S.

1973-01-01

The response of a thin, elastic plate to a harmonic force which drives the plate from below and a compressible air stream with a viscous boundary layer flowing parallel to the upper surface along the length was investigated. Equations governing the forced response of the coupled plate-aerodynamic system are derived along with appropriate boundary conditions. Calculations of basic solution parameters for a linear velocity profile and for a Blasius profile showed that the same system response could be obtained from each profile if appropriate values of boundary layer thickness were chosen for each profile.

Direct Determination of the Dependence of the Surface Shear and Dilatational Viscosities on the Thermodynamic State of the Interface: Theoretical Foundations.

PubMed

Lopez; Hirsa

1998-10-01

Recent developments in nonlinear optical techniques for noninvasive probing of a surfactant influenced gas/liquid interface allow for the measurement of the surfactant surface concentration, c, and thus provide new opportunities for the direct determination of its intrinsic viscosities. Here, we present the theoretical foundations, based on the Boussinesq-Scriven surface model without the usual simplification of constant viscosities, for an experimental technique to directly measure the surface shear (µs) and dilatational (kappas) viscosities of a Newtonian interface as functions of the surfactant surface concentration. This ability to directly measure the surfactant concentration permits the use of a simple surface flow for the measurement of the surface viscosities. The requirements are that the interface must be nearly flat, and the flow steady, axisymmetric, and swirling; these flow conditions can be achieved in the deep-channel viscometer driven at relatively fast rates. The tangential stress balance on such an interface leads to two equations; the balance in the azimuthal direction involves only µs and its gradients, and the balance in the radial direction involves both µs and kappas and their gradients. By further exploiting recent developments in laser-based flow measuring techniques, the surface velocities and their gradients which appear in the two equations can be measured directly. The surface tension gradient, which appears in the radial balance equation, is incorporated from the equation of state for the surfactant system and direct measurements of the surfactant surface concentration distribution. The stress balance equations are then ordinary differential equations in the surface viscosities as functions of radial position, which can be readily integrated. Since c is measured as a function of radial position, we then have a direct measurement of µs and kappas as functions of c. Numerical computations of the Navier-Stokes equations are performed to determine the appropriate conditions to achieve the requisite secondary flow. Copyright 1998 Academic Press.

Technical Guidelines on Performing a Sediment Erosion and Deposition Assessment (SEDA) at Superfund Sites

DTIC Science & Technology

2014-09-01

that 1) identifies the processes and mechanisms that might result in erosion, 2) determines the most appropriate methods to use in assessing...fluid mechanics , driving forces of flows in surface waters, turbulence, hydrodynamic governing equations, scale analysis, and types of hydrodynamic...2 requires the following: 1) establishing the MNR mechanisms responsible for declining contaminant concentrations (e.g., burial as the major

The chemical (not mechanical) paradigm of thermodynamics of colloid and interface science.

PubMed

Kaptay, George

2018-06-01

In the most influential monograph on colloid and interfacial science by Adamson three fundamental equations of "physical chemistry of surfaces" are identified: the Laplace equation, the Kelvin equation and the Gibbs adsorption equation, with a mechanical definition of surface tension by Young as a starting point. Three of them (Young, Laplace and Kelvin) are called here the "mechanical paradigm". In contrary it is shown here that there is only one fundamental equation of the thermodynamics of colloid and interface science and all the above (and other) equations of this field follow as its derivatives. This equation is due to chemical thermodynamics of Gibbs, called here the "chemical paradigm", leading to the definition of surface tension and to 5 rows of equations (see Graphical abstract). The first row is the general equation for interfacial forces, leading to the Young equation, to the Bakker equation and to the Laplace equation, etc. Although the principally wrong extension of the Laplace equation formally leads to the Kelvin equation, using the chemical paradigm it becomes clear that the Kelvin equation is generally incorrect, although it provides right results in special cases. The second row of equations provides equilibrium shapes and positions of phases, including sessile drops of Young, crystals of Wulff, liquids in capillaries, etc. The third row of equations leads to the size-dependent equations of molar Gibbs energies of nano-phases and chemical potentials of their components; from here the corrected versions of the Kelvin equation and its derivatives (the Gibbs-Thomson equation and the Freundlich-Ostwald equation) are derived, including equations for more complex problems. The fourth row of equations is the nucleation theory of Gibbs, also contradicting the Kelvin equation. The fifth row of equations is the adsorption equation of Gibbs, and also the definition of the partial surface tension, leading to the Butler equation and to its derivatives, including the Langmuir equation and the Szyszkowski equation. Positioning the single fundamental equation of Gibbs into the thermodynamic origin of colloid and interface science leads to a coherent set of correct equations of this field. The same provides the chemical (not mechanical) foundation of the chemical (not mechanical) discipline of colloid and interface science. Copyright © 2018 Elsevier B.V. All rights reserved.

Dynamic analysis of a hollow cylinder subject to a dual traveling force imposed on its inner surface

NASA Astrophysics Data System (ADS)

Lee, Sooyoung; Seok, Jongwon

2015-03-01

The dynamic behavior of a hollow cylinder under a dual traveling force applied to the inner surface is investigated in this study. The cylinder is constrained at both the top and bottom surfaces not to move in the length direction but free in other directions. And a dual force travels at a constant velocity along the length direction on the inner surface of the hollow cylinder. The resulting governing field equations and the associated boundary conditions are ruled by the general Hooke's law. Due to the nature of the field equations, proper adjoint system of equations and biorthogonality conditions were derived in a precise and detailed manner. To solve these field equations in this study, the method of separation of variable is used and the method of Fro¨benius is employed for the differential equations in the radial direction. Using the field equations, the eigenanalyses on both the original and its adjoint system were performed with great care, which results in the eigenfunction sets of both systems. The biorthogonality conditions were applied to the field equations to obtain the discretized equation for each mode. Using the solutions of the discretized equations that account for the boundary forcing terms, the critical speed for a dual traveling force for each mode could be computed.

Estimating changes to groundwater discharge temperature under altered climate conditions

NASA Astrophysics Data System (ADS)

Manga, M.; Burns, E. R.; Zhu, Y.; Zhan, H.; Williams, C. F.; Ingebritsen, S.; Dunham, J.

2017-12-01

Changes in groundwater temperature resulting from climate-driven boundary conditions (recharge and land surface temperature) can be evaluated using new analytical solutions of the groundwater heat transport equation. These steady-state solutions account for land-surface boundary conditions, hydrology, and geothermal and viscous heating, and can be used to identify the key physical processes that control thermal responses of groundwater-fed ecosystems to climate change, in particular (1) groundwater recharge rate and temperature and (2) land-surface temperature transmitted through the vadose zone. Also, existing transient solutions of conduction are compared with a new solution for advective transport of heat to estimate the timing of groundwater-discharge response to changes in recharge and land surface temperature. As an example, the new solutions are applied to the volcanic Medicine Lake highlands, California, USA, and associated Fall River Springs complexes that host groundwater-dependent ecosystems. In this system, high-elevation groundwater temperatures are strongly affected only by recharge conditions, but as the vadose zone thins away from the highlands, changes to the average annual land surface temperature will also influence groundwater temperatures. Transient response to temperature change depends on both the conductive timescale and the rate at which recharge delivers heat. Most of the thermal response of groundwater at high elevations will occur within 20 years of a shift in recharge temperatures, but the lower-elevation Fall River Springs will respond more slowly, with about half of the conductive response occurring within the first 20 years and about half of the advective response to higher recharge temperatures occurring in approximately 60 years.

Concentration Dependences of the Surface Tension and Density of Solutions of Acetone-Ethanol-Water Systems at 293 K

NASA Astrophysics Data System (ADS)

Dadashev, R. Kh.; Dzhambulatov, R. S.; Mezhidov, V. Kh.; Elimkhanov, D. Z.

2018-05-01

Concentration dependences of the surface tension and density of solutions of three-component acetone-ethanol-water systems and the bounding binary systems at 273 K are studied. The molar volume, adsorption, and composition of surface layers are calculated. Experimental data and calculations show that three-component solutions are close to ideal ones. The surface tensions of these solutions are calculated using semi-empirical and theoretical equations. Theoretical equations qualitatively convey the concentration dependence of surface tension. A semi-empirical method based on the Köhler equation allows us to predict the concentration dependence of surface tension within the experimental error.

Comment on 'Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies'.

PubMed

Gutman, E M

2010-10-27

In a recent publication by Olives (2010 J. Phys.: Condens. Matter 22 085005) he studied 'the thermodynamics and mechanics of the surface of a deformable body, following and refining the general approach of Gibbs' and believed that 'a new definition of the surface stress is given'. However, using the usual way of deriving the equations of Gibbs-Duhem type the author, nevertheless, has fallen into a mathematical discrepancy because he has tried to unite in one equation different thermodynamic systems and 'a new definition of the surface stress' has appeared known in the usual theory of elasticity.

Kinetics modelling of color deterioration during thermal processing of tomato paste with the use of response surface methodology

NASA Astrophysics Data System (ADS)

Ganje, Mohammad; Jafari, Seid Mahdi; Farzaneh, Vahid; Malekjani, Narges

2018-06-01

To study the kinetics of color degradation, the tomato paste was designed to be processed at three different temperatures including 60, 70 and 80 °C for 25, 50, 75 and 100 min. a/b ratio, total color difference, saturation index and hue angle were calculated with the use of three main color parameters including L (lightness), a (redness-greenness) and b (yellowness-blueness) values. Kinetics of color degradation was developed by Arrhenius equation and the alterations were modelled with the use of response surface methodology (RSM). It was detected that all of the studied responses followed a first order reaction kinetics with an exception in TCD parameter (zeroth order). TCD and a/b respectively with the highest and lowest activation energy presented the highest sensitivity to the temperature alterations. The maximum and minimum rates of alterations were observed by TCD and b parameters, respectively. It was obviously determined that all of the studied parameters (responses) were affected by the selected independent parameters.

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

Growing surfaces with anomalous diffusion: Results for the fractal Kardar-Parisi-Zhang equation

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2003-09-01

In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. It is shown that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, the self-consistent expansion (SCE) is used to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the fractal KPZ equation is suggested and the upper critical dimension of this model is discussed.

Active motion on curved surfaces

NASA Astrophysics Data System (ADS)

Castro-Villarreal, Pavel; Sevilla, Francisco J.

2018-05-01

A theoretical analysis of active motion on curved surfaces is presented in terms of a generalization of the telegrapher equation. Such a generalized equation is explicitly derived as the polar approximation of the hierarchy of equations obtained from the corresponding Fokker-Planck equation of active particles diffusing on curved surfaces. The general solution to the generalized telegrapher equation is given for a pulse with vanishing current as initial data. Expressions for the probability density and the mean squared geodesic displacement are given in the limit of weak curvature. As an explicit example of the formulated theory, the case of active motion on the sphere is presented, where oscillations observed in the mean squared geodesic displacement are explained.

Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium

USGS Publications Warehouse

Iverson, R.M.

1993-01-01

Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass conservation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameter B, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of Iverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data. ?? 1993 International Association for Mathematical Geology.

Multiple Equilibria Associated with Response of the ITCZ to Seasonal SST Forcing

NASA Technical Reports Server (NTRS)

Chao, Winston C.

1998-01-01

Supported by numerical experiment results, the abrupt change of the location of the intertropical convergence zone (ITCZ), from the equatorial trough flow regime to the monsoon trough flow regime is interpreted as a subcritical instability. The existence of these multiple quasi-equilibria is due to the balance of two "forces" on the ITCZ: one toward the equator, due to the earth's rotation, has a nonlinear latitudinal dependence; and the other toward the latitude of the sea surface (or ground) temperature peak has a relatively linear latitudinal dependence. This work pivots on the finding that the ITCZ and Hadley circulation can still exist without the pole-to-equator gradient of radiative-convective equilibrium temperature.

Thermal diffusivity determination using heterodyne phase insensitive transient grating spectroscopy

NASA Astrophysics Data System (ADS)

Dennett, Cody A.; Short, Michael P.

2018-06-01

The elastic and thermal transport properties of opaque materials may be measured using transient grating spectroscopy (TGS) by inducing and monitoring periodic excitations in both reflectivity and surface displacement. The "phase grating" response encodes both properties of interest, but complicates quantitative analysis by convolving temperature dynamics with surface displacement dynamics. Thus, thermal transport characteristics are typically determined using the "amplitude grating" response to isolate the surface temperature dynamics. However, this signal character requires absolute heterodyne phase calibration and contains no elastic property information. Here, a method is developed by which phase grating TGS measurements may be consistently analyzed to determine thermal diffusivity with no prior knowledge of the expected properties. To demonstrate this ability, the wavelength-dependent 1D effective thermal diffusivity of pure germanium is measured using this type of response and found to be consistent with theoretical predictions made by solving the Boltzmann transport equation. This ability to determine the elastic and thermal properties from a single set of TGS measurements will be particularly advantageous for new in situ implementations of the technique being used to study dynamic materials systems.

Equations for obtaining melting points for the ternary system ethylene glycol/sodium chloride/water and their application to cryopreservation.

PubMed

Woods, E J; Zieger, M A; Gao, D Y; Critser, J K

1999-06-01

The present study describes the H(2)O-NaCl-ethylene glycol ternary system by using a differential scanning calorimeter to measure melting points (T(m)) of four different ratios (R) of ethylene glycol to NaCl and then devising equations to fit the experimental measurements. Ultimately an equation is derived which characterizes the liquidus surface above the eutectic for any R value in the system. This study focuses on ethylene glycol in part because of recent evidence indicating it may be less toxic to pancreatic islets than Me(2)SO, which is currently used routinely for islet cryopreservation. The resulting physical data and previously determined information regarding the osmotic characteristics of canine pancreatic islets are combined in a mathematical model to describe the volumetric response to equilibrium-rate freezing in varying initial concentrations of ethylene glycol. Copyright 1999 Academic Press.

Simple equations guide high-frequency surface-wave investigation techniques

USGS Publications Warehouse

Xia, J.; Xu, Y.; Chen, C.; Kaufmann, R.D.; Luo, Y.

2006-01-01

We discuss five useful equations related to high-frequency surface-wave techniques and their implications in practice. These equations are theoretical results from published literature regarding source selection, data-acquisition parameters, resolution of a dispersion curve image in the frequency-velocity domain, and the cut-off frequency of high modes. The first equation suggests Rayleigh waves appear in the shortest offset when a source is located on the ground surface, which supports our observations that surface impact sources are the best source for surface-wave techniques. The second and third equations, based on the layered earth model, reveal a relationship between the optimal nearest offset in Rayleigh-wave data acquisition and seismic setting - the observed maximum and minimum phase velocities, and the maximum wavelength. Comparison among data acquired with different offsets at one test site confirms the better data were acquired with the suggested optimal nearest offset. The fourth equation illustrates that resolution of a dispersion curve image at a given frequency is directly proportional to the product of a length of a geophone array and the frequency. We used real-world data to verify the fourth equation. The last equation shows that the cut-off frequency of high modes of Love waves for a two-layer model is determined by shear-wave velocities and the thickness of the top layer. We applied this equation to Rayleigh waves and multi-layer models with the average velocity and obtained encouraging results. This equation not only endows with a criterion to distinguish high modes from numerical artifacts but also provides a straightforward means to resolve the depth to the half space of a layered earth model. ?? 2005 Elsevier Ltd. All rights reserved.

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

NASA Technical Reports Server (NTRS)

Hu, Fang; Pizzo, Michelle E.; Nark, Douglas M.

2017-01-01

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Reaction formulation for radiation and scattering from plates, corner reflectors and dielectric-coated cylinders

NASA Technical Reports Server (NTRS)

Wang, N. N.

1974-01-01

The reaction concept is employed to formulate an integral equation for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders. The surface-current density on the conducting surface is expanded with subsectional bases. The dielectric layer is modeled with polarization currents radiating in free space. Maxwell's equation and the boundary conditions are employed to express the polarization-current distribution in terms of the surface-current density on the conducting surface. By enforcing reaction tests with an array of electric test sources, the moment method is employed to reduce the integral equation to a matrix equation. Inversion of the matrix equation yields the current distribution, and the scattered field is then obtained by integrating the current distribution. The theory, computer program and numerical results are presented for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders.

Surface-slip equations for multicomponent, nonequilibrium air flow

NASA Technical Reports Server (NTRS)

Gupta, Roop N.; Scott, Carl D.; Moss, James N.; Goglia, Gene

1985-01-01

Equations are presented for the surface slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds-number, high-altitude flight regime of a space vehicle. These are obtained from closed-form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities have been obtained in a form which can readily be employed in flow-field computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate species-concentration boundary condition for a multicomponent mixture in absence of slip.

The evolution of methods for noise prediction of high speed rotors and propellers in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1986-01-01

Linear wave equation models which have been used over the years at NASA Langley for describing noise emissions from high speed rotating blades are summarized. The noise sources are assumed to lie on a moving surface, and analysis of the situation has been based on the Ffowcs Williams-Hawkings (FW-H) equation. Although the equation accounts for two surface and one volume source, the NASA analyses have considered only the surface terms. Several variations on the FW-H model are delineated for various types of applications, noting the computational benefits of removing the frequency dependence of the calculations. Formulations are also provided for compact and noncompact sources, and features of Long's subsonic integral equation and Farassat's high speed integral equation are discussed. The selection of subsonic or high speed models is dependent on the Mach number of the blade surface where the source is located.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rofouie, P.; Rey, A. D., E-mail: alejandro.rey@mail.mcgill.ca; Pasini, D.

Periodic surface nano-wrinkling is found throughout biological liquid crystalline materials, such as collagen films, spider silk gland ducts, exoskeleton of beetles, and flower petals. These surface ultrastructures are responsible for structural colors observed in some beetles and plants that can dynamically respond to external conditions, such as humidity and temperature. In this paper, the formation of the surface undulations is investigated through the interaction of anisotropic interfacial tension, swelling through hydration, and capillarity at free surfaces. Focusing on the cellulosic cholesteric liquid crystal (CCLC) material model, the generalized shape equation for anisotropic interfaces using the Cahn-Hoffman capillarity vector and themore » Rapini-Papoular anchoring energy are applied to analyze periodic nano-wrinkling in plant-based plywood free surfaces with water-induced cholesteric pitch gradients. Scaling is used to derive the explicit relations between the undulations’ amplitude expressed as a function of the anchoring strength and the spatially varying pitch. The optical responses of the periodic nano-structured surfaces are studied through finite difference time domain simulations indicating that CCLC surfaces with spatially varying pitch reflect light in a wavelength higher than that of a CCLC’s surface with constant pitch. This structural color change is controlled by the pitch gradient through hydration. All these findings provide a foundation to understand structural color phenomena in nature and for the design of optical sensor devices.« less

Thermal effect of climate change on groundwater-fed ecosystems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burns, Erick R.; Zhu, Yonghui; Zhan, Hongbin

Groundwater temperature changes will lag surface temperature changes from a changing climate. Steady state solutions of the heat-transport equations are used to identify key processes that control the long-term thermal response of springs and other groundwater discharge to climate change, in particular changes in (1) groundwater recharge rate and temperature and (2) land-surface temperature transmitted through the vadose zone. Transient solutions are developed to estimate the time required for new thermal signals to arrive at ecosystems. The solution is applied to the volcanic Medicine Lake highlands, California, USA, and associated springs complexes that host groundwater-dependent ecosystems. In this system, uppermore » basin groundwater temperatures are strongly affected only by recharge conditions. However, as the vadose zone thins away from the highlands, changes in the average annual land-surface temperature also influence groundwater temperatures. Transient response to temperature change depends on both the conductive time scale and the rate at which recharge delivers heat. Most of the thermal response of groundwater at high elevations will occur within 20 years of a shift in recharge temperatures, but the large lower elevation springs will respond more slowly, with about half of the conductive response occurring within the first 20 years and about half of the advective response to higher recharge temperatures occurring in approximately 60 years.« less

Thermal effect of climate change on groundwater-fed ecosystems

DOE PAGES

Burns, Erick R.; Zhu, Yonghui; Zhan, Hongbin; ...

2017-04-24

Groundwater temperature changes will lag surface temperature changes from a changing climate. Steady state solutions of the heat-transport equations are used to identify key processes that control the long-term thermal response of springs and other groundwater discharge to climate change, in particular changes in (1) groundwater recharge rate and temperature and (2) land-surface temperature transmitted through the vadose zone. Transient solutions are developed to estimate the time required for new thermal signals to arrive at ecosystems. The solution is applied to the volcanic Medicine Lake highlands, California, USA, and associated springs complexes that host groundwater-dependent ecosystems. In this system, uppermore » basin groundwater temperatures are strongly affected only by recharge conditions. However, as the vadose zone thins away from the highlands, changes in the average annual land-surface temperature also influence groundwater temperatures. Transient response to temperature change depends on both the conductive time scale and the rate at which recharge delivers heat. Most of the thermal response of groundwater at high elevations will occur within 20 years of a shift in recharge temperatures, but the large lower elevation springs will respond more slowly, with about half of the conductive response occurring within the first 20 years and about half of the advective response to higher recharge temperatures occurring in approximately 60 years.« less

Development of a Response Surface Thermal Model for Orion Mated to the International Space Station

NASA Technical Reports Server (NTRS)

Miller, Stephen W.; Meier, Eric J.

2010-01-01

A study was performed to determine if a Design of Experiments (DOE)/Response Surface Methodology could be applied to on-orbit thermal analysis and produce a set of Response Surface Equations (RSE) that accurately predict vehicle temperatures. The study used an integrated thermal model of the International Space Station and the Orion Outer mold line model. Five separate factors were identified for study: yaw, pitch, roll, beta angle, and the environmental parameters. Twenty external Orion temperatures were selected as the responses. A DOE case matrix of 110 runs was developed. The data from these cases were analyzed to produce an RSE for each of the temperature responses. The initial agreement between the engineering data and the RSE predictions was encouraging, although many RSEs had large uncertainties on their predictions. Fourteen verification cases were developed to test the predictive powers of the RSEs. The verification showed mixed results with some RSE predicting temperatures matching the engineering data within the uncertainty bands, while others had very large errors. While this study to not irrefutably prove that the DOE/RSM approach can be applied to on-orbit thermal analysis, it does demonstrate that technique has the potential to predict temperatures. Additional work is needed to better identify the cases needed to produce the RSEs

Thermal effect of climate change on groundwater-fed ecosystems

NASA Astrophysics Data System (ADS)

Burns, Erick R.; Zhu, Yonghui; Zhan, Hongbin; Manga, Michael; Williams, Colin F.; Ingebritsen, Steven E.; Dunham, Jason B.

2017-04-01

Groundwater temperature changes will lag surface temperature changes from a changing climate. Steady state solutions of the heat-transport equations are used to identify key processes that control the long-term thermal response of springs and other groundwater discharge to climate change, in particular changes in (1) groundwater recharge rate and temperature and (2) land-surface temperature transmitted through the vadose zone. Transient solutions are developed to estimate the time required for new thermal signals to arrive at ecosystems. The solution is applied to the volcanic Medicine Lake highlands, California, USA, and associated springs complexes that host groundwater-dependent ecosystems. In this system, upper basin groundwater temperatures are strongly affected only by recharge conditions. However, as the vadose zone thins away from the highlands, changes in the average annual land-surface temperature also influence groundwater temperatures. Transient response to temperature change depends on both the conductive time scale and the rate at which recharge delivers heat. Most of the thermal response of groundwater at high elevations will occur within 20 years of a shift in recharge temperatures, but the large lower elevation springs will respond more slowly, with about half of the conductive response occurring within the first 20 years and about half of the advective response to higher recharge temperatures occurring in approximately 60 years.

Thermal effect of climate change on groundwater-fed ecosystems

USGS Publications Warehouse

Burns, Erick; Zhu, Yonghui; Zhan, Hongbin; Manga, Michael; Williams, Colin F.; Ingebritsen, Steven E.; Dunham, Jason B.

2017-01-01

Groundwater temperature changes will lag surface temperature changes from a changing climate. Steady state solutions of the heat-transport equations are used to identify key processes that control the long-term thermal response of springs and other groundwater discharge to climate change, in particular changes in (1) groundwater recharge rate and temperature and (2) land-surface temperature transmitted through the vadose zone. Transient solutions are developed to estimate the time required for new thermal signals to arrive at ecosystems. The solution is applied to the volcanic Medicine Lake highlands, California, USA, and associated springs complexes that host groundwater-dependent ecosystems. In this system, upper basin groundwater temperatures are strongly affected only by recharge conditions. However, as the vadose zone thins away from the highlands, changes in the average annual land-surface temperature also influence groundwater temperatures. Transient response to temperature change depends on both the conductive time scale and the rate at which recharge delivers heat. Most of the thermal response of groundwater at high elevations will occur within 20 years of a shift in recharge temperatures, but the large lower elevation springs will respond more slowly, with about half of the conductive response occurring within the first 20 years and about half of the advective response to higher recharge temperatures occurring in approximately 60 years.

Low-frequency surface waves on semi-bounded magnetized quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moradi, Afshin, E-mail: a.moradi@kut.ac.ir

2016-08-15

The propagation of low-frequency electrostatic surface waves on the interface between a vacuum and an electron-ion quantum plasma is studied in the direction perpendicular to an external static magnetic field which is parallel to the interface. A new dispersion equation is derived by employing both the quantum magnetohydrodynamic and Poisson equations. It is shown that the dispersion equations for forward and backward-going surface waves are different from each other.

An analysis of a charring ablator with thermal nonequilibrium, chemical kinetics, and mass transfer

NASA Technical Reports Server (NTRS)

Clark, R. K.

1973-01-01

The differential equations governing the transient response of a one-dimensional ablative thermal protection system are presented for thermal nonequilibrium between the pyrolysis gases and the char layer and with finite rate chemical reactions occurring. The system consists of three layers (the char layer, the uncharred layer, and an optical insulation layer) with concentrated heat sinks at the back surface and between the second and third layers. The equations are solved numerically by using a modified implicit finite difference scheme to obtain solutions for the thickness of the charred and uncharred layers, surface recession and pyrolysis rates, solid temperatures, porosity profiles, and profiles of pyrolysis-gas temperature, pressure, composition, and flow rate. Good agreement is obtained between numerical results and exact solutions for a number of simplified cases. The complete numerical analysis is used to obtain solutions for an ablative system subjected to a constant heating environment. Effects of thermal, chemical, and mass transfer processes are shown.

Do sophisticated epistemic beliefs predict meaningful learning? Findings from a structural equation model of undergraduate biology learning

NASA Astrophysics Data System (ADS)

Lee, Silvia Wen-Yu; Liang, Jyh-Chong; Tsai, Chin-Chung

2016-10-01

This study investigated the relationships among college students' epistemic beliefs in biology (EBB), conceptions of learning biology (COLB), and strategies of learning biology (SLB). EBB includes four dimensions, namely 'multiple-source,' 'uncertainty,' 'development,' and 'justification.' COLB is further divided into 'constructivist' and 'reproductive' conceptions, while SLB represents deep strategies and surface learning strategies. Questionnaire responses were gathered from 303 college students. The results of the confirmatory factor analysis and structural equation modelling showed acceptable model fits. Mediation testing further revealed two paths with complete mediation. In sum, students' epistemic beliefs of 'uncertainty' and 'justification' in biology were statistically significant in explaining the constructivist and reproductive COLB, respectively; and 'uncertainty' was statistically significant in explaining the deep SLB as well. The results of mediation testing further revealed that 'uncertainty' predicted surface strategies through the mediation of 'reproductive' conceptions; and the relationship between 'justification' and deep strategies was mediated by 'constructivist' COLB. This study provides evidence for the essential roles some epistemic beliefs play in predicting students' learning.

Recommendations for the U.S. Coast Guard Survival Prediction Tool

DTIC Science & Technology

2009-04-01

model. Not enough data to support modeling of how alcohol impairs swimming ability. Experimental evidence shows no significant cooling effect 50...equation. When matched for physical attributes, females cool more quickly than males due to lower metabolic response and greater surface-area-to-mass...April 2009 However, the average female has about 10% more body fat than the average male so, on average, males cool faster than females. (Tipton

Plasmon dispersion in a multilayer solid torus in terms of three-term vector recurrence relations and matrix continued fractions

DOE PAGES

Garapati, K. V.; Bagherian, M.; Passian, A.; ...

2018-01-03

Toroidal confinement, which has played a crucial role in magnetized plasmas and Tokamak physics, is emerging as an effective means to obtain useful electronic and optical response in solids. In particular, excitation of surface plasmons in metal nanorings by photons or electrons finds important applications due to the engendered field distribution and electromagnetic energy confinement. However, in contrast to the case of a plasma, often the solid nanorings are multilayered and/or embedded in a medium. The non-simply connected geometry of the torus results in surface modes that are not linearly independent. A three-term difference equation was recently shown to arisemore » when seeking the nonretarded plasmon dispersion relations for a stratified solid torus (Garapati et al 2017 Phys. Rev. B 95 165422). The reported generalized plasmon dispersion relations are here investigated in terms of the involved matrix continued fractions and their convergence properties including the determinant forms of the dispersion relations obtained for computing the plasmon eigenmodes. We also present the intricacies of the derivation and properties of the Green's function employed to solve the three term amplitude equation that determines the response of the toroidal structure to arbitrary external excitations.« less

System Synthesis in Preliminary Aircraft Design using Statistical Methods

NASA Technical Reports Server (NTRS)

DeLaurentis, Daniel; Mavris, Dimitri N.; Schrage, Daniel P.

1996-01-01

This paper documents an approach to conceptual and preliminary aircraft design in which system synthesis is achieved using statistical methods, specifically design of experiments (DOE) and response surface methodology (RSM). These methods are employed in order to more efficiently search the design space for optimum configurations. In particular, a methodology incorporating three uses of these techniques is presented. First, response surface equations are formed which represent aerodynamic analyses, in the form of regression polynomials, which are more sophisticated than generally available in early design stages. Next, a regression equation for an overall evaluation criterion is constructed for the purpose of constrained optimization at the system level. This optimization, though achieved in a innovative way, is still traditional in that it is a point design solution. The methodology put forward here remedies this by introducing uncertainty into the problem, resulting a solutions which are probabilistic in nature. DOE/RSM is used for the third time in this setting. The process is demonstrated through a detailed aero-propulsion optimization of a high speed civil transport. Fundamental goals of the methodology, then, are to introduce higher fidelity disciplinary analyses to the conceptual aircraft synthesis and provide a roadmap for transitioning from point solutions to probabalistic designs (and eventually robust ones).

Plasmon dispersion in a multilayer solid torus in terms of three-term vector recurrence relations and matrix continued fractions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garapati, K. V.; Bagherian, M.; Passian, A.

Toroidal confinement, which has played a crucial role in magnetized plasmas and Tokamak physics, is emerging as an effective means to obtain useful electronic and optical response in solids. In particular, excitation of surface plasmons in metal nanorings by photons or electrons finds important applications due to the engendered field distribution and electromagnetic energy confinement. However, in contrast to the case of a plasma, often the solid nanorings are multilayered and/or embedded in a medium. The non-simply connected geometry of the torus results in surface modes that are not linearly independent. A three-term difference equation was recently shown to arisemore » when seeking the nonretarded plasmon dispersion relations for a stratified solid torus (Garapati et al 2017 Phys. Rev. B 95 165422). The reported generalized plasmon dispersion relations are here investigated in terms of the involved matrix continued fractions and their convergence properties including the determinant forms of the dispersion relations obtained for computing the plasmon eigenmodes. We also present the intricacies of the derivation and properties of the Green's function employed to solve the three term amplitude equation that determines the response of the toroidal structure to arbitrary external excitations.« less

Solving the incompressible surface Navier-Stokes equation by surface finite elements

NASA Astrophysics Data System (ADS)

Reuther, Sebastian; Voigt, Axel

2018-01-01

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.

The response of an ocean general circulation model to surface wind stress produced by an atmospheric general circulation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, B.; Schneider, E.K.

1995-10-01

Two surface wind stress datasets for 1979-91, one based on observations and the other from an investigation of the COLA atmospheric general circulation model (AGCM) with prescribed SST, are used to drive the GFDL ocean general circulation model. These two runs are referred to as the control and COLA experiments, respectively. Simulated SST and upper-ocean heat contents (HC) in the tropical Pacific Ocean are compared with observations and between experiments. Both simulation reproduced the observed mean SST and HC fields as well as their annual cycles realistically. Major errors common to both runs are colder than observed SST in themore » eastern equatorial ocean and HC in the western Pacific south of the equator, with errors generally larger in the COLA experiment. New errors arising from the AGCM wind forcing include higher SST near the South American coast throughout the year and weaker HC gradients along the equator in boreal spring. The former is associated with suppressed coastal upwelling by weak along shore AGCM winds, and the latter is caused by weaker equatorial easterlies in boreal spring. The low-frequency ENSO fluctuations are also realistic for both runs. Correlations between the observed and simulated SST anomalies from the COLA simulation are as high as those from the control run in the central equatorial Pacific. A major problem in the COLA simulation is the appearance of unrealistic tropical cold anomalies during the boreal spring of mature El Nino years. These anomalies propagate along the equator from the western Pacific to the eastern coast in about three months, and temporarily eliminate the warm SST and HC anomalies in the eastern Pacific. This erroneous oceanic response in the COLA simulation is caused by a reversal of the westerly wind anomalies on the equator, associated with an unrealistic southward shift of the ITCZ in boreal spring during El Nino events. 66 refs., 16 figs.« less

Reactive solute transport in streams: A surface complexation approach for trace metal sorption

USGS Publications Warehouse

Runkel, Robert L.; Kimball, Briant A.; McKnight, Diane M.; Bencala, Kenneth E.

1999-01-01

A model for trace metals that considers in-stream transport, metal oxide precipitation-dissolution, and pH-dependent sorption is presented. Linkage between a surface complexation submodel and the stream transport equations provides a framework for modeling sorption onto static and/or dynamic surfaces. A static surface (e.g., an iron- oxide-coated streambed) is defined as a surface with a temporally constant solid concentration. Limited contact between solutes in the water column and the static surface is considered using a pseudokinetic approach. A dynamic surface (e.g., freshly precipitated metal oxides) has a temporally variable solid concentration and is in equilibrium with the water column. Transport and deposition of solute mass sorbed to the dynamic surface is represented in the stream transport equations that include precipitate settling. The model is applied to a pH-modification experiment in an acid mine drainage stream. Dissolved copper concentrations were depressed for a 3 hour period in response to the experimentally elevated pH. After passage of the pH front, copper was desorbed, and dissolved concentrations returned to ambient levels. Copper sorption is modeled by considering sorption to aged hydrous ferric oxide (HFO) on the streambed (static surface) and freshly precipitated HFO in the water column (dynamic surface). Comparison of parameter estimates with reported values suggests that naturally formed iron oxides may be more effective in removing trace metals than synthetic oxides used in laboratory studies. The model's ability to simulate pH, metal oxide precipitation-dissolution, and pH-dependent sorption provides a means of evaluating the complex interactions between trace metal chemistry and hydrologic transport at the field scale.

Method of sections in analytical calculations of pneumatic tires

NASA Astrophysics Data System (ADS)

Tarasov, V. N.; Boyarkina, I. V.

2018-01-01

Analytical calculations in the pneumatic tire theory are more preferable in comparison with experimental methods. The method of section of a pneumatic tire shell allows to obtain equations of intensities of internal forces in carcass elements and bead rings. Analytical dependencies of intensity of distributed forces have been obtained in tire equator points, on side walls (poles) and pneumatic tire bead rings. Along with planes in the capacity of secant surfaces cylindrical surfaces are used for the first time together with secant planes. The tire capacity equation has been obtained using the method of section, by means of which a contact body is cut off from the tire carcass along the contact perimeter by the surface which is normal to the bearing surface. It has been established that the Laplace equation for the solution of tasks of this class of pneumatic tires contains two unknown values that requires the generation of additional equations. The developed computational schemes of pneumatic tire sections and new equations allow to accelerate the pneumatic tire structure improvement process during engineering.

Boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Panaras, Argyris G.

1987-01-01

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

Inhomogeneous Jacobi equation for minimal surfaces and perturbative change in holographic entanglement entropy

NASA Astrophysics Data System (ADS)

Ghosh, Avirup; Mishra, Rohit

2018-04-01

The change in holographic entanglement entropy (HEE) for small fluctuations about pure anti-de Sitter (AdS) is obtained by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal surface. However it is known that change in the embedding appears at second order or higher. It was shown that these changes in the embedding can be calculated in the 2 +1 dimensional case by solving a "generalized geodesic deviation equation." We generalize this result to arbitrary dimensions by deriving an inhomogeneous form of the Jacobi equation for minimal surfaces. The solutions of this equation map a minimal surface in a given space time to a minimal surface in a space time which is a perturbation over the initial space time. Using this we perturbatively calculate the changes in HEE up to second order for boosted black brane like perturbations over AdS4.

Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation

NASA Astrophysics Data System (ADS)

Chun, Sehun

2017-07-01

Applying the method of moving frames to Maxwell's equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell's equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has been available only to isotropic material, because of the difficulty of satisfying the Rankine-Hugoniot conditions in anisotropic media. The second is to solve numerically Maxwell's equations on curved surfaces without the metric tensor and composite meshes. For numerical validation, spectral convergences are displayed for both two-dimensional anisotropic media and isotropic spheres. In the first application, invisible two-dimensional metamaterial cloaks are simulated with a relatively coarse mesh by both the lossless Drude model and the piecewisely-parametered layered model. In the second application, extremely low frequency propagation on various surfaces such as spheres, irregular surfaces, and non-convex surfaces is demonstrated.

Global boundary flattening transforms for acoustic propagation under rough sea surfaces.

PubMed

Oba, Roger M

2010-07-01

This paper introduces a conformal transform of an acoustic domain under a one-dimensional, rough sea surface onto a domain with a flat top. This non-perturbative transform can include many hundreds of wavelengths of the surface variation. The resulting two-dimensional, flat-topped domain allows direct application of any existing, acoustic propagation model of the Helmholtz or wave equation using transformed sound speeds. Such a transform-model combination applies where the surface particle velocity is much slower than sound speed, such that the boundary motion can be neglected. Once the acoustic field is computed, the bijective (one-to-one and onto) mapping permits the field interpolation in terms of the original coordinates. The Bergstrom method for inverse Riemann maps determines the transform by iterated solution of an integral equation for a surface matching term. Rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the Helmholtz equation.

Sea surface temperature: Observations from geostationary satellites

NASA Astrophysics Data System (ADS)

Bates, John J.; Smith, William L.

1985-11-01

A procedure is developed for estimating sea surface temperatures (SST) from multispectral image data acquired from the VISSR atmospheric sounder (VAS) on the geostationary GOES satellites. Theoretical regression equations for two and three infrared window channels are empirically tuned by using clear field of view satellite radiances matched with reports of SST from NOAA fixed environmental buoys from 1982. The empirical regression equations are then used to produce daily regional analyses of SST. The daily analyses are used to study the response of SST's to the passage of Hurricane Alicia (1983) and Hurricane Debbie (1982) and are also used as a first guess surface temperature in the retrieval of atmospheric temperature and moisture profiles over the oceanic regions. Monthly mean SST's for the western North Atlantic and the eastern equatorial Pacific during March and July 1982 were produced for use in the NASA/JPL SST intercomparison workshop series. Workshop results showed VAS SST's have a scatter of 0.8°-1.0°C and a slight warm bias with respect to the other measurements of SST. Subsequently, a second set of VAS/ buoy matches collected during 1983 and 1984 was used to produce a set of bias corrected regression relations for VAS.

Thickness shear mode (TSM) resonators used for biosensing

NASA Astrophysics Data System (ADS)

Bailey, Claude A.; Fiebor, Ben; Yen, Wei; Vodyanoy, Vitaly; Cernosek, Richard W.; Chin, Bryan A.

2002-02-01

The Auburn University Detection and Food Safety Center has demonstrated real-time biosensor for the detection of Salmonella typimhurium, consisting of a thickness shear-mode (TSM) quartz resonator with antibodies immobilized in a Langmuir-Blodgett surface film. Scanning Electron Microscopy (SEM) images of bound Salmonella bacteria to both polished and unpolished TSM resonators were taken to correlate the mass of the bound organism to the Sauerbrey equation. Theoretical frequency shifts for unpolished TSM resonators predicted by the Sauerbrey equation are much smaller than experimentally measured frequency shift. The Salmonella detector operates in a liquid environment. The viscous properties of this liquid overlayer could influence the TSM resonator's response. Various liquid media were studied as a function of temperature (0 to 50 degree(s)C). The chicken exudate samples with varying fat content show coagulation occurring at temperatures above 35 degree(s)C. Kinematic viscosity test were performed with buffer solutions containing varying quantities of Salmonella bacteria. Since the TSM resonators only entrain a boundary layer of fluid near the surface, they do not respond to these background viscous property changes. Bilk viscosity increases when bacteria concentrations are high. This paper describes investigations of TSM resonator surface acoustic interactions - mass, fluid viscosity, and viscoelasticity - that affect the sensor.

A new approach to spherically symmetric junction surfaces and the matching of FLRW regions

NASA Astrophysics Data System (ADS)

Kirchner, U.

2004-08-01

We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann Lemaître Robertson Walker (FLRW) models. We discuss 'vacuum bubbles' and closed open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time.

Active control of wake/blade-row interaction noise through the use of blade surface actuators

NASA Technical Reports Server (NTRS)

Kousen, Kenneth A.; Verdon, Joseph M.

1993-01-01

A combined analytical/computational approach for controlling of the noise generated by wake/blade-row interaction through the use of anti-sound actuators on the blade surfaces is described. A representative two-dimensional section of a fan stage, composed of an upstream fan rotor and a downstream fan exit guide vane (FEGV), is examined. An existing model for the wakes generated by the rotor is analyzed to provide realistic magnitudes for the vortical excitations imposed at the inlet to the FEGV. The acoustic response of the FEGV is determined at multiples of the blade passing frequency (BPF) by using the linearized unsteady flow analysis, LINFLO. Acoustic field contours are presented at each multiple of BPF illustrating the generated acoustic response disturbances. Anti-sound is then provided by placing oscillating control surfaces, whose lengths and locations are specified arbitrarily, on the blades. An analysis is then conducted to determine the complex amplitudes required for the control surface motions to best reduce the noise. It is demonstrated that if the number of acoustic response modes to be controlled is equal to the number of available independent control surfaces, complete noise cancellation can be achieved. A weighted least squares minimization procedure for the control equations is given for cases in which the number of acoustic modes exceeds the number of available control surfaces. The effectiveness of the control is measured by the magnitude of a propagating acoustic response vector, which is related to the circumferentially averaged sound pressure level (SPL), and is minimized by a standard least-squares minimization procedure.

Scaling of heat transfer augmentation due to mechanical distortions in hypervelocity boundary layers

NASA Astrophysics Data System (ADS)

Flaherty, W.; Austin, J. M.

2013-10-01

We examine the response of hypervelocity boundary layers to global mechanical distortions due to concave surface curvature. Surface heat transfer and visual boundary layer thickness data are obtained for a suite of models with different concave surface geometries. Results are compared to predictions using existing approximate methods. Near the leading edge, good agreement is observed, but at larger pressure gradients, predictions diverge significantly from the experimental data. Up to a factor of five underprediction is reported in regions with greatest distortion. Curve fits to the experimental data are compared with surface equations. We demonstrate that reasonable estimates of the laminar heat flux augmentation may be obtained as a function of the local turning angle for all model geometries, even at the conditions of greatest distortion. This scaling may be explained by the application of Lees similarity. As a means of introducing additional local distortions, vortex generators are used to impose streamwise structures into the boundary layer. The response of the large scale vortices to an adverse pressure gradient is investigated. Surface streak evolution is visualized over the different surface geometries using fast response pressure sensitive paint. For a flat plate baseline case, heat transfer augmentation at similar levels to turbulent flow is measured. For the concave geometries, increases in heat transfer by factors up to 2.6 are measured over the laminar values. The scaling of heat transfer with turning angle that is identified for the laminar boundary layer response is found to be robust even in the presence of the imposed vortex structures.

Active control of wake/blade-row interaction noise through the use of blade surface actuators

NASA Astrophysics Data System (ADS)

Kousen, Kenneth A.; Verdon, Joseph M.

1993-12-01

A combined analytical/computational approach for controlling of the noise generated by wake/blade-row interaction through the use of anti-sound actuators on the blade surfaces is described. A representative two-dimensional section of a fan stage, composed of an upstream fan rotor and a downstream fan exit guide vane (FEGV), is examined. An existing model for the wakes generated by the rotor is analyzed to provide realistic magnitudes for the vortical excitations imposed at the inlet to the FEGV. The acoustic response of the FEGV is determined at multiples of the blade passing frequency (BPF) by using the linearized unsteady flow analysis, LINFLO. Acoustic field contours are presented at each multiple of BPF illustrating the generated acoustic response disturbances. Anti-sound is then provided by placing oscillating control surfaces, whose lengths and locations are specified arbitrarily, on the blades. An analysis is then conducted to determine the complex amplitudes required for the control surface motions to best reduce the noise. It is demonstrated that if the number of acoustic response modes to be controlled is equal to the number of available independent control surfaces, complete noise cancellation can be achieved. A weighted least squares minimization procedure for the control equations is given for cases in which the number of acoustic modes exceeds the number of available control surfaces. The effectiveness of the control is measured by the magnitude of a propagating acoustic response vector, which is related to the circumferentially averaged sound pressure level (SPL), and is minimized by a standard least-squares minimization procedure.

Unsteady, Transonic Flow Around Delta Wings Undergoing Coupled and Natural Modes Response: A Multidisciplinary Problem

NASA Technical Reports Server (NTRS)

Menzies, Margaret Anne

1996-01-01

The unsteady, three-dimensional Navier-Stokes equations coupled with the Euler equations of rigid-body dynamics are sequentially solved to simulate and analyze the aerodynamic response of a high angle of attack delta wing undergoing oscillatory motion. The governing equations of fluid flow and dynamics of the multidisciplinary problem are solved using a time-accurate solution of the laminar, unsteady, compressible, full Navier- Stokes equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. The primary model under consideration consists of a 65 deg swept, sharp-edged, cropped delta wing of zero thickness at 20 deg angle of attack. In a freestream of Mach 0.85 and Reynolds number of 3.23 x 10(exp 6), the flow over the upper surface of the wing develops a complex shock system which interacts with the leading-edge primary vortices producing vortex breakdown. The effect of the oscillatory motion of the wing on the vortex breakdown and overall aerodynamic response is detailed to provide insight to the complicated physics associated with unsteady flows and the phenomenon of wing rock. Forced sinusoidal single and coupled mode rolling and pitching motion is presented for the wing in a transonic freestream. The Reynolds number, frequency of oscillation, and the phase angle are varied. Comparison between the single and coupled mode forced rolling and pitching oscillation cases illustrate the effects of coupling the motion. This investigation shows that even when coupled, forced rolling oscillation at a reduced frequency of 2(pi) eliminates the vortex breakdown which results in an increase in lift. The coupling effect for in phase forced oscillations show that the lift coefficient of the pitching-alone case and the rolling-moment coefficient of the rolling-alone case dominate the resulting response. However, with a phase lead in the pitching motion, the coupled motion results in a non-periodic response of the rolling moment. The second class of problems involve releasing the wing in roll to respond to the flowfield. Two models of sharp-edged delta wings, the previous 65 deg swept model and an 80 deg swept, sharp-edged delta wing, are used to observe the aerodynamic response of a wing free to roll in a transonic and subsonic freestream, respectively. These cases demonstrate damped oscillations, self-sustained limit cycle oscillations, and divergent rolling oscillations. Ultimately, an active control model using a mass injection system was applied on the surface of the wing to suppress the self-sustained limit cycle oscillation known as wing rock. Comparisons with experimental investigations complete this study, validating the analysis and illustrating the complex details afforded by computational investigations.

Tangle-Free Mesh Motion for Ablation Simulations

NASA Technical Reports Server (NTRS)

Droba, Justin

2016-01-01

Problems involving mesh motion-which should not be mistakenly associated with moving mesh methods, a class of adaptive mesh redistribution techniques-are of critical importance in numerical simulations of the thermal response of melting and ablative materials. Ablation is the process by which material vaporizes or otherwise erodes due to strong heating. Accurate modeling of such materials is of the utmost importance in design of passive thermal protection systems ("heatshields") for spacecraft, the layer of the vehicle that ensures survival of crew and craft during re-entry. In an explicit mesh motion approach, a complete thermal solve is first performed. Afterwards, the thermal response is used to determine surface recession rates. These values are then used to generate boundary conditions for an a posteriori correction designed to update the location of the mesh nodes. Most often, linear elastic or biharmonic equations are used to model this material response, traditionally in a finite element framework so that complex geometries can be simulated. A simple scheme for moving the boundary nodes involves receding along the surface normals. However, for all but the simplest problem geometries, evolution in time following such a scheme will eventually bring the mesh to intersect and "tangle" with itself, inducing failure. This presentation demonstrates a comprehensive and sophisticated scheme that analyzes the local geometry of each node with help from user-provided clues to eliminate the tangle and enable simulations on a wide-class of difficult problem geometries. The method developed is demonstrated for linear elastic equations but is general enough that it may be adapted to other modeling equations. The presentation will explicate the inner workings of the tangle-free mesh motion algorithm for both two and three-dimensional meshes. It will show abstract examples of the method's success, including a verification problem that demonstrates its accuracy and correctness. The focus of the presentation will be on the algorithm; specifics on how the techniques may be used in spacecraft design will be not discussed.

Stress Regression Analysis of Asphalt Concrete Deck Pavement Based on Orthogonal Experimental Design and Interlayer Contact

NASA Astrophysics Data System (ADS)

Wang, Xuntao; Feng, Jianhu; Wang, Hu; Hong, Shidi; Zheng, Supei

2018-03-01

A three-dimensional finite element box girder bridge and its asphalt concrete deck pavement were established by ANSYS software, and the interlayer bonding condition of asphalt concrete deck pavement was assumed to be contact bonding condition. Orthogonal experimental design is used to arrange the testing plans of material parameters, and an evaluation of the effect of different material parameters in the mechanical response of asphalt concrete surface layer was conducted by multiple linear regression model and using the results from the finite element analysis. Results indicated that stress regression equations can well predict the stress of the asphalt concrete surface layer, and elastic modulus of waterproof layer has a significant influence on stress values of asphalt concrete surface layer.

Mechanics of adsorption-deformation coupling in porous media

NASA Astrophysics Data System (ADS)

Zhang, Yida

2018-05-01

This work extends Coussy's macroscale theory for porous materials interacting with adsorptive fluid mixtures. The solid-fluid interface is treated as an independent phase that obeys its own mass, momentum and energy balance laws. As a result, a surface strain energy term appears in the free energy balance equation of the solid phase, which further introduces the so-called adsorption stress in the constitutive equations of the porous skeleton. This establishes a fundamental link between the adsorption characteristics of the solid-fluid interface and the mechanical response of the porous media. The thermodynamic framework is quite general in that it recovers the coupled conduction laws, Gibbs isotherm and the Shuttleworth's equation for surface stress, and imposes no constraints on the magnitude of deformation and the functional form of the adsorption isotherms. A rich variety of coupling between adsorption and deformation is recovered as a result of combining different poroelastic models (isotropic vs. anisotropic, linear vs. nonlinear) and adsorption models (unary vs. mixture adsorption, uncoupled vs. stretch-dependent adsorption). These predictions are discussed against the backdrop of recent experimental data on coal swelling subjected to CO2 and CO2sbnd CH4 injections, showing the capability and versatility of the theory in capturing adsorption-induced deformation of porous materials.

Aeroelastic Response of Nonlinear Wing Section By Functional Series Technique

NASA Technical Reports Server (NTRS)

Marzocca, Piergiovanni; Librescu, Liviu; Silva, Walter A.

2000-01-01

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Aeroelastic Response of Nonlinear Wing Section by Functional Series Technique

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Marzocca, Piergiovanni

2001-01-01

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

A new solution-adaptive grid generation method for transonic airfoil flow calculations

NASA Technical Reports Server (NTRS)

Nakamura, S.; Holst, T. L.

1981-01-01

The clustering algorithm is controlled by a second-order, ordinary differential equation which uses the airfoil surface density gradient as a forcing function. The solution to this differential equation produces a surface grid distribution which is automatically clustered in regions with large gradients. The interior grid points are established from this surface distribution by using an interpolation scheme which is fast and retains the desirable properties of the original grid generated from the standard elliptic equation approach.

Tunable nano-wrinkling of chiral surfaces: Structure and diffraction optics

NASA Astrophysics Data System (ADS)

Rofouie, P.; Pasini, D.; Rey, A. D.

2015-09-01

Periodic surface nano-wrinkling is found throughout biological liquid crystalline materials, such as collagen films, spider silk gland ducts, exoskeleton of beetles, and flower petals. These surface ultrastructures are responsible for structural colors observed in some beetles and plants that can dynamically respond to external conditions, such as humidity and temperature. In this paper, the formation of the surface undulations is investigated through the interaction of anisotropic interfacial tension, swelling through hydration, and capillarity at free surfaces. Focusing on the cellulosic cholesteric liquid crystal (CCLC) material model, the generalized shape equation for anisotropic interfaces using the Cahn-Hoffman capillarity vector and the Rapini-Papoular anchoring energy are applied to analyze periodic nano-wrinkling in plant-based plywood free surfaces with water-induced cholesteric pitch gradients. Scaling is used to derive the explicit relations between the undulations' amplitude expressed as a function of the anchoring strength and the spatially varying pitch. The optical responses of the periodic nano-structured surfaces are studied through finite difference time domain simulations indicating that CCLC surfaces with spatially varying pitch reflect light in a wavelength higher than that of a CCLC's surface with constant pitch. This structural color change is controlled by the pitch gradient through hydration. All these findings provide a foundation to understand structural color phenomena in nature and for the design of optical sensor devices.

A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.

PubMed

Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc

2012-12-11

The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.

Calculation of transonic flows using an extended integral equation method

NASA Technical Reports Server (NTRS)

Nixon, D.

1976-01-01

An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

Heterogeneous nucleation in multi-component vapor on a partially wettable charged conducting particle. II. The generalized Laplace, Gibbs-Kelvin, and Young equations and application to nucleation.

PubMed

Noppel, M; Vehkamäki, H; Winkler, P M; Kulmala, M; Wagner, P E

2013-10-07

Based on the results of a previous paper [M. Noppel, H. Vehkamäki, P. M. Winkler, M. Kulmala, and P. E. Wagner, J. Chem. Phys. 139, 134107 (2013)], we derive a thermodynamically consistent expression for reversible or minimal work needed to form a dielectric liquid nucleus of a new phase on a charged insoluble conducting sphere within a uniform macroscopic one- or multicomponent mother phase. The currently available model for ion-induced nucleation assumes complete spherical symmetry of the system, implying that the seed ion is immediately surrounded by the condensing liquid from all sides. We take a step further and treat more realistic geometries, where a cap-shaped liquid cluster forms on the surface of the seed particle. We derive the equilibrium conditions for such a cluster. The equalities of chemical potentials of each species between the nucleus and the vapor represent the conditions of chemical equilibrium. The generalized Young equation that relates contact angle with surface tensions, surface excess polarizations, and line tension, also containing the electrical contribution from triple line excess polarization, expresses the condition of thermodynamic equilibrium at three-phase contact line. The generalized Laplace equation gives the condition of mechanical equilibrium at vapor-liquid dividing surface: it relates generalized pressures in neighboring bulk phases at an interface with surface tension, excess surface polarization, and dielectric displacements in neighboring phases with two principal radii of surface curvature and curvatures of equipotential surfaces in neighboring phases at that point. We also re-express the generalized Laplace equation as a partial differential equation, which, along with electrostatic Laplace equations for bulk phases, determines the shape of a nucleus. We derive expressions that are suitable for calculations of the size and composition of a critical nucleus (generalized version of the classical Kelvin-Thomson equation).

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

Comparison of sigma(o) obtained from the conventional definition with sigma(o) appearing in the radar equation for randomly rough surfaces

NASA Technical Reports Server (NTRS)

Levine, D. M.

1981-01-01

A comparison is made of the radar cross section of rough surface calculated in one case from the conventional definition and obtained in the second case directly from the radar equation. The validity of the conventional definition representing the cross section appearing in the radar equation is determined. The analysis is executed in the special case of perfectly conducting, randomly corrugated surfaces in the physical optics limit. The radar equation is obtained by solving for the radiation scattered from an arbitrary source back to a colocated antenna. The signal out of the receiving antenna is computed from this solution and the result put into a form recognizeable as the radar equation. The conventional definition is obtained by solving a similar problem but for backscatter from an incident planewave. It is shown that these tow forms for sigma are the same if the observer is far enough from the surface.

A microacoustic analysis including viscosity and thermal conductivity to model the effect of the protective cap on the acoustic response of a MEMS microphone

PubMed Central

Homentcovschi, D.; Miles, R. N.; Loeppert, P. V.; Zuckerwar, A. J.

2013-01-01

An analysis is presented of the effect of the protective cover on the acoustic response of a miniature silicon microphone. The microphone diaphragm is contained within a small rectangular enclosure and the sound enters through a small hole in the enclosure's top surface. A numerical model is presented to predict the variation in the sound field with position within the enclosure. An objective of this study is to determine up to which frequency the pressure distribution remains sufficiently uniform so that a pressure calibration can be made in free space. The secondary motivation for this effort is to facilitate microphone design by providing a means of predicting how the placement of the microphone diaphragm in the package affects the sensitivity and frequency response. While the size of the package is typically small relative to the wavelength of the sounds of interest, because the dimensions of the package are on the order of the thickness of the viscous boundary layer, viscosity can significantly affect the distribution of sound pressure around the diaphragm. In addition to the need to consider viscous effects, it is shown here that one must also carefully account for thermal conductivity to properly represent energy dissipation at the system's primary acoustic resonance frequency. The sound field is calculated using a solution of the linearized system consisting of continuity equation, Navier-Stokes equations, the state equation and the energy equation using a finite element approach. The predicted spatial variation of both the amplitude and phase of the sound pressure is shown over the range of audible frequencies. Excellent agreement is shown between the predicted and measured effects of the package on the microphone's sensitivity. PMID:24701031

Frequency-constant Q, unity and disorder

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hargreaves, N.D.

1995-12-31

In exploration geophysics we obtain information about the earth by observing its response to different types of applied force. The response can cover the full range of possible Q values (where Q, the quality factor, is a measure of energy dissipation), from close to infinity in the case of deep crustal seismic to close to 0 in the case of many electromagnetic methods. When Q is frequency-constant, however, the various types of response have a common scaling behavior and can be described as being self-affine. The wave-equation then takes on a generalised form, changing from the standard wave-equation at Qmore » = {infinity} to the diffusion equation at Q = 0, via lossy, diffusive, propagation at intermediate Q values. Solutions of this wave-diffusion equation at any particular Q value can be converted to an equivalent set of results for any other Q value. In particular it is possible to convert from diffusive to wave propagation by a mapping from Q < {infinity} to Q = {infinity}. In the context of seismic sounding this is equivalent to applying inverse Q-filtering; in a more general context the mapping integrates different geophysical observations by referencing them to the common result at Q = {infinity}. The self-affinity of the observations for frequency-constant Q is an expression of scale invariance in the fundamental physical properties of the medium of propagation, this being the case whether the mechanism of diffusive propagation is scattering of intrinsic attenuation. Scale invariance, or fractal scaling, is a general property of disordered systems; the assumption of frequency-constant Q not only implies a unity between different geophysical observations, but also suggests that it is the disordered nature of the earth`s sub-surface that is the unifying factor.« less

Hugoniot equation of state of rock materials under shock compression

PubMed Central

Braithwaite, C. H.; Zhao, J.

2017-01-01

Two sets of shock compression tests (i.e. conventional and reverse impact) were conducted to determine the shock response of two rock materials using a plate impact facility. Embedded manganin stress gauges were used for the measurements of longitudinal stress and shock velocity. Photon Doppler velocimetry was used to capture the free surface velocity of the target. Experimental data were obtained on a fine-grained marble and a coarse-grained gabbro over a shock pressure range of approximately 1.5–12 GPa. Gabbro exhibited a linear Hugoniot equation of state (EOS) in the pressure–particle velocity (P–up) plane, while for marble a nonlinear response was observed. The EOS relations between shock velocity (US) and particle velocity (up) are linearly fitted as US = 2.62 + 3.319up and US = 5.4 85 + 1.038up for marble and gabbro, respectively. This article is part of the themed issue ‘Experimental testing and modelling of brittle materials at high strain rates’. PMID:27956506

The study of micro-inextensible piezoelectric cantilever plate

NASA Astrophysics Data System (ADS)

Chen, L. H.; Xu, J. W.; Zhang, W.

2018-06-01

In this paper, a micro-inextensible piezoelectric cantilever plate is analyzed and its nonlinear dynamic behaviour is studied. The nonlinear oscillation differential equation is established by using Hamilton’s principle with the application of strain gradient theory to consider the size effect, and inextensible theory to consider the large deformation and rotation effect of cantilever plate. Based on MATLAB software, using the Runge-Kuta method, we can obtain the response of the nonlinear oscillation differential equation. The influences of the strain gradient length scale parameter and voltage on the dynamic response of micro piezoelectric cantilever plate are investigated separately. The results confirmed an increase of the stiffness of the system by using the strain gradient theory and the amplitude of the vibration is reduced. The vibration of the system can be controlled by applying an active voltage. The effect of external excitation frequency on nonlinear dynamic behaviour is considered by using Poincare surface of section and diagrams of waveforms, phase and bifurcation.

Modeling the Shock Hugoniot in Porous Materials

NASA Astrophysics Data System (ADS)

Cochrane, Kyle R.; Shulenburger, Luke; Mattsson, Thomas R.; Lane, J. Matthew D.; Weck, Philippe F.; Vogler, Tracy J.; Desjarlais, Michael P.

2017-06-01

Porous materials are present in many scenarios from planetary science to ICF. Understanding how porosity modifies the behavior of the shock Hugoniot in an equation of state is key to being able to predictively simulate experiments. For example, modeling shocks in under-dense iron oxide can aid in understanding planetary formation and silica aerogel can be used to approximate the shock response of deuterium. Simulating the shock response of porous materials presents a variety of theoretical challenges, but by combining ab initio calculations with a surface energy and porosity model, we are able to accurately represent the shock Hugoniot. Finally, we show that this new approach can be used to calculate the Hugoniot of porous materials using existing tabular equations of state. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Impulse response and spatio-temporal wave-packets: The common feature of rogue waves, tsunami, and transition to turbulence

NASA Astrophysics Data System (ADS)

Bhaumik, Swagata; Sengupta, Tapan K.

2017-12-01

Here, we present the impulse response of the canonical zero pressure gradient boundary layer from the dynamical system approach. The fundamental physical mechanism of the impulse response is in creation of a spatio-temporal wave-front (STWF) by a localized, time-impulsive wall excitation of the boundary layer. The present research is undertaken to explain the unit process of diverse phenomena in geophysical fluid flows and basic hydrodynamics. Creation of a tsunami has been attributed to localized events in the ocean-bed caused by earthquakes, landslides, or volcanic eruptions, whose manifestation is in the run up to the coast by surface waves of massive amplitude but of very finite fetch. Similarly rogue waves have often been noted; a coherent account of the same is yet to appear, although some explanations have been proposed. Our studies in both two- and three-dimensional frameworks in Sengupta and Bhaumik ["Onset of turbulence from the receptivity stage of fluid flows," Phys. Rev. Lett. 107(15), 154501 (2011)] and Bhaumik and Sengupta ["Precursor of transition to turbulence: Spatiotemporal wave front," Phys. Rev. E 89(4), 043018 (2014)] have shown that the STWF provides the central role for causing transition to turbulence by reproducing carefully conducted transition experiments. Here, we furthermore relax the condition of time behavior and use a Dirac-delta wall excitation for the impulse response. The present approach is not based on any simplification of the governing Navier-Stokes equation (NSE), which is unlike solving a nonlinear shallow water equation and/or nonlinear Schrödinger equation. The full nonlinear Navier-Stokes equation (NSE) is solved here using high accuracy dispersion relation preserving numerical schemes and using appropriate formulation of the NSE which minimizes error. The adopted numerical methods and formulation have been extensively validated with respect to various external and internal 2D and 3D flow problems. We also present results from the Orr-Sommerfeld equation to show that the origin of the STWF is via a linear mechanism. Nonlinearity and nonparallelism play the central role in causing these phenomena of geophysics and transition to turbulence.

Transient response in granular quasi-two-dimensional bounded heap flow.

PubMed

Xiao, Hongyi; Ottino, Julio M; Lueptow, Richard M; Umbanhowar, Paul B

2017-10-01

We study the transition between steady flows of noncohesive granular materials in quasi-two-dimensional bounded heaps by suddenly changing the feed rate. In both experiments and simulations, the primary feature of the transition is a wedge of flowing particles that propagates downstream over the rising free surface with a wedge front velocity inversely proportional to the square root of time. An additional longer duration transient process continues after the wedge front reaches the downstream wall. The entire transition is well modeled as a moving boundary problem with a diffusionlike equation derived from local mass balance and a local relation between the flux and the surface slope.

Protein electrostatics: a review of the equations and methods used to model electrostatic equations in biomolecules--applications in biotechnology.

PubMed

Neves-Petersen, Maria Teresa; Petersen, Steffen B

2003-01-01

The molecular understanding of the initial interaction between a protein and, e.g., its substrate, a surface or an inhibitor is essentially an understanding of the role of electrostatics in intermolecular interactions. When studying biomolecules it is becoming increasingly evident that electrostatic interactions play a role in folding, conformational stability, enzyme activity and binding energies as well as in protein-protein interactions. In this chapter we present the key basic equations of electrostatics necessary to derive the equations used to model electrostatic interactions in biomolecules. We will also address how to solve such equations. This chapter is divided into two major sections. In the first part we will review the basic Maxwell equations of electrostatics equations called the Laws of Electrostatics that combined will result in the Poisson equation. This equation is the starting point of the Poisson-Boltzmann (PB) equation used to model electrostatic interactions in biomolecules. Concepts as electric field lines, equipotential surfaces, electrostatic energy and when can electrostatics be applied to study interactions between charges will be addressed. In the second part we will arrive at the electrostatic equations for dielectric media such as a protein. We will address the theory of dielectrics and arrive at the Poisson equation for dielectric media and at the PB equation, the main equation used to model electrostatic interactions in biomolecules (e.g., proteins, DNA). It will be shown how to compute forces and potentials in a dielectric medium. In order to solve the PB equation we will present the continuum electrostatic models, namely the Tanford-Kirkwood and the modified Tandord-Kirkwood methods. Priority will be given to finding the protonation state of proteins prior to solving the PB equation. We also present some methods that can be used to map and study the electrostatic potential distribution on the molecular surface of proteins. The combination of graphical visualisation of the electrostatic fields combined with knowledge about the location of key residues on the protein surface allows us to envision atomic models for enzyme function. Finally, we exemplify the use of some of these methods on the enzymes of the lipase family.

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

NASA Technical Reports Server (NTRS)

Williams, S. D.; Curry, D. M.

1977-01-01

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics.

PubMed

Stratoudaki, Theodosia; Ellwood, Robert; Sharples, Steve; Clark, Matthew; Somekh, Michael G; Collison, Ian J

2011-04-01

A dual frequency mixing technique has been developed for measuring velocity changes caused by material nonlinearity. The technique is based on the parametric interaction between two surface acoustic waves (SAWs): The low frequency pump SAW generated by a transducer and the high frequency probe SAW generated and detected using laser ultrasonics. The pump SAW stresses the material under the probe SAW. The stress (typically <5 MPa) is controlled by varying the timing between the pump and probe waves. The nonlinear interaction is measured as a phase modulation of the probe SAW and equated to a velocity change. The velocity-stress relationship is used as a measure of material nonlinearity. Experiments were conducted to observe the pump-probe interaction by changing the pump frequency and compare the nonlinear response of aluminum and fused silica. Experiments showed these two materials had opposite nonlinear responses, consistent with previously published data. The technique could be applied to life-time predictions of engineered components by measuring changes in nonlinear response caused by fatigue.

Optimization of reaction parameters of radiation induced grafting of 1-vinylimidazole onto poly(ethylene-co-tetraflouroethene) using response surface method

NASA Astrophysics Data System (ADS)

Nasef, Mohamed Mahmoud; Aly, Amgad Ahmed; Saidi, Hamdani; Ahmad, Arshad

2011-11-01

Radiation induced grafting of 1-vinylimidazole (1-VIm) onto poly(ethylene-co-tetraflouroethene) (ETFE) was investigated. The grafting parameters such as absorbed dose, monomer concentration, grafting time and temperature were optimized using response surface method (RSM). The Box-Behnken module available in the design expert software was used to investigate the effect of reaction conditions (independent parameters) varied in four levels on the degree of grafting ( G%) (response parameter). The model yielded a polynomial equation that relates the linear, quadratic and interaction effects of the independent parameters to the response parameter. The analysis of variance (ANOVA) was used to evaluate the results of the model and detect the significant values for the independent parameters. The optimum parameters to achieve a maximum G% were found to be monomer concentration of 55 vol%, absorbed dose of 100 kGy, time in the range of 14-20 h and a temperature of 61 °C. Fourier transform infrared (FTIR), thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) were used to investigate the properties of the obtained films and provide evidence for grafting.

Temporal upscaling of instantaneous evapotranspiration on clear-sky days using the constant reference evaporative fraction method with fixed or variable surface resistances at two cropland sites

NASA Astrophysics Data System (ADS)

Tang, Ronglin; Li, Zhao-Liang; Sun, Xiaomin; Bi, Yuyun

2017-01-01

Surface evapotranspiration (ET) is an important component of water and energy in land and atmospheric systems. This paper investigated whether using variable surface resistances in the reference ET estimates from the full-form Penman-Monteith (PM) equation could improve the upscaled daily ET estimates in the constant reference evaporative fraction (EFr, the ratio of actual to reference grass/alfalfa ET) method on clear-sky days using ground-based measurements. Half-hourly near-surface meteorological variables and eddy covariance (EC) system-measured latent heat flux data on clear-sky days were collected at two sites with different climatic conditions, namely, the subhumid Yucheng station in northern China and the arid Yingke site in northwestern China and were used as the model input and ground-truth, respectively. The results showed that using the Food and Agriculture Organization (FAO)-PM equation, the American Society of Civil Engineers-PM equation, and the full-form PM equation to estimate the reference ET in the constant EFr method produced progressively smaller upscaled daily ET at a given time from midmorning to midafternoon. Using all three PM equations produced the best results at noon at both sites regardless of whether the energy imbalance of the EC measurements was closed. When the EC measurements were not corrected for energy imbalance, using variable surface resistance in the full-form PM equation could improve the ET upscaling in the midafternoon, but worse results may occur in the midmorning to noon. Site-to-site and time-to-time variations were found in the performances of a given PM equation (with fixed or variable surface resistances) before and after the energy imbalance was closed.

Dynamic equations for an isotropic spherical shell using the power series method and surface differential operators

NASA Astrophysics Data System (ADS)

Okhovat, Reza; Boström, Anders

2017-04-01

Dynamic equations for an isotropic spherical shell are derived by using a series expansion technique. The displacement field is split into a scalar (radial) part and a vector (tangential) part. Surface differential operators are introduced to decrease the length of all equations. The starting point is a power series expansion of the displacement components in the thickness coordinate relative to the mid-surface of the shell. By using the expansions of the displacement components, the three-dimensional elastodynamic equations yield a set of recursion relations among the expansion functions that can be used to eliminate all but the four of lowest order and to express higher order expansion functions in terms of those of lowest orders. Applying the boundary conditions on the surfaces of the spherical shell and eliminating all but the four lowest order expansion functions give the shell equations as a power series in the shell thickness. After lengthy manipulations, the final four shell equations are obtained in a relatively compact form which are given to second order in shell thickness explicitly. The eigenfrequencies are compared to exact three-dimensional theory with excellent agreement and to membrane theory.

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

Published literature on the application of the finite-element method to solving the equations of two-dimensional surface-water flow in the horizontal plane is reviewed in this report. The finite-element method is ideally suited to modeling two-dimensional flow over complex topography with spatially variable resistance. A two-dimensional finite-element surface-water flow model with depth and vertically averaged velocity components as dependent variables allows the user great flexibility in defining geometric features such as the boundaries of a water body, channels, islands, dikes, and embankments. The following topics are reviewed in this report: alternative formulations of the equations of two-dimensional surface-water flow in the horizontal plane; basic concepts of the finite-element method; discretization of the flow domain and representation of the dependent flow variables; treatment of boundary conditions; discretization of the time domain; methods for modeling bottom, surface, and lateral stresses; approaches to solving systems of nonlinear equations; techniques for solving systems of linear equations; finite-element alternatives to Galerkin's method of weighted residuals; techniques of model validation; and preparation of model input data. References are listed in the final chapter.

Structural Response of the Earth's Crust to an Extra-Terrestrial Source of Stress by Identifying its Characteristic Pattern

NASA Astrophysics Data System (ADS)

Dasgupta, B.

2016-12-01

The earth's crust is a geodynamic realm, which is constantly evolving. Due to its dynamic nature, the crust is constantly being subjected to remodelling. The earth's crustal response to stress is a result of isostatic compensation. The crust is also a living proof of yesteryears' dynamics. Extra-terrestrial agents of deformation refers to meteorites, asteroids etc. These are catastrophic events that influence a larger area (considering larger impact bodies). They effect the crust from outside, hence leave behind very specific structural signatures.Consider an extra-terrestrial object impacting the earth's crust. The problem can be broken down into 3 parts: Pre Impact (kinematics of the object and nature of surface of impact); Syn Impact (dissipation of energy and formation of crater); and Post Impact (structural response, geophysical anomalies and effect on biota)Upon impact, the projectile penetrates the earth's crust to a depth of twice its diameter. Shock waves generated due impact propagate in all possible directions. The reflected waves cause complete melting and vaporization of the impact body. At the same time, increased internal energy of the system melts the target rock. Depending on the thickness and density of crustal matter, its' interaction with the mantle is determined. Data collection from such impact sites is the first step towards its theoretical modeling. Integrating geophysical (seismic, magnetic), paleomagnetic, geochemical and geo-chronological data one can determine the kinematic parameters that governed the event. A working model that illustrates the crustal responses to extraterrestrial stress of extreme magnitude cannot be qualitative. Hence the most fundamental thing at this point is quantification of these parameters. The variables form a `mass-energy equation', a simple theorem in Classical Physics. This project is directed to give the equation its shape. The equation will be the foundation on which the simulation model will rest. Mass energy equation for Hyper velocity bolide impact mechanics: E1 + E2 = E3 + E4 + E5)

Viscoelastic representation of surface waves in patchy saturated poroelastic media

NASA Astrophysics Data System (ADS)

Zhang, Yu; Xu, Yixian; Xia, Jianghai; Ping, Ping; Zhang, Shuangxi

2014-08-01

Wave-induced flow is observed as the dominated factor for P wave propagation at seismic frequencies. This mechanism has a mesoscopic scale nature. The inhomogeneous unsaturated patches are regarded larger than the pore size, but smaller than the wavelength. Surface wave, e.g., Rayleigh wave, which propagates along the free surface, generated by the interfering of body waves is also affected by the mesoscopic loss mechanisms. Recent studies have reported that the effect of the wave-induced flow in wave propagation shows a relaxation behavior. Viscoelastic equivalent relaxation function associated with the wave mode can describe the kinetic nature of the attenuation. In this paper, the equivalent viscoelastic relaxation functions are extended to take into account the free surface for the Rayleigh surface wave propagation in patchy saturated poroelastic media. Numerical results for the frequency-dependent velocity and attenuation and the time-dependent dynamical responses for the equivalent Rayleigh surface wave propagation along an interface between vacuum and patchy saturated porous media are reported in the low-frequency range (0.1-1,000 Hz). The results show that the dispersion and attenuation and kinetic characteristics of the mesoscopic loss effect for the surface wave can be effectively represented in the equivalent viscoelastic media. The simulation of surface wave propagation within mesoscopic patches requires solving Biot's differential equations in very small grid spaces, involving the conversion of the fast P wave energy diffusion into the Biot slow wave. This procedure requires a very large amount of computer consumption. An efficient equivalent approach for this patchy saturated poroelastic media shows a more convenient way to solve the single phase viscoelastic differential equations.

Surface plasticity: theory and computation

NASA Astrophysics Data System (ADS)

Esmaeili, A.; Steinmann, P.; Javili, A.

2017-11-01

Surfaces of solids behave differently from the bulk due to different atomic rearrangements and processes such as oxidation or aging. Such behavior can become markedly dominant at the nanoscale due to the large ratio of surface area to bulk volume. The surface elasticity theory (Gurtin and Murdoch in Arch Ration Mech Anal 57(4):291-323, 1975) has proven to be a powerful strategy to capture the size-dependent response of nano-materials. While the surface elasticity theory is well-established to date, surface plasticity still remains elusive and poorly understood. The objective of this contribution is to establish a thermodynamically consistent surface elastoplasticity theory for finite deformations. A phenomenological isotropic plasticity model for the surface is developed based on the postulated elastoplastic multiplicative decomposition of the surface superficial deformation gradient. The non-linear governing equations and the weak forms thereof are derived. The numerical implementation is carried out using the finite element method and the consistent elastoplastic tangent of the surface contribution is derived. Finally, a series of numerical examples provide further insight into the problem and elucidate the key features of the proposed theory.

Erosion over time on severely disturbed granitic soils: a model

Treesearch

W. F. Megahan

1974-01-01

A negative exponential equation containing three parameters was derived to describe time trends in surface erosion on severely disturbed soils. Data from four different studies of surface erosion on roads constructed from the granitic materials found in the Idaho Batholith were used to develop equation parameters. The evidence suggests that surface "armoring...

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

A composite velocity procedure for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1982-01-01

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

NASA Astrophysics Data System (ADS)

Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu

2018-03-01

A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.

Transient response of an active nonlinear sandwich piezolaminated plate

NASA Astrophysics Data System (ADS)

Oveisi, Atta; Nestorović, Tamara

2017-04-01

In this paper, the dynamic modelling and active vibration control of a piezolaminated plate with geometrical nonlinearities are investigated using a semi-analytical approach. For active vibration control purposes, the core orthotropic elastic layer is assumed to be perfectly bonded with two piezo-layers on its top and bottom surfaces which act as sensor and actuator, respectively. In the modelling procedure, the piezo-layers are assumed to be connected via a proportional derivative (PD) feedback control law. Hamilton's principle is employed to acquire the strong form of the dynamic equation in terms of additional higher order strain expressions by means of von Karman strain-displacement correlation. The obtained nonlinear partial differential equation (NPDE) is converted to a system of nonlinear ordinary differential equations (NODEs) by engaging Galerkin method and using the orthogonality of shape functions for the simply supported boundary conditions. Then, the resulting system of NODEs is solved numerically by employing the built-in Mathematica function, "NDSolve". Next, the vibration attenuation performance is evaluated and sensitivity of the closed-loop system is investigated for several control parameters and the external disturbance parameters. The proposed solution in open loop configuration is validated by finite element (FE) package ABAQUS both in the spatial domain and for the time-/frequency-dependent response.

Modeling of surface effects in crystalline materials within the framework of gradient crystal plasticity

NASA Astrophysics Data System (ADS)

Peng, Xiang-Long; Husser, Edgar; Huang, Gan-Yun; Bargmann, Swantje

2018-03-01

A finite-deformation gradient crystal plasticity theory is developed, which takes into account the interaction between dislocations and surfaces. The model captures both energetic and dissipative effects for surfaces penetrable by dislocations. By taking advantage of the principle of virtual power, the surface microscopic boundary equations are obtained naturally. Surface equations govern surface yielding and hardening. A thin film under shear deformation serves as a benchmark problem for validation of the proposed model. It is found that both energetic and dissipative surface effects significantly affect the plastic behavior.

ELECTROKINETIC PHENOMENA. II : THE FACTOR OF PROPORTIONALITY FOR CATAPHORETIC AND ELECTROENDOSMOTIC MOBILITIES.

PubMed

Abramson, H A

1930-07-20

Two theories which predict different values for the ratio of V(E), the electroendosmotic velocity of a liquid past a surface, to V(p), the electric mobility of a particle of the same surface through the same liquid are discussed. The theory demanding that See PDF for Equation was supported by certain data of van der Grinten for a glass surface. Re-calculation of van der Grinten's data reveals that the ratio varies between 2.1 and 2.8. These results are in accord with previous data of Abramson. It is pointed out that glass is unsuitable for the investigation. The ratio See PDF for Equation is here determined for a flat surface and particles when both are covered by the same proteins. Under these conditions See PDF for Equation The theory is similarly tested for a round surface using a micro-cataphoresis cell. It is shown that See PDF for Equation for a round surface is approximately 1.00. These findings are confirmatory of previous data supporting the view that cataphoretic mobility is independent of the size and shape of the particles when all particles compared have similar surface constitutions.

A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems

NASA Technical Reports Server (NTRS)

Avis, L. M.

1976-01-01

Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.

Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

ERIC Educational Resources Information Center

Hwang, Chi-en; Cleary, T. Anne

The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

The evolution equation for the flame surface density in turbulent premixed combustion

NASA Technical Reports Server (NTRS)

Trouve, A.; Poinsot, T.

1992-01-01

One central ingredient in flamelet models for turbulent premixed combustion is the flame surface density. This quantity conveys most of the effects of the turbulence on the rate of energy release and is obtained via a modeled transport equation, called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact, but unclosed, formulation for the turbulent Sigma-equation. In this exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the flame surface density and the turbulent flame stretch are not available from experiments and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the obvious, complementary approach to get basic information on these fundamental quantities. Three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, the effects of the Lewis number on the rate of production of flame surface area are described in great detail and meaningful comparisons with flamelet models can be performed. The analysis reveals in particular the tendency of the models to overpredict flame surface dissipation as well as their inability to reproduce variations due to thermo-diffusive phenomena. Thanks to the detailed information produced by a DNS-based analysis, this type of comparison not only underscores the shortcomings of current models but also suggests ways to improve them.

The rigidity and mobility of screw dislocations in a thin film

NASA Astrophysics Data System (ADS)

Wang, Fei

2018-07-01

An equation of screw dislocations in a thin film is derived for arbitrary boundary conditions. The boundary conditions can be the free surface, the fixed surface or the gradient loading imposed on the surface. The new equation makes it possible to study changes in the dislocation structure under various gradient stress applied to the surface. The rigidity and mobility of screw dislocations in a thin film are explored by using the equation. It is found that the screw dislocation core in a thin film is like a Hookean body with a specific shear stress applied to the surface. Free-surface effects on the Peierls stress are investigated and compared with previous studies. An abnormal behavior of the Peierls stress of screw dislocations in a soft-inclusion film between two rigid films is predicted theoretically.

Bifurcation Analysis and Nonlinear Decay of a Tumor in the Presence of an Immune Response

NASA Astrophysics Data System (ADS)

López, Álvaro G.; Seoane, Jesús M.; Sanjuán, Miguel A. F.

2017-12-01

The decay of a planar compact surface that is reduced through its boundary is considered. The interest of this problem lies in the fact that it can represent the destruction of a solid tumor by a population of immune cells. The theory of curves is utilized to derive the rate at which the area of the set decreases. Firstly, the process is represented as a discrete dynamical system. A recurrence equation describing the shrinkage of the area at any step is deduced. Then, a continuum limit is attained to derive an ordinary differential equation that governs the decay of the set. The solutions to the differential equation and its implications are discussed, and numerical simulations are carried out to test the accuracy of the decay law. Finally, the dynamics of a tumor-immune aggregate is inspected using this law and the theory of bifurcations. As the ratio of immune destruction to tumor growth increases, a saddle-node bifurcation stabilizes the tumor-free fixed point.

Gravity as Elasticity of Spacetime:

NASA Astrophysics Data System (ADS)

Padmanabhan, T.

It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, l≫(Gℏ/c3)1/2. The long wavelength description of spacetime, based on Einstein's equations, is similar to the description of a continuum solid made of a large number of microscopic degrees of freedom. This paradigm provides a novel interpretation of coordinate transformations as deformations of "spacetime solid" and allows one to obtain Einstein's equations as a consistency condition in the long wavelength limit. The entropy contributed by the microscopic degrees of freedom reduces to a pure surface contribution when Einstein's equations are satisfied. The horizons arises as "defects" in the "spacetime solid" (in the sense of well-defined singular points) and contributes an entropy which is one quarter of the horizon area. Finally, the response of the microstructure to vacuum energy leads to a near cancellation of the cosmological constant, leaving behind a tiny fluctuation which matches with the observed value.

Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks.

PubMed

Chabanon, Morgan; Rangamani, Padmini

2018-03-28

Formation of membrane necks is crucial for fission and fusion in lipid bilayers. In this work, we seek to answer the following fundamental question: what is the relationship between protein-induced spontaneous mean curvature and the Gaussian curvature at a membrane neck? Using an augmented Helfrich model for lipid bilayers to include membrane-protein interaction, we solve the shape equation on catenoids to find the field of spontaneous curvature that satisfies mechanical equilibrium of membrane necks. In this case, the shape equation reduces to a variable coefficient Helmholtz equation for spontaneous curvature, where the source term is proportional to the Gaussian curvature. We show how this latter quantity is responsible for non-uniform distribution of spontaneous curvature in minimal surfaces. We then explore the energetics of catenoids with different spontaneous curvature boundary conditions and geometric asymmetries to show how heterogeneities in spontaneous curvature distribution can couple with Gaussian curvature to result in membrane necks of different geometries.

Scattering of Lamb waves by cracks in a composite graphite fiber-reinforced epoxy plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu K.; Shah, Arvind

1990-01-01

Recent investigations of space construction techniques have explored the used of composite materials in the construction of space stations and platforms. These composites offer superior strength to weight ratio and are thermally stable. For example, a composite material being considered is laminates of graphite fibers in an epoxy matrix. The overall effective elastic constants of such a medium can be calculated from fiber and matrix properties by using an effective modulus theory as shown in Datta, el. al. The investigation of propagation and scattering of elastic waves in composite materials is necessary in order to develop an ability to characterize cracks and predict the reliability of composite structures. The objective of this investigation is the characterization of a surface breaking crack by ultrasonic techniques. In particular, the use of Lamb waves for this purpose is studied here. The Lamb waves travel through the plate, encountering a crack, and scatter. Of interest is the modeling of the scattered wave in terms of the Lamb wave modes. The direct problem of propagation and scattering of Lamb waves by a surface breaking crack has been analyzed. This would permit an experimentalist to characterize the crack by comparing the measured response to the analytical model. The plate is assumed to be infinite in the x and y directions with a constant thickness in the z direction. The top and bottom surfaces are traction free. Solving the governing wave equations and using the stress-free boundary conditions results in the dispersion equation. This equation yields the guided modes in the homogeneous plate. The theoretical model is a hybrid method that combines analytical and finite elements techniques to describe the scattered displacements. A finite region containing the defects is discretized by finite elements. Outside the local region, the far field solution is expressed as a Fourier summation of the guided modes obtained from the dispersion equation. Continuity of tractions and displacements at the boundaries of the two regions provides the necessary equations to determine the expansion coefficients and the nodal displacements. In the hybrid method used here these defects can be of arbitrary shapes as well as inclusions of different materials.

A Reduced-Order Model for Evaluating the Dynamic Response of Multilayer Plates to Impulsive Loads

DTIC Science & Technology

2016-04-12

01-0307 4UNCLASSIFIED: Distribution Statement A. Approved for public release; distribution is unlimited SAE INTERNATIONAL Based on the concepts of...Apply double Fourier Transform on the wave equations: 2� 2 + 2 � = 0 ; 2� 2 + 2 � = 0 Where ...into 2x2 matrices, and the source vector 0 ≠ 0 if loads apply on top surface. • Construct a 4Nx4N global scattering matrix for entire

The Shock and Vibration Digest. Volume 12, Number 8,

DTIC Science & Technology

1980-08-01

half tme coefficient of 0.315 in the above lamina. Sequential delamination began when a strip equation because two surfaces are formed). of width D in...a striker plate. Each specimen study of the two-dimensional ( plane -strain) response was subjected to two separate impact loadings: an of an elastic...laminated plate; they used a finite ele- in- plane impact and a so-called shear-bending impact. ment/normal mode technique. The physical behavior The

Application of a Numerical Inverse Laplace Integration Method to Surface Loading on a Viscoelastic Compressible Earth Model

NASA Astrophysics Data System (ADS)

Tanaka, Yoshiyuki; Klemann, Volker; Okuno, Jun'ichi

2009-09-01

Normal mode approaches for calculating viscoelastic responses of self-gravitating and compressible spherical earth models have an intrinsic problem of determining the roots of the secular equation and the associated residues in the Laplace domain. To bypass this problem, a method based on numerical inverse Laplace integration was developed by T anaka et al. (2006, 2007) for computations of viscoelastic deformation caused by an internal dislocation. The advantage of this approach is that the root-finding problem is avoided without imposing additional constraints on the governing equations and earth models. In this study, we apply the same algorithm to computations of viscoelastic responses to a surface load and show that the results obtained by this approach agree well with those obtained by a time-domain approach that does not need determinations of the normal modes in the Laplace domain. Using the elastic earth model PREM and a convex viscosity profile, we calculate viscoelastic load Love numbers ( h, l, k) for compressible and incompressible models. Comparisons between the results show that effects due to compressibility are consistent with results obtained by previous studies and that the rate differences between the two models total 10-40%. This will serve as an independent method to confirm results obtained by time-domain approaches and will usefully increase the reliability when modeling postglacial rebound.

Extension of Gibbs-Duhem equation including influences of external fields

NASA Astrophysics Data System (ADS)

Guangze, Han; Jianjia, Meng

2018-03-01

Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion

NASA Astrophysics Data System (ADS)

McBride, A. T.; Javili, A.; Steinmann, P.; Bargmann, S.

2011-10-01

Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.

SPM of nonlinear surface plasmon waveguides

NASA Astrophysics Data System (ADS)

Li, Yuee; Zhang, Xiaoping

2008-10-01

Pulse propagation equation of nonlinear dispersion surface plasmon waveguide is educed strictly from wave equation. The nonlinear coefficient is defined and then used to assess and compare the nonlinear characteristic of three popular 1-D surface plasmon waveguides: the single metal-dielectric interface, the metal slab bounded by dielectric and the dielectric slab bounded by metal. SPM (self-phase modulation) of the typical surface plasmon waveguide is predicted and discussed.

Overview of the CHarring Ablator Response (CHAR) Code

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Oliver, A. Brandon; Kirk, Benjamin S.; Salazar, Giovanni; Droba, Justin

2016-01-01

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation and contact interfaces, and example simulations are included. Finally, a discussion of ongoing development efforts is presented.

Comments on the article entitled “Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” by D.J. Bottomley, Lasse Makkonen and Kari Kolari [Surf. Sci. 603 (2009) 97

NASA Astrophysics Data System (ADS)

Hecquet, Pascal

2010-02-01

In the Shuttleworth's equation gij=γδij+dγ/dɛij, γ is the surface energy and gij is the surface stress with respect to the corresponding bulk quantity. At equilibrium and T=0 K, the bulk energy is the cohesive energy and the bulk stress is zero ( p=0). For i=j ( ɛii is hydrostatic) and for a flat surface, we show that the equilibrium surface stress gii corresponds to a surface pressure located mainly at the first monolayer and that the presence of the surface energy γ in the Shuttleworth's equation results from the matter conservation rule. Indeed, γ is an energy calculated per constant unit area while the atomic surface varies with the deformation as ( 1+ɛii). The equilibrium surface stress gii present at the surface is parallel to the surface. When gii is positive, this signifies that the surface atoms tend to contract together in the direction i even if the bulk pressure p is zero.

Stress-intensity factor equations for cracks in three-dimensional finite bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Raju, I. S.

1981-01-01

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

A Pressure-Dependent Damage Model for Energetic Materials

DTIC Science & Technology

2013-04-01

appropriate damage nucleation and evolution laws, and the equation of state ) with its reactive response. 15. SUBJECT TERMS pressure-dependent...evolution laws, and the equation of state ) with its reactive response. INTRODUCTION Explosions and deflagrations are classifications of sub-detonative...energetic material’s mechanical response (through the yield criterion, damage evolution and equation of state ) with its reactive response. DAMAGE-FREE

Engineered microtopographies and surface chemistries direct cell attachment and function

NASA Astrophysics Data System (ADS)

Magin, Chelsea Marie

Harrison, in 1914, first recognized that cells respond to physicochemical cues such as substratum topography when he observed that fibroblasts elongated while cultured on spider silk. Recently, techniques developed in the micro-electronics industry have been used to create molds for producing microscaled topographies with various shapes and spatial arrangements. Although these patterning techniques are well-established, very little is known about the mechanisms underlying cell sensing and response to microtopographies. In this work cellular micro-environments with varying surface topographies and chemistries were evaluated with marine organisms and mammalian cells to investigate cellular sensing and response. Biofouling---the accumulation of micro-organisms, plants, and animals on submerged surfaces---is an environmental and economic concern. Engineered topographies, replicated in polydimethylsiloxane elastomer (PDMSe) and functionalized poly(ethylene glycol)-dimethacrylate (PEGDMA) hydrogels, were evaluated for inhibition of marine fouling organism attachment. Microtopographies replicated in PDMSe inhibited attachment of the marine bacterium, Cobetia marina up to 99% versus smooth. The average normalized attachment densities of cells of C. marina and zoospores of the green algae Ulva on PDMSe topographies scaled inversely with the Engineered Roughness Index (ERIII), a representation of surface energy. Attachment densities of Ulva from four assays and C. marina from two growth phases to PDMSe surfaces scaled inversely with one equation: ERI II multiplied by the Reynolds number of the organism (Re) (R 2 = 0.77). The same microtopographies created in PDMSe reduced the initial attachment density and attachment strength of cells of the diatoms Navicula incerta and Seminavis robusta compared to smooth PDMSe. The average normalized attachment density of Navicula after exposure to shear stress (48 Pa) was correlated with the contact area between the diatom and a topographically modified surface (R2=0.82). Functionalized PEGDMA hydrogels significantly reduced attachment and attachment strength of Navicula and C. marina. These hydrogels also reduced attachment of zoospores of Ulva compared to PDMSe. Attachment of Ulva to microtopographies in PDMSe and PEGDMA-co-HEMA negatively correlated with ERIII*Re (R2 = 0.94 and R2 = 0.99, respectively). Incorporating a surface energy term into this equation created a correlation between the attachment densities of cells from two evolutionarily diverse groups on substrates of two surface chemistries with an equation that describes the various microtopographies and surface chemistries in terms of surface energy (R2 = 0.80). The current Attachment Model can now be used to design engineered antifouling surface microtopographies and chemistries that inhibit the attachment of organisms from three evoluntionarily diverse groups. Hydrogels based on PEGDMA were also chosen as a substratum material for mammalian cell culture. Capturing endothelial progenitor cells (EPCs) and inducing differentiation into the endothelial cell (EC) phenotype is the ideal way to re-endothelialize a small-diameter vascular graft. Substratum elasticity has been reported to direct stem cell differentiation into specific lineages. Functionalized PEGDMA hydrogels provided good compliance, high fidelity of topographic features and sites for surface modification with biomolecules. Fibronectin grafting and topography both increased EC attachment. This combination of adjustable elasticity, surface chemistry and topography has the potential to promote the capture and differentiation of EPCs into a confluent EC monolayer. Engineered microtopographies replicated in PDMSe directed elongation and alignment of human coronary artery endothelial cells (HCAECs) and human coronary artery smooth muscle cells (HCASMCs) compared to smooth surfaces. Engineered cellular micro-environments were created with specific surface energies defined by chemistry and topography to successfully direct cell attachment and function.

Unsteady seepage flow over sloping beds in response to multiple localized recharge

NASA Astrophysics Data System (ADS)

Bansal, Rajeev K.

2017-05-01

New generalized solutions of linearized Boussinesq equation are derived to approximate the dynamic behavior of subsurface seepage flow induced by multiple localized time-varying recharges over sloping ditch-drain aquifer system. The mathematical model is based on extended Dupuit-Forchheimer assumption and treats the spatial location of recharge basins as additional parameter. Closed form analytic expressions for spatio-temporal variations in water head distribution and discharge rate into the drains are obtained by solving the governing flow equation using eigenvalue-eigenfunction method. Downward and zero-sloping aquifers are treated as special cases of main results. A numerical example is used for illustration of combined effects of various parameters such as spatial coordinates of the recharge basin, aquifer's bed slope, and recharge rate on the dynamic profiles of phreatic surface.

Feasibility of optimizing trimetazidine dihydrochloride release from controlled porosity osmotic pump tablets of directly compressed cores

PubMed Central

Habib, Basant A.; Rehim, Randa T. Abd El; Nour, Samia A.

2013-01-01

The aim of this study was to develop and optimize Trimetazidine dihydrochloride (TM) controlled porosity osmotic pump (CPOP) tablets of directly compressed cores. A 23 full factorial design was used to study the influence of three factors namely: PEG400 (10% and 25% based on coating polymer weight), coating level (10% and 20% of tablet core weight) and hole diameter (0 “no hole” and 1 mm). Other variables such as tablet cores, coating mixture of ethylcellulose (4%) and dibutylphthalate (2%) in 95% ethanol and pan coating conditions were kept constant. The responses studied (Yi) were cumulative percentage released after 2 h (Q%2h), 6 h (Q%6h), 12 h (Q%12h) and regression coefficient of release data fitted to zero order equation (RSQzero), for Y1, Y2, Y3, and Y4, respectively. Polynomial equations were used to study the influence of different factors on each response individually. Response surface methodology and multiple response optimization were used to search for an optimized formula. Response variables for the optimized formula were restricted to 10% ⩽ Y1 ⩽ 20%, 40% ⩽ Y2 ⩽ 60%, 80% ⩽ Y3 ⩽ 100%, and Y4 > 0.9. The statistical analysis of the results revealed that PEG400 had positive effects on Q%2h, Q%6h and Q%12h, hole diameter had positive effects on all responses and coating level had positive effect on Q%6h, Q%12h and negative effect on RSQzero. Full three factor interaction (3FI) equations were used for representation of all responses except Q%2h which was represented by reduced (3FI) equation. Upon exploring the experimental space, no formula in the tested range could satisfy the required constraints. Thus, direct compression of TM cores was not suitable for formation of CPOP tablets. Preliminary trials of CPOP tablets with wet granulated cores were promising with an intact membrane for 12 h and high RSQzero. Further improvement of these formulations to optimize TM release will be done in further studies. PMID:25685502

Externally driven magnetic granular layers at a liquid/air interface: self-organization, flows and magnetic order

NASA Astrophysics Data System (ADS)

Snezhko, Alexey

2007-03-01

Collective dynamics and pattern formation in ensembles of magnetic microparticles suspended at the liquid/air interface and subjected to an alternating magnetic field are studied. Experiments reveal a new type of nontrivially ordered dynamic self-assembled structures (``snakes'') emerging in such systems in a certain range of field magnitudes and frequencies. These remarkable structures are directly related to surface waves in the liquid generated by the collective response of magnetic microparticles to the alternating magnetic field. In addition, a large-scale vortex flows are induced in the vicinity of the dynamic structures. Some features of the self-localized snake structures can be understood in the framework of an amplitude equation for parametric waves coupled to the conservation law equation describing the evolution of the magnetic particle density. Self-assembled snakes have a complex magnetic order: the segments of the snake exhibit long-range antiferromagnetic ordering mediated by the surface wave, while each segment is composed of ferromagnetically aligned chains of microparticles. A phenomenological model describing magnetic behavior of the magnetic snakes in external magnetic fields is proposed.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Effects of geometric modulation and surface potential heterogeneity on electrokinetic flow and solute transport in a microchannel

NASA Astrophysics Data System (ADS)

Bera, Subrata; Bhattacharyya, S.

2017-12-01

A numerical investigation is performed on the electroosmotic flow (EOF) in a surface-modulated microchannel to induce enhanced solute mixing. The channel wall is modulated by placing surface-mounted obstacles of trigonometric shape along which the surface potential is considered to be different from the surface potential of the homogeneous part of the wall. The characteristics of the electrokinetic flow are governed by the Laplace equation for the distribution of external electric potential; the Poisson equation for the distribution of induced electric potential; the Nernst-Planck equations for the distribution of ions; and the Navier-Stokes equations for fluid flow simultaneously. These nonlinear coupled set of governing equations are solved numerically by a control volume method over the staggered system. The influence of the geometric modulation of the surface, surface potential heterogeneity and the bulk ionic concentration on the EOF is analyzed. Vortical flow develops near a surface modulation, and it becomes stronger when the surface potential of the modulated region is in opposite sign to the surface potential of the homogeneous part of the channel walls. Vortical flow also depends on the Debye length when the Debye length is in the order of the channel height. Pressure drop along the channel length is higher for a ribbed wall channel compared to the grooved wall case. The pressure drop decreases with the increase in the amplitude for a grooved channel, but increases for a ribbed channel. The mixing index is quantified through the standard deviation of the solute distribution. Our results show that mixing index is higher for the ribbed channel compared to the grooved channel with heterogeneous surface potential. The increase in potential heterogeneity in the modulated region also increases the mixing index in both grooved and ribbed channels. However, the mixing performance, which is the ratio of the mixing index to pressure drop, reduces with the rise in the surface potential heterogeneity.

Effects of geometric modulation and surface potential heterogeneity on electrokinetic flow and solute transport in a microchannel

NASA Astrophysics Data System (ADS)

Bera, Subrata; Bhattacharyya, S.

2018-04-01

A numerical investigation is performed on the electroosmotic flow (EOF) in a surface-modulated microchannel to induce enhanced solute mixing. The channel wall is modulated by placing surface-mounted obstacles of trigonometric shape along which the surface potential is considered to be different from the surface potential of the homogeneous part of the wall. The characteristics of the electrokinetic flow are governed by the Laplace equation for the distribution of external electric potential; the Poisson equation for the distribution of induced electric potential; the Nernst-Planck equations for the distribution of ions; and the Navier-Stokes equations for fluid flow simultaneously. These nonlinear coupled set of governing equations are solved numerically by a control volume method over the staggered system. The influence of the geometric modulation of the surface, surface potential heterogeneity and the bulk ionic concentration on the EOF is analyzed. Vortical flow develops near a surface modulation, and it becomes stronger when the surface potential of the modulated region is in opposite sign to the surface potential of the homogeneous part of the channel walls. Vortical flow also depends on the Debye length when the Debye length is in the order of the channel height. Pressure drop along the channel length is higher for a ribbed wall channel compared to the grooved wall case. The pressure drop decreases with the increase in the amplitude for a grooved channel, but increases for a ribbed channel. The mixing index is quantified through the standard deviation of the solute distribution. Our results show that mixing index is higher for the ribbed channel compared to the grooved channel with heterogeneous surface potential. The increase in potential heterogeneity in the modulated region also increases the mixing index in both grooved and ribbed channels. However, the mixing performance, which is the ratio of the mixing index to pressure drop, reduces with the rise in the surface potential heterogeneity.

Shock compression response of highly reactive Ni + Al multilayered thin foils

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kelly, Sean C.; Thadhani, Naresh N., E-mail: naresh.thadhani@mse.gatech.edu

2016-03-07

The shock-compression response of Ni + Al multilayered thin foils is investigated using laser-accelerated thin-foil plate-impact experiments over the pressure range of 2 to 11 GPa. The foils contain alternating Ni and Al layers (parallel but not flat) of nominally 50 nm bilayer spacing. The goal is to determine the equation of state and shock-induced reactivity of these highly reactive fully dense thin-foil materials. The laser-accelerated thin-foil impact set-up involved combined use of photon-doppler-velocimetry to monitor the acceleration and impact velocity of an aluminum flyer, and VISAR interferometry was used to monitor the back free-surface velocity of the impacted Ni + Al multilayered target. The shock-compressionmore » response of the Ni + Al target foils was determined using experimentally measured parameters and impedance matching approach, with error bars identified considering systematic and experimental errors. Meso-scale CTH shock simulations were performed using real imported microstructures of the cross-sections of the multilayered Ni + Al foils to compute the Hugoniot response (assuming no reaction) for correlation with their experimentally determined equation of state. It was observed that at particle velocities below ∼150 m/s, the experimentally determined equation of state trend matches the CTH-predicted inert response and is consistent with the observed unreacted state of the recovered Ni + Al target foils from this velocity regime. At higher particle velocities, the experimentally determined equation of state deviates from the CTH-predicted inert response. A complete and self-sustained reaction is also seen in targets recovered from experiments performed at these higher particle velocities. The deviation in the measured equation of state, to higher shock speeds and expanded volumes, combined with the observation of complete reaction in the recovered multilayered foils, confirmed via microstructure characterization, is indicative of the occurrence of shock-induced chemical reaction occurring in the time-scale of the high-pressure state. TEM characterization of recovered shock-compressed (unreacted) Ni + Al multilayered foils exhibits distinct features of constituent mixing revealing jetted layers and inter-mixed regions. These features were primarily observed in the proximity of the undulations present in the alternating layers of the Ni + Al starting foils, suggesting the important role of such instabilities in promoting shock-induced intermetallic-forming reactions in the fully dense highly exothermic multilayered thin foils.« less

Marangoni Effects of a Drop in an Extensional Flow: The Role of Surfactant Physical Chemistry

NASA Technical Reports Server (NTRS)

Stebe, Kathleen J.; Balasubramaniam, R. (Technical Monitor)

2002-01-01

While the changes in stresses caused by surfactant adsorption on non-deforming interfaces have been fairly well established, prior to this work, there were few studies addressing how surfactants alter stresses on strongly deforming interfaces. We chose the model problem of a drop in a uniaxial extensional flow to study these stress conditions To model surfactant effects at fluid interfaces, a proper description of the dependence of the surface tension on surface concentration, the surface equation of state, is required. We have adopted a surface equation of state that accounts for the maximum coverage limit; that is, because surfactants have a finite cross sectional area, there is an upper bound to the amount of surfactant that can adsorb in a monolayer. The surface tension reduces strongly only when this maximum coverage is approached. Since the Marangoni stresses go as the derivative of the surface equation of state times the surface concentration gradient, the non-linear equation of state determines both the effect of surfactants in the normal stress jump, (which is balanced by the product of the mean curvature of the interface times the surface tension), and the tangential stress jump, which is balanced by Marangoni stresses. First, the effects of surface coverage and intermolecular interactions among surfactants which drive aggregation of surfactants in the interface were studied. (see Pawar and Stebe, Physics of Fluids).

Adaptive focusing of laser radiation onto a rough reflecting surface through the turbulent and nonlinear atmosphere

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeriy V.

2004-12-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual coherence function (MCF) for the backscattered (returned) wave. The resulting evolution equation for the MCF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation of the transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.

Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1993-01-01

The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.

Dissolution of solid dosage form. II. Equations for the dissolution of nondisintegrating tablet under the sink condition.

PubMed

Yonezawa, Y; Shirakura, K; Otsuka, A; Sunada, H

1991-03-01

An equation for dissolution from the whole surface of a nondisintegrating single component tablet under the sink condition was derived. Also, equations for several dissolution manners of the tablet under the sink condition were derived in the postulation of the dominant dissolution rate constant which determines the dissolution manner. The applicability or validity of these equations were examined by the dissolution measurements with nondisintegrating single component tablets. About one-tenth the amount of the amount needed to saturate the solution was used to prepare a tablet, and dissolution measurements were carried out with the tablet whose flat or side surface was masked with an adhesive tape in accordance with the conditions for derivation of equations. Among the derived equations, dissolution from the whole surface of a tablet was expressed by a form similar to the cube root law equation for particles. Hence, a single component tablet compressed by the use of a suitable amount was thought to behave like a single crystal. Also, equations derived for several dissolution manners were thought to be applicable for the dissolution of a nonspherical particle and crystal concerning the crystal's habit and its dissolution property, and the extended applicability was examined by converting the crystal into a simplified or idealized form, i.e., rectangle or plate.

Instrumented Taylor anvil-on-rod impact tests for validating applicability of standard strength models to transient deformation states

NASA Astrophysics Data System (ADS)

Eakins, D. E.; Thadhani, N. N.

2006-10-01

Instrumented Taylor anvil-on-rod impact tests have been conducted on oxygen-free electronic copper to validate the accuracy of current strength models for predicting transient states during dynamic deformation events. The experiments coupled the use of high-speed digital photography to record the transient deformation states and laser interferometry to monitor the sample back (free surface) velocity as a measure of the elastic/plastic wave propagation through the sample length. Numerical continuum dynamics simulations of the impact and plastic wave propagation employing the Johnson-Cook [Proceedings of the Seventh International Symposium on Ballistics, 1983, The Netherlands (Am. Def. Prep. Assoc. (ADPA)), pp. 541-547], Zerilli-Armstrong [J. Appl. Phys. C1, 1816 (1987)], and Steinberg-Guinan [J. Appl. Phys. 51, 1498 (1980)] constitutive equations were used to generate transient deformation profiles and the free surface velocity traces. While these simulations showed good correlation with the measured free surface velocity traces and the final deformed sample shape, varying degrees of deviations were observed between the photographed and calculated specimen profiles at intermediate deformation states. The results illustrate the usefulness of the instrumented Taylor anvil-on-rod impact technique for validating constitutive equations that can describe the path-dependent deformation response and can therefore predict the transient and final deformation states.

Lump Solitons in Surface Tension Dominated Flows

NASA Astrophysics Data System (ADS)

Milewski, Paul; Berger, Kurt

1999-11-01

The Kadomtsev-Petviashvilli I equation (KPI) which models small-amplitude, weakly three-dimensional surface-tension dominated long waves is integrable and allows for algebraically decaying lump solitary waves. It is not known (theoretically or numerically) whether the full free-surface Euler equations support such solutions. We consider an intermediate model, the generalised Benney-Luke equation (gBL) which is isotropic (not weakly three-dimensional) and contains KPI as a limit. We show numerically that: 1. gBL supports lump solitary waves; 2. These waves collide elastically and are stable; 3. They are generated by resonant flow over an obstacle.

Human body surface area: a theoretical approach.

PubMed

Wang, Jianfeng; Hihara, Eiji

2004-04-01

Knowledge of the human body surface area has important applications in medical practice, garment design, and other engineering sizing. Therefore, it is not surprising that several expressions correlating body surface area with direct measurements of body mass and length have been reported in the literature. In the present study, based on the assumption that the exterior shape of the human body is the result of convex and concave deformations from a basic cylinder, we derive a theoretical equation minimizing body surface area (BSA) at a fixed volume (V): BSA=(9pi VL)(0.5), where L is the reference length of the body. Assuming a body density value of 1,000 kg.m(-3), the equation becomes BSA=(BM.BH/35.37)(0.5), where BSA is in square meters, BM is the body mass in kilograms, and BH is the body height in meters. BSA values calculated by means of this equation fall within +/-7% of the values obtained by means of the equations available in the literature, in the range of BSA from children to adults. It is also suggested that the above equation, which is obtained by minimizing the outer body surface at a fixed volume, implies a fundamental relation set by the geometrical constraints governing the growth and the development of the human body.

Effective Control of Computationally Simulated Wing Rock in Subsonic Flow

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Menzies, Margaret A.

1997-01-01

The unsteady compressible, full Navier-Stokes (NS) equations and the Euler equations of rigid-body dynamics are sequentially solved to simulate the delta wing rock phenomenon. The NS equations are solved time accurately, using the implicit, upwind, Roe flux-difference splitting, finite-volume scheme. The rigid-body dynamics equations are solved using a four-stage Runge-Kutta scheme. Once the wing reaches the limit-cycle response, an active control model using a mass injection system is applied from the wing surface to suppress the limit-cycle oscillation. The active control model is based on state feedback and the control law is established using pole placement techniques. The control law is based on the feedback of two states: the roll-angle and roll velocity. The primary model of the computational applications consists of a 80 deg swept, sharp edged, delta wing at 30 deg angle of attack in a freestream of Mach number 0.1 and Reynolds number of 0.4 x 10(exp 6). With a limit-cycle roll amplitude of 41.1 deg, the control model is applied, and the results show that within one and one half cycles of oscillation, the wing roll amplitude and velocity are brought to zero.

A new aerodynamic integral equation based on an acoustic formula in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

Photosynthesis sensitivity to climate change in land surface models

NASA Astrophysics Data System (ADS)

Manrique-Sunen, Andrea; Black, Emily; Verhoef, Anne; Balsamo, Gianpaolo

2016-04-01

Accurate representation of vegetation processes within land surface models is key to reproducing surface carbon, water and energy fluxes. Photosynthesis determines the amount of CO2 fixated by plants as well as the water lost in transpiration through the stomata. Photosynthesis is calculated in land surface models using empirical equations based on plant physiological research. It is assumed that CO2 assimilation is either CO2 -limited, radiation -limited ; and in some models export-limited (the speed at which the products of photosynthesis are used by the plant) . Increased levels of atmospheric CO2 concentration tend to enhance photosynthetic activity, but the effectiveness of this fertilization effect is regulated by environmental conditions and the limiting factor in the photosynthesis reaction. The photosynthesis schemes at the 'leaf level' used by land surface models JULES and CTESSEL have been evaluated against field photosynthesis observations. Also, the response of photosynthesis to radiation, atmospheric CO2 and temperature has been analysed for each model, as this is key to understanding the vegetation response that climate models using these schemes are able to reproduce. Particular emphasis is put on the limiting factor as conditions vary. It is found that while at present day CO2 concentrations export-limitation is only relevant at low temperatures, as CO2 levels rise it becomes an increasingly important restriction on photosynthesis.

Response of the Surface Circulation of the Arabian Sea to Monsoonal Forcing

NASA Astrophysics Data System (ADS)

Beal, L. M.; Hormann, V.; Lumpkin, R.; Foltz, G. R.

2014-12-01

We use two decades of drifter and satellite data to examine the monthly evolution of the surface circulation of the Arabian Sea, which reverses annually in response to the Indian monsoon winds. Most significantly, we find that in the transition from winter to summer circulations, northward flow appears along the length of the western boundary as early as March or April, one or two months before the onset of the southwest monsoon winds. This reversal is initiated by annual Rossby waves, which in turn are initiated by wind curl forcing during the previous southwest monsoon. These results lead us to speculate that there is an oceanic mechanism through which one monsoon may precondition the next. Previous studies of monsoon circulations with lower temporal resolution have highlighted basin-wide currents and connections that are not found to exist in the monthly fields. In particular, we find that the Northeast Monsoon Current does not reach the western boundary and there is no counter-rotating gyre system during boreal winter. South of the equator, the eastward-flowing South Equatorial Counter Current (SECC) is present year-round, even though equatorial winds are strongly influenced by the monsoons. Semi-annual variability of the SECC is governed by Ekman pumping over the south equatorial gyre (or Seychelles dome) and, surprisingly, it is weakest during the northeast monsoon. This region has important influence on the atmosphere and its link to the monsoons deserves further investigation. The East African Coastal Current feeds into the SECC from the boundary. During the southwest monsoon it overshoots the equator and splits, feeding both northward into the Somali Current and eastward into the SECC after looping back across the equator. This apparent retroflection of the EACC is what was previously known as the southern gyre and is obscured at the surface by strong, locally wind-driven, cross-equatorial Ekman transport. Finally, there is broad, strong eastward flow at the mouth of the Gulf of Aden throughout the southwest monsoon, which is influenced by the curvature and bifurcation of the atmospheric monsoon jet.

The Thin Oil Film Equation

NASA Technical Reports Server (NTRS)

Brown, James L.; Naughton, Jonathan W.

1999-01-01

A thin film of oil on a surface responds primarily to the wall shear stress generated on that surface by a three-dimensional flow. The oil film is also subject to wall pressure gradients, surface tension effects and gravity. The partial differential equation governing the oil film flow is shown to be related to Burgers' equation. Analytical and numerical methods for solving the thin oil film equation are presented. A direct numerical solver is developed where the wall shear stress variation on the surface is known and which solves for the oil film thickness spatial and time variation on the surface. An inverse numerical solver is also developed where the oil film thickness spatial variation over the surface at two discrete times is known and which solves for the wall shear stress variation over the test surface. A One-Time-Level inverse solver is also demonstrated. The inverse numerical solver provides a mathematically rigorous basis for an improved form of a wall shear stress instrument suitable for application to complex three-dimensional flows. To demonstrate the complexity of flows for which these oil film methods are now suitable, extensive examination is accomplished for these analytical and numerical methods as applied to a thin oil film in the vicinity of a three-dimensional saddle of separation.

More Issues in Observed-Score Equating

ERIC Educational Resources Information Center

van der Linden, Wim J.

2013-01-01

This article is a response to the commentaries on the position paper on observed-score equating by van der Linden (this issue). The response focuses on the more general issues in these commentaries, such as the nature of the observed scores that are equated, the importance of test-theory assumptions in equating, the necessity to use multiple…

Optical testing using the transport-of-intensity equation.

PubMed

Dorrer, C; Zuegel, J D

2007-06-11

The transport-of-intensity equation links the intensity and phase of an optical source to the longitudinal variation of its intensity in the presence of Fresnel diffraction. This equation can be used to provide a simple, accurate spatial-phase measurement for optical testing of flat surfaces. The properties of this approach are derived. The experimental demonstration is performed by quantifying the surface variations induced by the magnetorheological finishing process on laser rods.

A Digital Program for Calculating the Interaction Between Flexible Structures, Unsteady Aerodynamics and Active Controls

NASA Technical Reports Server (NTRS)

Peele, E. L.; Adams, W. M., Jr.

1979-01-01

A computer program, ISAC, is described which calculates the stability and response of a flexible airplane equipped with active controls. The equations of motion relative to a fixed inertial coordinate system are formulated in terms of the airplane's rigid body motion and its unrestrained normal vibration modes. Unsteady aerodynamic forces are derived from a doublet lattice lifting surface theory. The theoretical basis for the program is briefly explained together with a description of input data and output results.

Chain pooling to minimize prediction error in subset regression. [Monte Carlo studies using population models

NASA Technical Reports Server (NTRS)

Holms, A. G.

1974-01-01

Monte Carlo studies using population models intended to represent response surface applications are reported. Simulated experiments were generated by adding pseudo random normally distributed errors to population values to generate observations. Model equations were fitted to the observations and the decision procedure was used to delete terms. Comparison of values predicted by the reduced models with the true population values enabled the identification of deletion strategies that are approximately optimal for minimizing prediction errors.

Calculation of afterbody flows with a composite velocity formulation

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rubin, S. G.; Khosla, P. K.

1983-01-01

A recently developed technique for numerical solution of the Navier-Stokes equations for subsonic, laminar flows is investigated. It is extended here to allow for the computation of transonic and turbulent flows. The basic approach involves a multiplicative composite of the appropriate velocity representations for the inviscid and viscous flow regions. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli equation for the pressure, while the continuity equation reduces to the familiar potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary layers. The velocity components are computed with a coupled strongly implicity procedure. For transonic flows the artificial compressibility method is used to treat supersonic regions. Calculations are made for both laminar and turbulent flows over axisymmetric afterbody configurations. Present results compare favorably with other numerical solutions and/or experimental data.

Excitation, response, and fatigue life estimation methods for the structural design of externally blown flaps

NASA Technical Reports Server (NTRS)

Ungar, E. E.; Chandiramani, K. L.; Barger, J. E.

1972-01-01

Means for predicting the fluctuating pressures acting on externally blown flap surfaces are developed on the basis of generalizations derived from non-dimensionalized empirical data. Approaches for estimation of the fatigue lives of skin-stringer and honeycomb-core sandwich flap structures are derived from vibration response analyses and panel fatigue data. Approximate expressions for fluctuating pressures, structural response, and fatigue life are combined to reveal the important parametric dependences. The two-dimensional equations of motion of multi-element flap systems are derived in general form, so that they can be specialized readily for any particular system. An introduction is presented of an approach to characterizing the excitation pressures and structural responses which makes use of space-time spectral concepts and promises to provide useful insights, as well as experimental and analytical savings.

On the mechanics of continua with boundary energies and growing surfaces

NASA Astrophysics Data System (ADS)

Papastavrou, Areti; Steinmann, Paul; Kuhl, Ellen

2013-06-01

Many biological systems are coated by thin films for protection, selective absorption, or transmembrane transport. A typical example is the mucous membrane covering the airways, the esophagus, and the intestine. Biological surfaces typically display a distinct mechanical behavior from the bulk; in particular, they may grow at different rates. Growth, morphological instabilities, and buckling of biological surfaces have been studied intensely by approximating the surface as a layer of finite thickness; however, growth has never been attributed to the surface itself. Here, we establish a theory of continua with boundary energies and growing surfaces of zero thickness in which the surface is equipped with its own potential energy and is allowed to grow independently of the bulk. In complete analogy to the kinematic equations, the balance equations, and the constitutive equations of a growing solid body, we derive the governing equations for a growing surface. We illustrate their spatial discretization using the finite element method, and discuss their consistent algorithmic linearization. To demonstrate the conceptual differences between volume and surface growth, we simulate the constrained growth of the inner layer of a cylindrical tube. Our novel approach toward continua with growing surfaces is capable of predicting extreme growth of the inner cylindrical surface, which more than doubles its initial area. The underlying algorithmic framework is robust and stable; it allows to predict morphological changes due to surface growth during the onset of buckling and beyond. The modeling of surface growth has immediate biomedical applications in the diagnosis and treatment of asthma, gastritis, obstructive sleep apnoea, and tumor invasion. Beyond biomedical applications, the scientific understanding of growth-induced morphological instabilities and surface wrinkling has important implications in material sciences, manufacturing, and microfabrication, with applications in soft lithography, metrology, and flexible electronics.

Documentation of the Surface-Water Routing (SWR1) Process for modeling surface-water flow with the U.S. Geological Survey Modular Ground-Water Model (MODFLOW-2005)

USGS Publications Warehouse

Hughes, Joseph D.; Langevin, Christian D.; Chartier, Kevin L.; White, Jeremy T.

2012-01-01

A flexible Surface-Water Routing (SWR1) Process that solves the continuity equation for one-dimensional and two-dimensional surface-water flow routing has been developed for the U.S. Geological Survey three-dimensional groundwater model, MODFLOW-2005. Simple level- and tilted-pool reservoir routing and a diffusive-wave approximation of the Saint-Venant equations have been implemented. Both methods can be implemented in the same model and the solution method can be simplified to represent constant-stage elements that are functionally equivalent to the standard MODFLOW River or Drain Package boundary conditions. A generic approach has been used to represent surface-water features (reaches) and allows implementation of a variety of geometric forms. One-dimensional geometric forms include rectangular, trapezoidal, and irregular cross section reaches to simulate one-dimensional surface-water features, such as canals and streams. Two-dimensional geometric forms include reaches defined using specified stage-volume-area-perimeter (SVAP) tables and reaches covering entire finite-difference grid cells to simulate two-dimensional surface-water features, such as wetlands and lakes. Specified SVAP tables can be used to represent reaches that are smaller than the finite-difference grid cell (for example, isolated lakes), or reaches that cannot be represented accurately using the defined top of the model. Specified lateral flows (which can represent point and distributed flows) and stage-dependent rainfall and evaporation can be applied to each reach. The SWR1 Process can be used with the MODFLOW Unsaturated Zone Flow (UZF1) Package to permit dynamic simulation of runoff from the land surface to specified reaches. Surface-water/groundwater interactions in the SWR1 Process are mathematically defined to be a function of the difference between simulated stages and groundwater levels, and the specific form of the reach conductance equation used in each reach. Conductance can be specified directly or calculated as a function of the simulated wetted perimeter and defined reach bed hydraulic properties, or as a weighted combination of both reach bed hydraulic properties and horizontal hydraulic conductivity. Each reach can be explicitly coupled to a single specific groundwater-model layer or coupled to multiple groundwater-model layers based on the reach geometry and groundwater-model layer elevations in the row and column containing the reach. Surface-water flow between reservoirs is simulated using control structures. Surface-water flow between reaches, simulated by the diffusive-wave approximation, can also be simulated using control structures. A variety of control structures have been included in the SWR1 Process and include (1) excess-volume structures, (2) uncontrolled-discharge structures, (3) pumps, (4) defined stage-discharge relations, (5) culverts, (6) fixed- or movable-crest weirs, and (7) fixed or operable gated spillways. Multiple control structures can be implemented in individual reaches and are treated as composite flow structures. Solution of the continuity equation at the reach-group scale (a single reach or a user-defined collection of individual reaches) is achieved using exact Newton methods with direct solution methods or exact and inexact Newton methods with Krylov sub-space methods. Newton methods have been used in the SWR1 Process because of their ability to solve nonlinear problems. Multiple SWR1 time steps can be simulated for each MODFLOW time step, and a simple adaptive time-step algorithm, based on user-specified rainfall, stage, flow, or convergence constraints, has been implemented to better resolve surface-water response. A simple linear- or sigmoid-depth scaling approach also has been implemented to account for increased bed roughness at small surface-water depths and to increase numerical stability. A line-search algorithm also has been included to improve the quality of the Newton-step upgrade vector, if possible. The SWR1 Process has been benchmarked against one- and two-dimensional numerical solutions from existing one- and two-dimensional numerical codes that solve the dynamic-wave approximation of the Saint-Venant equations. Two-dimensional solutions test the ability of the SWR1 Process to simulate the response of a surface-water system to (1) steady flow conditions for an inclined surface (solution of Manning's equation), and (2) transient inflow and rainfall for an inclined surface. The one-dimensional solution tests the ability of the SWR1 Process to simulate a looped network with multiple upstream inflows and several control structures. The SWR1 Process also has been compared to a level-pool reservoir solution. A synthetic test problem was developed to evaluate a number of different SWR1 solution options and simulate surface-water/groundwater interaction. The solution approach used in the SWR1 Process may not be applicable for all surface-water/groundwater problems. The SWR1 Process is best suited for modeling long-term changes (days to years) in surface-water and groundwater flow. Use of the SWR1 Process is not recommended for modeling the transient exchange of water between streams and aquifers when local and convective acceleration and other secondary effects (for example, wind and Coriolis forces) are substantial. Dam break evaluations and two-dimensional evaluations of spatially extensive domains are examples where acceleration terms and secondary effects would be significant, respectively.

Nonlinear response from transport theory and quantum field theory at finite temperature

NASA Astrophysics Data System (ADS)

Carrington, M. E.; Defu, Hou; Kobes, R.

2001-07-01

We study the nonlinear response in weakly coupled hot φ4 theory. We obtain an expression for a quadratic shear viscous response coefficient using two different formalisms: transport theory and response theory. The transport theory calculation is done by assuming a local equilibrium form for the distribution function and expanding in the gradient of the local four dimensional velocity field. By performing a Chapman-Enskog expansion on the Boltzmann equation we obtain a hierarchy of equations for the coefficients of the expanded distribution function. To do the response theory calculation we use Zubarev's techniques in nonequilibrium statistical mechanics to derive a generalized Kubo formula. Using this formula allows us to obtain the quadratic shear viscous response from the three-point retarded Green function of the viscous shear stress tensor. We use the closed time path formalism of real time finite temperature field theory to show that this three-point function can be calculated by writing it as an integral equation involving a four-point vertex. This four-point vertex can in turn be obtained from an integral equation which represents the resummation of an infinite series of ladder and extended-ladder diagrams. The connection between transport theory and response theory is made when we show that the integral equation for this four-point vertex has exactly the same form as the equation obtained from the Boltzmann equation for the coefficient of the quadratic term of the gradient expansion of the distribution function. We conclude that calculating the quadratic shear viscous response using transport theory and keeping terms that are quadratic in the gradient of the velocity field in the Chapman-Enskog expansion of the Boltzmann equation is equivalent to calculating the quadratic shear viscous response from response theory using the next-to-linear response Kubo formula, with a vertex given by an infinite resummation of ladder and extended-ladder diagrams.

Electrostatic and electrodynamic response properties of nanostructures

NASA Astrophysics Data System (ADS)

Ayaz, Yuksel

1999-11-01

This thesis addresses the problem of nanostructure dielectric response to excitation by electric fields, both in the electrostatic c→infinity and the electrodynamic regimes. The nanostructures treated include planar quantum wells and quantum wires embedded in the vicinity of the bounding surface of the host semiconductor medium. Various cases are analyzed, including a single well or wire, a double well or wire, a lattice of N wells or wires and an infinite superlattice of wells or wires. The host medium is considered to have phonons and/or a bulk semiconductor plasma which interact with the plasmons of the embedded quantum wells or wires, and the host plasma is treated in both the local "cold" plasma regime and the nonlocal "hot" plasma regime. New hybridized quantum plasma collective modes emerge from these studies. The techniques employed here include the variational differential formulation of integral equations for the inverse dielectric function (in electrostatic case) and the dyadic Green's function (in the electrodynamic case) for the various systems described above. These integral equations are then solved in frequency-position representation by a variety of techniques depending on the geometrical features of the particular problem. Explicit closed form solutions for the inverse dielectric function or dyadic Green's function facilitate identification of the coupled collective modes in terms of their frequency poles, and the residues at the pole positions provide the relative amplitudes with which these normal modes respond to external excitation. Interesting features found include, for example, explicit formulas showing the transference of coupling of a two dimensional (2D) quantum well plasmon from a surface phonon to a bulk phonon as the 2D quantum well is displaced away from the bounding surface, deeper into the medium.

Climatic impact of Amazon deforestation - a mechanistic model study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ning Zeng; Dickinson, R.E.; Xubin Zeng

1996-04-01

Recent general circulation model (GCM) experiments suggest a drastic change in the regional climate, especially the hydrological cycle, after hypothesized Amazon basinwide deforestation. To facilitate the theoretical understanding os such a change, we develop an intermediate-level model for tropical climatology, including atmosphere-land-ocean interaction. The model consists of linearized steady-state primitive equations with simplified thermodynamics. A simple hydrological cycle is also included. Special attention has been paid to land-surface processes. It generally better simulates tropical climatology and the ENSO anomaly than do many of the previous simple models. The climatic impact of Amazon deforestation is studied in the context of thismore » model. Model results show a much weakened Atlantic Walker-Hadley circulation as a result of the existence of a strong positive feedback loop in the atmospheric circulation system and the hydrological cycle. The regional climate is highly sensitive to albedo change and sensitive to evapotranspiration change. The pure dynamical effect of surface roughness length on convergence is small, but the surface flow anomaly displays intriguing features. Analysis of the thermodynamic equation reveals that the balance between convective heating, adiabatic cooling, and radiation largely determines the deforestation response. Studies of the consequences of hypothetical continuous deforestation suggest that the replacement of forest by desert may be able to sustain a dry climate. Scaling analysis motivated by our modeling efforts also helps to interpret the common results of many GCM simulations. When a simple mixed-layer ocean model is coupled with the atmospheric model, the results suggest a 1{degrees}C decrease in SST gradient across the equatorial Atlantic Ocean in response to Amazon deforestation. The magnitude depends on the coupling strength. 66 refs., 16 figs., 4 tabs.« less

Methods and equations for estimating peak streamflow per square mile in Virginia’s urban basins

USGS Publications Warehouse

Austin, Samuel H.

2014-01-01

Models are presented that describe Virginia urban area annual peak streamflow per square mile based on basin percent urban area and basin drainage area. Equations are provided to estimate Virginia urban peak flow per square mile of basin drainage area in each of the following annual exceedance probability categories: 0.995, 0.99, 0.95, 0.9, 0.8, 0.67, 0.5, 0.43, 0.2, 0.1, 0.04, 0.02, 0.01, 0.005, and 0.002 (recurrence intervals of 1.005, 1.01, 1.05, 1.11, 1.25, 1.49, 2.0, 2.3, 5, 10, 25, 50, 100, 200, and 500 years, respectively). Equations apply to Virginia drainage basins ranging in size from no less than 1.2 mi2 to no more than 2,400 mi2 containing at least 10 percent urban area, and not more than 96 percent urban area. A total of 115 Virginia drainage basins were analyzed. Actual-by-predicted plots and leverage plots for response variables and explanatory variables in each peak-flow annual exceedance probability category indicate robust model fits and significant explanatory power. Equations for 8 of 15 urban peak-flow response surface models yield R-square values greater than 0.8. Relations identified in statistical models, describing significant increases in urban peak stream discharges as basin urban area increases, affirm empirical relations reported in past studies of change in stream discharge, lag times, and physical streamflow processes, most notably those detailed for urban areas in northern Virginia.

Mechanical Balance Laws for Boussinesq Models of Surface Water Waves

NASA Astrophysics Data System (ADS)

Ali, Alfatih; Kalisch, Henrik

2012-06-01

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it appears that the expressions for many of these quantities are not known. This work presents a systematic derivation of mass, momentum and energy densities and fluxes associated with a general family of Boussinesq systems. The derivation is based on a reconstruction of the velocity field and the pressure in the fluid column below the free surface, and the derivation of differential balance equations which are of the same asymptotic validity as the evolution equations. It is shown that all these mechanical quantities can be expressed in terms of the principal dependent variables of the Boussinesq system: the surface excursion η and the horizontal velocity w at a given level in the fluid.

A direct method of extracting surface recombination velocity from an electron beam induced current line scan

NASA Astrophysics Data System (ADS)

Ong, Vincent K. S.

1998-04-01

The extraction of diffusion length and surface recombination velocity in a semiconductor with the use of an electron beam induced current line scan has traditionally been done by fitting the line scan into complicated theoretical equations. It was recently shown that a much simpler equation is sufficient for the extraction of diffusion length. The linearization coefficient is the only variable that is needed to be adjusted in the curve fitting process. However, complicated equations are still necessary for the extraction of surface recombination velocity. It is shown in this article that it is indeed possible to extract surface recombination velocity with a simple equation, using only one variable, the linearization coefficient. An intuitive feel for the reason behind the method was discussed. The accuracy of the method was verified with the use of three-dimensional computer simulation, and was found to be even slightly better than that of the best existing method.

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects.

PubMed

Chebakov, R; Kaplunov, J; Rogerson, G A

2016-02-01

The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assumed to considerably exceed the associated internal lengthscale. The leading-order long-wave approximation is shown to coincide formally with the 'local' problem for a half-space with a vertical inhomogeneity localized near the surface. Subsequent asymptotic analysis of the inhomogeneity results in an explicit correction to the classical boundary conditions on the surface. The order of the correction is greater than the order of the better-known correction to the governing differential equations. The refined boundary conditions enable us to evaluate the interior solution outside a narrow boundary layer localized near the surface. As an illustration, the effect of non-local elastic phenomena on the Rayleigh wave speed is investigated.

Hydrodynamic water impact. [Apollo spacecraft waterlanding

NASA Technical Reports Server (NTRS)

Kettleborough, C. F.

1972-01-01

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

Steady state model for the thermal regimes of shells of airships and hot air balloons

NASA Astrophysics Data System (ADS)

Luchev, Oleg A.

1992-10-01

A steady state model of the temperature regime of airships and hot air balloons shells is developed. The model includes three governing equations: the equation of the temperature field of airships or balloons shell, the integral equation for the radiative fluxes on the internal surface of the shell, and the integral equation for the natural convective heat exchange between the shell and the internal gas. In the model the following radiative fluxes on the shell external surface are considered: the direct and the earth reflected solar radiation, the diffuse solar radiation, the infrared radiation of the earth surface and that of the atmosphere. For the calculations of the infrared external radiation the model of the plane layer of the atmosphere is used. The convective heat transfer on the external surface of the shell is considered for the cases of the forced and the natural convection. To solve the mentioned set of the equations the numerical iterative procedure is developed. The model and the numerical procedure are used for the simulation study of the temperature fields of an airship shell under the forced and the natural convective heat transfer.

Numerical Simulations of a Multiscale Model of Stratified Langmuir Circulation

NASA Astrophysics Data System (ADS)

Malecha, Ziemowit; Chini, Gregory; Julien, Keith

2012-11-01

Langmuir circulation (LC), a prominent form of wind and surface-wave driven shear turbulence in the ocean surface boundary layer (BL), is commonly modeled using the Craik-Leibovich (CL) equations, a phase-averaged variant of the Navier-Stokes (NS) equations. Although surface-wave filtering renders the CL equations more amenable to simulation than are the instantaneous NS equations, simulations in wide domains, hundreds of times the BL depth, currently earn the ``grand challenge'' designation. To facilitate simulations of LC in such spatially-extended domains, we have derived multiscale CL equations by exploiting the scale separation between submesoscale and BL flows in the upper ocean. The numerical algorithm for simulating this multiscale model resembles super-parameterization schemes used in meteorology, but retains a firm mathematical basis. We have validated our algorithm and here use it to perform multiscale simulations of the interaction between LC and upper ocean density stratification. ZMM, GPC, KJ gratefully acknowledge funding from NSF CMG Award 0934827.

Metrisability of Painlevé equations

NASA Astrophysics Data System (ADS)

Contatto, Felipe; Dunajski, Maciej

2018-02-01

We solve the metrisability problem for the six Painlevé equations, and more generally for all 2nd order ordinary differential equations with the Painlevé property, and determine for which of these equations their integral curves are geodesics of a (pseudo) Riemannian metric on a surface.

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

NASA Astrophysics Data System (ADS)

Wang, D.

2017-12-01

The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

The Mean Curvature of the Influence Surface of Wave Equation With Sources on a Moving Surface

NASA Technical Reports Server (NTRS)

Farassat, F.; Farris, Mark

1999-01-01

The mean curvature of the influence surface of the space-time point (x, t) appears in linear supersonic propeller noise theory and in the Kirchhoff formula for a supersonic surface. Both these problems are governed by the linear wave equation with sources on a moving surface. The influence surface is also called the Sigma - surface in the aeroacoustic literature. This surface is the locus, in a frame fixed to the quiescent medium, of all the points of a radiating surface f(x, t) = 0 whose acoustic signals arrive simultaneously to an observer at position x and at the time t. Mathematically, the Sigma- surface is produced by the intersection of the characteristic conoid of the space-time point (x, t) and the moving surface. In this paper, we derive the expression for the local mean curvature of the Sigma - space of the space-time point for a moving rigid or deformable surface f(x, t) = 0. This expression is a complicated function of the geometric and kinematic parameters of the surface f(x, t) = 0. Using the results of this paper, the solution of the governing wave equation of high speed propeller noise radiation as well as the Kirchhoff formula for a supersonic surface can be written as very compact analytic expression.

Nano-transfersomes as a novel carrier for transdermal delivery.

PubMed

Chaudhary, Hema; Kohli, Kanchan; Kumar, Vikash

2013-09-15

The aim of this study was to design and optimize a nano-transfersomes of Diclofenac diethylamine (DDEA) and Curcumin (CRM). A 3(3) factorial design (Box-Behnken) was used to derive a polynomial equation (second order) to construct 2-D (contour) and 3-D (Response Surface) plots for prediction of responses. The ratio of lipid to surfactant (X1), weight of lipid to surfactant (X2) and sonication time (X3) (independent variables) and dependent variables [entrapment efficiency of DDEA (Y1), entrapment efficiency of CRM (Y2), effect on particle size (Y3), flux of DDEA (Y4), and flux of CRM (Y5)] were studied. The 2-D and 3-D plots were drawn and a statistical validity of the polynomials was established to find the compositions of optimized formulation. The design established the role of the derived polynomial equation, 2-D and 3-D plots in predicting the values of dependent variables for the preparation and optimization of nano-transfersomes for transdermal drug release. Copyright © 2013 Elsevier B.V. All rights reserved.

Large-Deformation Displacement Transfer Functions for Shape Predictions of Highly Flexible Slender Aerospace Structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2013-01-01

Large deformation displacement transfer functions were formulated for deformed shape predictions of highly flexible slender structures like aircraft wings. In the formulation, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (Eulerian), physical (Lagrangian), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.

Empirical equation for predicting the surface tension of some liquid metals at their melting point

NASA Astrophysics Data System (ADS)

Ceotto, D.

2014-07-01

A new empirical equation is proposed for predicting the surface tension of some pure metals at their melting point. The investigation has been conducted adopting a statistical approach using some of the most accredited data available in literature. It is found that for Ag, Al, Au, Co, Cu, Fe, Ni, and Pb the surface tension can be conveniently expressed in function of the latent heat of fusion and of the geometrical parameters of an ideal liquid spherical drop. The equation proposed has been compared also with the model proposed by Lu and Jiang giving satisfactory agreement for the metals considered.

TOPICAL REVIEW: Electrowetting: from basics to applications

NASA Astrophysics Data System (ADS)

Mugele, Frieder; Baret, Jean-Christophe

2005-07-01

Electrowetting has become one of the most widely used tools for manipulating tiny amounts of liquids on surfaces. Applications range from 'lab-on-a-chip' devices to adjustable lenses and new kinds of electronic displays. In the present article, we review the recent progress in this rapidly growing field including both fundamental and applied aspects. We compare the various approaches used to derive the basic electrowetting equation, which has been shown to be very reliable as long as the applied voltage is not too high. We discuss in detail the origin of the electrostatic forces that induce both contact angle reduction and the motion of entire droplets. We examine the limitations of the electrowetting equation and present a variety of recent extensions to the theory that account for distortions of the liquid surface due to local electric fields, for the finite penetration depth of electric fields into the liquid, as well as for finite conductivity effects in the presence of AC voltage. The most prominent failure of the electrowetting equation, namely the saturation of the contact angle at high voltage, is discussed in a separate section. Recent work in this direction indicates that a variety of distinct physical effects—rather than a unique one—are responsible for the saturation phenomenon, depending on experimental details. In the presence of suitable electrode patterns or topographic structures on the substrate surface, variations of the contact angle can give rise not only to continuous changes of the droplet shape, but also to discontinuous morphological transitions between distinct liquid morphologies. The dynamics of electrowetting are discussed briefly. Finally, we give an overview of recent work aimed at commercial applications, in particular in the fields of adjustable lenses, display technology, fibre optics, and biotechnology-related microfluidic devices.

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

NASA Astrophysics Data System (ADS)

van der Neut, Joost; Vasconcelos, Ivan; Wapenaar, Kees

2015-11-01

Iterative substitution of the coupled Marchenko equations is a novel methodology to retrieve the Green's functions from a source or receiver array at an acquisition surface to an arbitrary location in an acoustic medium. The methodology requires as input the single-sided reflection response at the acquisition surface and an initial focusing function, being the time-reversed direct wavefield from the acquisition surface to a specified location in the subsurface. We express the iterative scheme that is applied by this methodology explicitly as the successive actions of various linear operators, acting on an initial focusing function. These operators involve multidimensional crosscorrelations with the reflection data and truncations in time. We offer physical interpretations of the multidimensional crosscorrelations by subtracting traveltimes along common ray paths at the stationary points of the underlying integrals. This provides a clear understanding of how individual events are retrieved by the scheme. Our interpretation also exposes some of the scheme's limitations in terms of what can be retrieved in case of a finite recording aperture. Green's function retrieval is only successful if the relevant stationary points are sampled. As a consequence, internal multiples can only be retrieved at a subsurface location with a particular ray parameter if this location is illuminated by the direct wavefield with this specific ray parameter. Several assumptions are required to solve the Marchenko equations. We show that these assumptions are not always satisfied in arbitrary heterogeneous media, which can result in incomplete Green's function retrieval and the emergence of artefacts. Despite these limitations, accurate Green's functions can often be retrieved by the iterative scheme, which is highly relevant for seismic imaging and inversion of internal multiple reflections.

Computational Investigation and Validation of Twin-Tail Buffet Response Including Dynamics and Control

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1998-01-01

Multidisciplinary tools for prediction of single rectangular-tail buffet are extended to single swept-back-tail buffet in transonic-speed flow, and multidisciplinary tools for prediction and control of twin-tail buffet are developed and presented. The configuration model consists of a sharp-edged delta wing with single or twin tails that are oriented normal to the wing surface. The tails are treated as cantilevered beams fixed at the root and allowed to oscillate in both bending and torsion. This complex multidisciplinary problem is solved sequentially using three sets of equations on a dynamic single or multi-block grid structure. The first set is the unsteady, compressible, Reynolds-averaged Navier-Stokes equations which are used for obtaining the flow field vector and the aerodynamic loads on the tails. The Navier-Stokes equations are solved accurately in time using the implicit, upwind, flux-difference splitting, finite volume scheme. The second set is the coupled bending and torsion aeroelastic equations of cantilevered beams which are used for obtaining the bending and torsion deflections of the tails. The aeroelastic equations'are solved accurately in time using, a fifth-order-accurate Runge-Kutta scheme. The third set is the grid-displacement equations and the rigid-body dynamics equations, which are used for updating the grid coordinates due to the tail deflections and rigid-body motions. The tail-buffet phenomenon is predicted for highly-swept, single vertical tail placed at the plane of geometric symmetry, and for highly-swept, vertical twin tails placed at three different spanwise separation distances. The investigation demonstrates the effects of structural inertial coupling and uncoupling of the bending and torsion modes of vibration, spanwise positions of the twin-tail, angle of attack, and pitching and rolling dynamic motions of the configuration model on the tail buffet loading and response. The fundamental issue of twin-tail buffet alleviation is addressed using two active flow-control methods. These methods are the tangential leading-edge blowing and the flow suction from the leading-edge vortex cores along their paths. Qualitative and quantitative comparisons with the available experimental data are presented. The comparisons indicate that the present multidisciplinary aeroelastic analysis tools are robust, accurate and efficient.

The Rangeland Hydrology and Erosion Model: A Dynamic Approach for Predicting Soil Loss on Rangelands

NASA Astrophysics Data System (ADS)

Hernandez, Mariano; Nearing, Mark A.; Al-Hamdan, Osama Z.; Pierson, Frederick B.; Armendariz, Gerardo; Weltz, Mark A.; Spaeth, Kenneth E.; Williams, C. Jason; Nouwakpo, Sayjro K.; Goodrich, David C.; Unkrich, Carl L.; Nichols, Mary H.; Holifield Collins, Chandra D.

2017-11-01

In this study, we present the improved Rangeland Hydrology and Erosion Model (RHEM V2.3), a process-based erosion prediction tool specific for rangeland application. The article provides the mathematical formulation of the model and parameter estimation equations. Model performance is assessed against data collected from 23 runoff and sediment events in a shrub-dominated semiarid watershed in Arizona, USA. To evaluate the model, two sets of primary model parameters were determined using the RHEM V2.3 and RHEM V1.0 parameter estimation equations. Testing of the parameters indicated that RHEM V2.3 parameter estimation equations provided a 76% improvement over RHEM V1.0 parameter estimation equations. Second, the RHEM V2.3 model was calibrated to measurements from the watershed. The parameters estimated by the new equations were within the lowest and highest values of the calibrated parameter set. These results suggest that the new parameter estimation equations can be applied for this environment to predict sediment yield at the hillslope scale. Furthermore, we also applied the RHEM V2.3 to demonstrate the response of the model as a function of foliar cover and ground cover for 124 data points across Arizona and New Mexico. The dependence of average sediment yield on surface ground cover was moderately stronger than that on foliar cover. These results demonstrate that RHEM V2.3 predicts runoff volume, peak runoff, and sediment yield with sufficient accuracy for broad application to assess and manage rangeland systems.

Inverting x,y grid coordinates to obtain latitude and longitude in the vanderGrinten projection

NASA Technical Reports Server (NTRS)

Rubincam, D. P.

1980-01-01

The latitude and longitude of a point on the Earth's surface are found from its x,y grid coordinates in the vanderGrinten projection. The latitude is a solution of a cubic equation and the longitude a solution of a quadratic equation. Also, the x,y grid coordinates of a point on the Earth's surface can be found if its latitude and longitude are known by solving two simultaneous quadratic equations.

Solvated dissipative electro-elastic network model of hydrated proteins

NASA Astrophysics Data System (ADS)

Martin, Daniel

2013-03-01

Elastic network models coarse grain proteins into a network of residue beads connected by springs. We add dissipative dynamics to this mechanical system by applying overdamped Langevin equations of motion to normal-mode vibrations of the network. In addition, the network is made heterogeneous and softened at the protein surface by accounting for hydration of the ionized residues. Solvation changes the network Hessian in two ways. Diagonal solvation terms soften the spring constants and off-diagonal dipole-dipole terms correlate displacements of the ionized residues. The model is used to formulate the response functions of the electrostatic potential and electric field appearing in theories of redox reactions and spectroscopy. We also formulate the dielectric response of the protein and find that solvation of the surface ionized residues leads to a slow relaxation peak in the dielectric loss spectrum, about two orders of magnitude slower than the main peak of protein relaxation. Finally, the solvated network is used to formulate the allosteric response of the protein to ion binding. The global thermodynamics of ion binding is not strongly affected by the network solvation, but it dramatically enhances conformational changes in response to placing a charge at the a the active site.

Solvated dissipative electro-elastic network model of hydrated proteins

NASA Astrophysics Data System (ADS)

Martin, Daniel R.; Matyushov, Dmitry V.

2012-10-01

Elastic network models coarse grain proteins into a network of residue beads connected by springs. We add dissipative dynamics to this mechanical system by applying overdamped Langevin equations of motion to normal-mode vibrations of the network. In addition, the network is made heterogeneous and softened at the protein surface by accounting for hydration of the ionized residues. Solvation changes the network Hessian in two ways. Diagonal solvation terms soften the spring constants and off-diagonal dipole-dipole terms correlate displacements of the ionized residues. The model is used to formulate the response functions of the electrostatic potential and electric field appearing in theories of redox reactions and spectroscopy. We also formulate the dielectric response of the protein and find that solvation of the surface ionized residues leads to a slow relaxation peak in the dielectric loss spectrum, about two orders of magnitude slower than the main peak of protein relaxation. Finally, the solvated network is used to formulate the allosteric response of the protein to ion binding. The global thermodynamics of ion binding is not strongly affected by the network solvation, but it dramatically enhances conformational changes in response to placing a charge at the active site of the protein.

Degradation of ticarcillin by subcritial water oxidation method: Application of response surface methodology and artificial neural network modeling.

PubMed

Yabalak, Erdal

2018-05-18

This study was performed to investigate the mineralization of ticarcillin in the artificially prepared aqueous solution presenting ticarcillin contaminated waters, which constitute a serious problem for human health. 81.99% of total organic carbon removal, 79.65% of chemical oxygen demand removal, and 94.35% of ticarcillin removal were achieved by using eco-friendly, time-saving, powerful and easy-applying, subcritical water oxidation method in the presence of a safe-to-use oxidizing agent, hydrogen peroxide. Central composite design, which belongs to the response surface methodology, was applied to design the degradation experiments, to optimize the methods, to evaluate the effects of the system variables, namely, temperature, hydrogen peroxide concentration, and treatment time, on the responses. In addition, theoretical equations were proposed in each removal processes. ANOVA tests were utilized to evaluate the reliability of the performed models. F values of 245.79, 88.74, and 48.22 were found for total organic carbon removal, chemical oxygen demand removal, and ticarcillin removal, respectively. Moreover, artificial neural network modeling was applied to estimate the response in each case and its prediction and optimizing performance was statistically examined and compared to the performance of central composite design.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Radiative forcing and climate response due to the presence of black carbon in cloud droplets

NASA Astrophysics Data System (ADS)

Wang, Zhili; Zhang, Hua; Li, Jiangnan; Jing, Xianwen; Lu, Peng

2013-05-01

Optical properties of clouds containing black carbon (BC) particles in their water droplets are calculated by using the Maxwell Garnett mixing rule and Mie theory. The obtained cloud optical properties were then applied to an interactive system by coupling an aerosol model with a General Circulation Model. This system is used to investigate the radiative forcing and the equilibrium climate response due to BC in cloud droplets. The simulated global annual mean radiative forcing at the top of the atmosphere due to the BC in cloud droplets is found to be 0.086 W m-2. Positive radiative forcing can be seen in Africa, South America, East and South Asia, and West Europe, with a maximum value of 1.5 W m-2 being observed in these regions. The enhanced cloud absorption is shown to increase the global annual mean values of solar heating rate, water vapor, and temperature, but to decrease the global annual mean cloud fraction. Finally, the global annual mean surface temperature is shown to increase by +0.08 K. The local maximum changes are found to be as low as -1.5 K and as high as +0.6 K. We show there has been a significant difference in surface temperature change in the Southern and Northern Hemisphere (+0.19 K and -0.04 K, respectively). Our results show that this interhemispheric asymmetry in surface temperature change could cause a corresponding change in atmospheric dynamics and precipitation. It is also found that the northern trade winds are enhanced in the Intertropical Convergence Zone (ITCZ). This results in northerly surface wind anomalies which cross the equator to converge with the enhanced southern trade winds in the tropics of Southern Hemisphere. This is shown to lead to an increase (a decrease) of vertical ascending motion and precipitation on the south (north) side of the equator, which could induce a southward shift in the tropical rainfall maximum related to the ITCZ.

Radiative forcing and climate response due to the presence of black carbon in cloud droplets

NASA Astrophysics Data System (ADS)

Wang, Z.; Zhang, H.; Li, J.; Jing, X.; Lu, P.

2013-05-01

Optical properties of clouds containing black carbon (BC) particles in their water droplets are calculated by using the Maxwell Garnett mixing rule and Mie theory. The obtained cloud optical properties were then applied to an interactive system by coupling an aerosol model with a General Circulation Model. This system is used to investigate the radiative forcing and the equilibrium climate response due to BC in cloud droplets. The simulated global annual mean radiative forcing at the top of the atmosphere due to the BC in cloud droplets is found to be 0.086 W m-2. Positive radiative forcing can be seen in Africa, South America, East and South Asia and West Europe, with a maximum value of 1.5 W m-2 being observed in these regions. The enhanced cloud absorption is shown to increase the global annual mean values of solar heating rate, water vapor and temperature, but to decrease the global annual mean cloud fraction. Finally, the global annual mean surface temperature is shown to increase by +0.08 K. The local maximum changes are found to be as low as -1.5 K and as high as +0.6 K. We show there has been a significant difference in surface temperature change in the Southern and Northern Hemisphere (+0.19 K and -0.04 K, respectively). Our results show that this interhemispheric asymmetry in surface temperature change could cause a corresponding change in atmospheric dynamics and precipitation. It is also found that the northern trade winds are enhanced in the Intertropical Convergence Zone (ITCZ). This results in northerly surface wind anomalies which cross the equator to converge with the enhanced southern trade winds in the tropics of Southern Hemisphere. This is shown to lead to an increase (a decrease) of vertical ascending motion and precipitation on the south (north) side of the equator, which could induce a southward shift in the tropical rainfall maximum related to the ITCZ.

Issac, Jason Cherian ses in transonic flow

NASA Technical Reports Server (NTRS)

Issac, Jason Cherion; Kapania, Rakesh K.

1993-01-01

Flutter analysis of a two degree of freedom airfoil in compressible flow is performed using a state-space representation of the unsteady aerodynamic behavior. Indicial response functions are used to represent the normal force and moment response of the airfoil. The structural equations of motion of the airfoil with bending and torsional degrees of freedom are coupled to the unsteady air loads and the aeroelastic system so modelled is solved as an eigenvalue problem to determine the stability. The aeroelastic equations are also directly integrated with respect to time and the time-domain results compared with the results from the eigenanalysis. A good agreement is obtained. The derivatives of the flutter speed obtained from the eigenanalysis are calculated with respect to the mass and stiffness parameters by both analytical and finite-difference methods for various transonic Mach numbers. The experience gained from the two degree of freedom model is applied to study the sensitivity of the flutter response of a wing with respect to various shape parameters. The parameters being considered are as follows: (1) aspect ratio; (2) surface area of the wing; (3) taper ratio; and (4) sweep. The wing deflections are represented by Chebyshev polynomials. The compressible aerodynamic state-space model used for the airfoil section is extended to represent the unsteady aerodynamic forces on a generally laminated tapered skewed wing. The aeroelastic equations are solved as an eigenvalue problem to determine the flutter speed of the wing. The derivatives of the flutter speed with respect to the shape parameters are calculated by both analytical and finite difference methods.

A three-dimensional kinematic model for the dissolution of crystals

NASA Astrophysics Data System (ADS)

Tellier, C. R.

1989-06-01

The two-dimensional kinematic theory developed by Frank is extended into three dimensions. It is shown that the theoretical equations for the propagation vector associated with the displacement of a moving surface element can be directly derived from the polar equation of the slowness surface.

Aspheric surface testing by irradiance transport equation

NASA Astrophysics Data System (ADS)

Shomali, Ramin; Darudi, Ahmad; Nasiri, Sadollah; Asgharsharghi Bonab, Armir

2010-10-01

In this paper a method for aspheric surface testing is presented. The method is based on solving the Irradiance Transport Equation (ITE).The accuracy of ITE normally depends on the amount of the pick to valley of the phase distribution. This subject is investigated by a simulation procedure.

Weak Hydrological Sensitivity to Temperature Change over Land, Independent of Climate Forcing

NASA Technical Reports Server (NTRS)

Samset, B. H.; Myhre, G.; Forster, P. M.; Hodnebrog, O.; Andrews, T.; Boucher, O.; Faluvegi, G.; Flaeschner, D.; Kasoar, M.; Kharin, V.;

[Optimization of vacuum belt drying process of Gardeniae Fructus in Reduning injection by Box-Behnken design-response surface methodology].

PubMed

Huang, Dao-sheng; Shi, Wei; Han, Lei; Sun, Ke; Chen, Guang-bo; Wu Jian-xiong; Xu, Gui-hong; Bi, Yu-an; Wang, Zhen-zhong; Xiao, Wei

2015-06-01

To optimize the belt drying process conditions optimization of Gardeniae Fructus extract from Reduning injection by Box-Behnken design-response surface methodology, on the basis of single factor experiment, a three-factor and three-level Box-Behnken experimental design was employed to optimize the drying technology of Gardeniae Fructus extract from Reduning injection. With drying temperature, drying time, feeding speed as independent variables and the content of geniposide as dependent variable, the experimental data were fitted to a second order polynomial equation, establishing the mathematical relationship between the content of geniposide and respective variables. With the experimental data analyzed by Design-Expert 8. 0. 6, the optimal drying parameter was as follows: the drying temperature was 98.5 degrees C , the drying time was 89 min, the feeding speed was 99.8 r x min(-1). Three verification experiments were taked under this technology and the measured average content of geniposide was 564. 108 mg x g(-1), which was close to the model prediction: 563. 307 mg x g(-1). According to the verification test, the Gardeniae Fructus belt drying process is steady and feasible. So single factor experiments combined with response surface method (RSM) could be used to optimize the drying technology of Reduning injection Gardenia extract.

Dynamics of liquid films exposed to high-frequency surface vibration

NASA Astrophysics Data System (ADS)

Manor, Ofer; Rezk, Amgad R.; Friend, James R.; Yeo, Leslie Y.

2015-05-01

We derive a generalized equation that governs the spreading of liquid films under high-frequency (MHz-order) substrate vibration in the form of propagating surface waves and show that this single relationship is universally sufficient to collectively describe the rich and diverse dynamic phenomena recently observed for the transport of oil films under such substrate excitation, in particular, Rayleigh surface acoustic waves. In contrast to low-frequency (Hz- to kHz-order) vibration-induced wetting phenomena, film spreading at such high frequencies arises from convective drift generated by the viscous periodic flow localized in a region characterized by the viscous penetration depth β-1≡(2μ /ρ ω ) 1 /2 adjacent to the substrate that is invoked directly by its vibration; μ and ρ are the viscosity and the density of the liquid, respectively, and ω is the excitation frequency. This convective drift is responsible for driving the spreading of thin films of thickness h ≪kl-1 , which spread self-similarly as t1 /4 along the direction of the drift corresponding to the propagation direction of the surface wave, kl being the wave number of the compressional acoustic wave that forms in the liquid due to leakage of the surface wave energy from the substrate into the liquid and t the time. Films of greater thicknesses h ˜kl-1≫β-1 , in contrast, are observed to spread with constant velocity but in a direction that opposes the drift and surface wave propagation due to the attenuation of the acoustic wave in the liquid. The universal equation derived allows for the collective prediction of the spreading of these thin and thick films in opposing directions.

Surface tensions of solutions containing dicarboxylic acid mixtures

NASA Astrophysics Data System (ADS)

Lee, Jae Young; Hildemann, Lynn M.

2014-06-01

Organic solutes tend to lower the surface tension of cloud condensation nuclei, allowing them to more readily activate. The surface tension of various dicarboxylic acid aerosol mixtures was measured at 20 °C using the Wilhelmy plate method. At lower concentrations, the surface tension of a solution with equi-molar mixtures of dicarboxylic acids closely followed that of a solution with the most surface-active organic component alone. Measurements of surface tension for these mixtures were lower than predictions using Henning's model and the modified Szyszkowski equation, by ˜1-2%. The calculated maximum surface excess (Γmax) and inverse Langmuir adsorption coefficient (β) from the modified Szyszkowski equation were both larger than measured values for 6 of the 7 mixtures tested. Accounting for the reduction in surface tension in the Köhler equation reduced the critical saturation ratio for these multi-component mixtures - changes were negligible for dry diameters of 0.1 and 0.5 μm, but a reduction from 1.0068 to 1.0063 was seen for the 4-dicarboxylic acid mixture with a dry diameter of 0.05 μm.

Piezoresistive microcantilever aptasensor for ricin detection and kinetic analysis

NASA Astrophysics Data System (ADS)

Liu, Zhi-Wei; Tong, Zhao-Yang; Liu, Bing; Hao, Lan-Qun; Mu, Xi-Hui; Zhang, Jin-Ping; Gao, Chuan

2015-04-01

Up to now, there has been no report on target molecules detection by a piezoresistive microcantilever aptasensor. In order to evaluate the test performance and investigate the response dynamic characteristics of a piezoresistive microcantilever aptasensor, a novel method for ricin detection and kinetic analysis based on a piezoresistive microcantilever aptasensor was proposed, where ricin aptamer was immobilised on the microcantilever surface by biotin-avidin binding system. Results showed that the detection limit of ricin was 0.04μg L-1 (S/N ≥ 3). A linear relationship between the response voltage and the concentration of ricin in the range of 0.2μg L-1-40μg L-1 was obtained, with the linear regression equation of ΔUe = 0.904C + 5.852 (n = 5, R = 0.991, p < 0.001). The sensor showed no response for abrin, BSA, and could overcome the influence of complex environmental disruptors, indicating high specificity and good selectivity. Recovery and reproducibility in the result of simulated samples (simulated water, soil, and flour sample) determination met the analysis requirements, which was 90.5˜95.5% and 7.85%˜9.39%, respectively. On this basis, a reaction kinetic model based on ligand-receptor binding and the relationship with response voltage was established. The model could well reflect the dynamic response of the sensor. The correlation coefficient (R) was greater than or equal to 0.9456 (p < 0.001). Response voltage (ΔUe) and response time (t0) obtained from the fitting equation on different concentrations of ricin fitted well with the measured values.

Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Padmanabhan, T.

2011-02-15

It has been known for several decades that Einstein's field equations, when projected onto a null surface, exhibit a structure very similar to the nonrelativistic Navier-Stokes equation. I show that this result arises quite naturally when gravitational dynamics is viewed as an emergent phenomenon. Extremizing the spacetime entropy density associated with the null surfaces leads to a set of equations which, when viewed in the local inertial frame, becomes identical to the Navier-Stokes equation. This is in contrast to the usual description of the Damour-Navier-Stokes equation in a general coordinate system, in which there appears a Lie derivative rather thanmore » a convective derivative. I discuss this difference, its importance, and why it is more appropriate to view the equation in a local inertial frame. The viscous force on fluid, arising from the gradient of the viscous stress-tensor, involves the second derivatives of the metric and does not vanish in the local inertial frame, while the viscous stress-tensor itself vanishes so that inertial observers detect no dissipation. We thus provide an entropy extremization principle that leads to the Damour-Navier-Stokes equation, which makes the hydrodynamical analogy with gravity completely natural and obvious. Several implications of these results are discussed.« less

Solutions of the equation of heat flow. [in and around sunspots

NASA Technical Reports Server (NTRS)

Margolis, S. H.; Knobloch, E.

1980-01-01

The geometry of sunspots has been used to suggest a problem in heat flow. The equation of heat transport is solved for the case of a cylinder with a given thermal conductivity imbedded in an otherwise uniform medium with different conductivity. The surface of this region radiates heat with flux proportional to temperature. At a lower surface, either in heat flux or temperature is held constant. The cylinder can have an anisotropic thermal conductivity. The variations in temperature along the radiating surface have been determined. A simple approximation is noted which has been found to give a general solution with acceptable accuracy. This method may be of some use in other situations requiring the solution of Laplace's equation with a free surface. The analysis is used to set limits on the ratio of diameter to depth for cases which preserve the sharp surface temperature transition across the cylinder.

Sensitivity analysis of a wing aeroelastic response

NASA Technical Reports Server (NTRS)

Kapania, Rakesh K.; Eldred, Lloyd B.; Barthelemy, Jean-Francois M.

1991-01-01

A variation of Sobieski's Global Sensitivity Equations (GSE) approach is implemented to obtain the sensitivity of the static aeroelastic response of a three-dimensional wing model. The formulation is quite general and accepts any aerodynamics and structural analysis capability. An interface code is written to convert one analysis's output to the other's input, and visa versa. Local sensitivity derivatives are calculated by either analytic methods or finite difference techniques. A program to combine the local sensitivities, such as the sensitivity of the stiffness matrix or the aerodynamic kernel matrix, into global sensitivity derivatives is developed. The aerodynamic analysis package FAST, using a lifting surface theory, and a structural package, ELAPS, implementing Giles' equivalent plate model are used.

The Buoyancy Budget With a Nonlinear Equation of State

NASA Astrophysics Data System (ADS)

Hieronymus, M. H.; Nycander, J.

2012-12-01

There has been a number of studies focusing on different aspects of having a nonlinear equation of state for seawater. Amongst other things it has been shown that the nonlinear equation of state has implications for the oceanic energy budget and that nonlinear processes can be a significant source of dense water production. This presentation will focus on the oceanic buoyancy budget. The nonlinear equation of state of seawater can introduce a sink or source of buoyancy when water parcels of unequal salinities and temperatures are mixed. A common example is the process known as cabbeling, which is responsible for forming a water mass that is denser than the original constituents in a mixture of two water masses with equal densities but different salinities and temperatures. This presentation will contain quantitative estimates of these nonlinear effects on the buoyancy budget of the global ocean. Because of these nonlinear effects there is a net sink of buoyancy in the oceans interior and the size of this sink can be determined from the buoyancy fluxes at the ocean boundaries. These boundary buoyancy fluxes are calculated using two surface heat flux climatologies one based on in situ measurements, the other on a reanalysis and in both cases using a nonlinear equation of state. The presentation also treats the buoyancy budget in the State of the art ocean model Nucleus for European Modelling of the Ocean (NEMO) and the results from NEMO are seen to be in good agreement with the buoyancy budgets based on the heat flux climatologies. Using the ocean model is a good complement to the surface flux climatologies, because in NEMO the buoyancy fluxes can be evaluated at all vertical model levels. This means that the vertical distribution of the buoyancy sink can be looked into. The results from NEMO shows that in large parts of the ocean the nonlinear buoyancy sink is the largest contribution to the buoyancy budget.

Pressure evolution equation for the particulate phase in inhomogeneous compressible disperse multiphase flows

NASA Astrophysics Data System (ADS)

Annamalai, Subramanian; Balachandar, S.; Sridharan, P.; Jackson, T. L.

2017-02-01

An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term "dispersed phase" represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.

A Newton method for the magnetohydrodynamic equilibrium equations

NASA Astrophysics Data System (ADS)

Oliver, Hilary James

We have developed and implemented a (J, B) space Newton method to solve the full nonlinear three dimensional magnetohydrodynamic equilibrium equations in toroidal geometry. Various cases have been run successfully, demonstrating significant improvement over Picard iteration, including a 3D stellarator equilibrium at β = 2%. The algorithm first solves the equilibrium force balance equation for the current density J, given a guess for the magnetic field B. This step is taken from the Picard-iterative PIES 3D equilibrium code. Next, we apply Newton's method to Ampere's Law by expansion of the functional J(B), which is defined by the first step. An analytic calculation in magnetic coordinates, of how the Pfirsch-Schlüter currents vary in the plasma in response to a small change in the magnetic field, yields the Newton gradient term (analogous to ∇f . δx in Newton's method for f(x) = 0). The algorithm is computationally feasible because we do this analytically, and because the gradient term is flux surface local when expressed in terms of a vector potential in an Ar=0 gauge. The equations are discretized by a hybrid spectral/offset grid finite difference technique, and leading order radial dependence is factored from Fourier coefficients to improve finite- difference accuracy near the polar-like origin. After calculating the Newton gradient term we transfer the equation from the magnetic grid to a fixed background grid, which greatly improves the code's performance.

Holographic Entanglement Entropy, SUSY & Calibrations

NASA Astrophysics Data System (ADS)

Colgáin, Eoin Ó.

2018-01-01

Holographic calculations of entanglement entropy boil down to identifying minimal surfaces in curved spacetimes. This generically entails solving second-order equations. For higher-dimensional AdS geometries, we demonstrate that supersymmetry and calibrations reduce the problem to first-order equations. We note that minimal surfaces corresponding to disks preserve supersymmetry, whereas strips do not.

Method for computing a roughness factor for veneer surfaces

Treesearch

Chung-Yun Hse

1972-01-01

Equations for determining the roughness factor (ratio of true surface to apparent area) of rotary-cut veneer were derived from an assumed tracheid model. With data measured on southern pine veneers, the equations indicated that the roughness factor of latewood was near unity, whereas that of earlywood was about 2.

Principles of the radiosity method versus radiative transfer for canopy reflectance modeling

NASA Technical Reports Server (NTRS)

Gerstl, Siegfried A. W.; Borel, Christoph C.

1992-01-01

The radiosity method is introduced to plant canopy reflectance modeling. We review the physics principles of the radiosity method which originates in thermal radiative transfer analyses when hot and cold surfaces are considered within a given enclosure. The radiosity equation, which is an energy balance equation for discrete surfaces, is described and contrasted with the radiative transfer equation, which is a volumetric energy balance equation. Comparing the strengths and weaknesses of the radiosity method and the radiative transfer method, we conclude that both methods are complementary to each other. Results of sample calculations are given for canopy models with up to 20,000 discrete leaves.

Aquarius reveals salinity structure of tropical instability waves

NASA Astrophysics Data System (ADS)

Lee, Tong; Lagerloef, Gary; Gierach, Michelle M.; Kao, Hsun-Ying; Yueh, Simon; Dohan, Kathleen

2012-06-01

Sea surface salinity (SSS) measurements from the Aquarius/SAC-D satellite during September-December 2011 provide the first satellite observations of the salinity structure of tropical instability waves (TIWs) in the Pacific. The related SSS anomaly has a magnitude of approximately ±0.5 PSU. Different from sea surface temperature (SST) and sea surface height anomaly (SSHA) where TIW-related propagating signals are stronger a few degrees away from the equator, the SSS signature of TIWs is largest near the equator in the eastern equatorial Pacific where salty South Pacific water meets the fresher Inter-tropical Convergence Zone water. The dominant westward propagation speed of SSS near the equator is approximately 1 m/s. This is twice as fast as the 0.5 m/s TIW speed widely reported in the literature, typically from SST and SSHA away from the equator. This difference is attributed to the more dominant 17-day TIWs near the equator that have a 1 m/s dominant phase speed and the stronger 33-day TIWs away from the equator that have a 0.5 m/s dominant phase speed. The results demonstrate the important value of Aquarius in studying TIWs.

Optimization of tetracycline hydrochloride adsorption on amino modified SBA-15 using response surface methodology.

PubMed

Hashemikia, Samaneh; Hemmatinejad, Nahid; Ahmadi, Ebrahim; Montazer, Majid

2015-04-01

Several researchers are focused on preparation of mesoporous silica as drug carriers with high loading efficiency to control or sustain the drug release. Carriers with highly loaded drug are utilized to minimize the time of drug intake. In this study, amino modified SBA-15 was synthesized through grafting with amino propyl triethoxy silane and then loaded with tetracycline hydrochloride. The drug loading was optimized by using the response surface method considering various factors including drug to silica ratio, operation time, and temperature. The drug to silica ratio indicated as the most influential factor on the drug loading yield. Further, a quadratic polynomial equation was developed to predict the loading percentage. The experimental results indicated reasonable agreement with the predicted values. The modified and drug loaded mesoporous particles were characterized by FT-IR, SEM, TEM, X-ray diffraction (XRD), elemental analysis and N2 adsorption-desorption. The release profiles of tetracycline-loaded particles were studied in different pH. Also, Higuchi equation was used to analyze the release profile of the drug and to evaluate the kinetic of drug release. The drug release rate followed the conventional Higuchi model that could be controlled by amino-functionalized SBA-15. Further, the drug delivery system based on amino modified SBA-15 exhibits novel features with an appropriate usage as an anti-bacterial drug delivery system with effective management of drug adsorption and release. Copyright © 2014 Elsevier Inc. All rights reserved.

Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces

NASA Astrophysics Data System (ADS)

Fasondini, Marco; Fornberg, Bengt; Weideman, J. A. C.

2017-09-01

We extend the numerical pole field solver (Fornberg and Weideman (2011) [12]) to enable the computation of the multivalued Painlevé transcendents, which are the solutions to the third, fifth and sixth Painlevé equations, on their Riemann surfaces. We display, for the first time, solutions to these equations on multiple Riemann sheets. We also provide numerical evidence for the existence of solutions to the sixth Painlevé equation that have pole-free sectors, known as tronquée solutions.

Finite element analysis of notch behavior using a state variable constitutive equation

NASA Technical Reports Server (NTRS)

Dame, L. T.; Stouffer, D. C.; Abuelfoutouh, N.

1985-01-01

The state variable constitutive equation of Bodner and Partom was used to calculate the load-strain response of Inconel 718 at 649 C in the root of a notch. The constitutive equation was used with the Bodner-Partom evolution equation and with a second evolution equation that was derived from a potential function of the stress and state variable. Data used in determining constants for the constitutive models was from one-dimensional smooth bar tests. The response was calculated for a plane stress condition at the root of the notch with a finite element code using constant strain triangular elements. Results from both evolution equations compared favorably with the observed experimental response. The accuracy and efficiency of the finite element calculations also compared favorably to existing methods.

Representing the effects of alpine grassland vegetation cover on the simulation of soil thermal dynamics by ecosystem models applied to the Qinghai-Tibetan Plateau

USGS Publications Warehouse

Yi, S.; Li, N.; Xiang, B.; Wang, X.; Ye, B.; McGuire, A.D.

2013-01-01

Soil surface temperature is a critical boundary condition for the simulation of soil temperature by environmental models. It is influenced by atmospheric and soil conditions and by vegetation cover. In sophisticated land surface models, it is simulated iteratively by solving surface energy budget equations. In ecosystem, permafrost, and hydrology models, the consideration of soil surface temperature is generally simple. In this study, we developed a methodology for representing the effects of vegetation cover and atmospheric factors on the estimation of soil surface temperature for alpine grassland ecosystems on the Qinghai-Tibetan Plateau. Our approach integrated measurements from meteorological stations with simulations from a sophisticated land surface model to develop an equation set for estimating soil surface temperature. After implementing this equation set into an ecosystem model and evaluating the performance of the ecosystem model in simulating soil temperature at different depths in the soil profile, we applied the model to simulate interactions among vegetation cover, freeze-thaw cycles, and soil erosion to demonstrate potential applications made possible through the implementation of the methodology developed in this study. Results showed that (1) to properly estimate daily soil surface temperature, algorithms should use air temperature, downward solar radiation, and vegetation cover as independent variables; (2) the equation set developed in this study performed better than soil surface temperature algorithms used in other models; and (3) the ecosystem model performed well in simulating soil temperature throughout the soil profile using the equation set developed in this study. Our application of the model indicates that the representation in ecosystem models of the effects of vegetation cover on the simulation of soil thermal dynamics has the potential to substantially improve our understanding of the vulnerability of alpine grassland ecosystems to changes in climate and grazing regimes.

Representing the effects of alpine grassland vegetation cover on the simulation of soil thermal dynamics by ecosystem models applied to the Qinghai-Tibetan Plateau

NASA Astrophysics Data System (ADS)

Yi, S.; Li, N.; Xiang, B.; Wang, X.; Ye, B.; McGuire, A. D.

2013-07-01

surface temperature is a critical boundary condition for the simulation of soil temperature by environmental models. It is influenced by atmospheric and soil conditions and by vegetation cover. In sophisticated land surface models, it is simulated iteratively by solving surface energy budget equations. In ecosystem, permafrost, and hydrology models, the consideration of soil surface temperature is generally simple. In this study, we developed a methodology for representing the effects of vegetation cover and atmospheric factors on the estimation of soil surface temperature for alpine grassland ecosystems on the Qinghai-Tibetan Plateau. Our approach integrated measurements from meteorological stations with simulations from a sophisticated land surface model to develop an equation set for estimating soil surface temperature. After implementing this equation set into an ecosystem model and evaluating the performance of the ecosystem model in simulating soil temperature at different depths in the soil profile, we applied the model to simulate interactions among vegetation cover, freeze-thaw cycles, and soil erosion to demonstrate potential applications made possible through the implementation of the methodology developed in this study. Results showed that (1) to properly estimate daily soil surface temperature, algorithms should use air temperature, downward solar radiation, and vegetation cover as independent variables; (2) the equation set developed in this study performed better than soil surface temperature algorithms used in other models; and (3) the ecosystem model performed well in simulating soil temperature throughout the soil profile using the equation set developed in this study. Our application of the model indicates that the representation in ecosystem models of the effects of vegetation cover on the simulation of soil thermal dynamics has the potential to substantially improve our understanding of the vulnerability of alpine grassland ecosystems to changes in climate and grazing regimes.

Helium atmospheric pressure plasma jets touching dielectric and metal surfaces

NASA Astrophysics Data System (ADS)

Norberg, Seth A.; Johnsen, Eric; Kushner, Mark J.

2015-07-01

Atmospheric pressure plasma jets (APPJs) are being investigated in the context plasma medicine and biotechnology applications, and surface functionalization. The composition of the surface being treated ranges from plastics, liquids, and biological tissue, to metals. The dielectric constant of these materials ranges from as low as 1.5 for plastics to near 80 for liquids, and essentially infinite for metals. The electrical properties of the surface are not independent variables as the permittivity of the material being treated has an effect on the dynamics of the incident APPJ. In this paper, results are discussed from a computational investigation of the interaction of an APPJ incident onto materials of varying permittivity, and their impact on the discharge dynamics of the plasma jet. The computer model used in this investigation solves Poisson's equation, transport equations for charged and neutral species, the electron energy equation, and the Navier-Stokes equations for the neutral gas flow. The APPJ is sustained in He/O2 = 99.8/0.2 flowing into humid air, and is directed onto dielectric surfaces in contact with ground with dielectric constants ranging from 2 to 80, and a grounded metal surface. Low values of relative permittivity encourage propagation of the electric field into the treated material and formation and propagation of a surface ionization wave. High values of relative permittivity promote the restrike of the ionization wave and the formation of a conduction channel between the plasma discharge and the treated surface. The distribution of space charge surrounding the APPJ is discussed.

Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations

NASA Astrophysics Data System (ADS)

Wieland, Wolfgang

2017-03-01

Witten's proof for the positivity of the ADM mass gives a definition of energy in terms of three-surface spinors. In this paper, we give a generalisation for the remaining six Poincaré charges at spacelike infinity, which are the angular momentum and centre of mass. The construction improves on certain three-surface spinor equations introduced by Shaw. We solve these equations asymptotically obtaining the ten Poincaré charges as integrals over the Nester-Witten two-form. We point out that the defining differential equations can be extended to three-surfaces of arbitrary signature and we study them on the entire boundary of a compact four-dimensional region of spacetime. The resulting quasi-local expressions for energy and angular momentum are integrals over a two-dimensional cross-section of the boundary. For any two consecutive such cross-sections, conservation laws are derived that determine the influx (outflow) of matter and gravitational radiation.

Sewall Wright's equation Deltaq=(q(1-q) partial differentialw/ partial differentialq)/2w.

PubMed

Edwards, A W

2000-02-01

An equation of Sewall Wright's expresses the change in the frequency of an allele under selection at a multiallelic locus as a function of the gradient of the mean fitness "surface" in the direction in which the relative proportions of the other alleles do not change. An attempt to derive this equation using conventional vector calculus shows that this description leads to a different equation and that the purported gradient in Wright's equation is not a gradient of the mean fitness surface except in the diallelic case, where the two equations are the same. It is further shown that if Fisher's angular transformation is applied to the diallelic case the genic variance is exactly equal to one-eighth of the square of the gradient of the mean fitness with respect to the transformed gene frequency. Copyright 2000 Academic Press.

Single- versus Double-Scoring of Trend Responses in Trend Score Equating with Constructed-Response Tests. Research Report. ETS RR-10-12

ERIC Educational Resources Information Center

Tan, Xuan; Ricker, Kathryn L.; Puhan, Gautam

2010-01-01

This study examines the differences in equating outcomes between two trend score equating designs resulting from two different scoring strategies for trend scoring when operational constructed-response (CR) items are double-scored--the single group (SG) design, where each trend CR item is double-scored, and the nonequivalent groups with anchor…

Mathematical modelling of surface water-groundwater flow and salinity interactions in the coastal zone

NASA Astrophysics Data System (ADS)

Spanoudaki, Katerina; Kampanis, Nikolaos A.

2014-05-01

Coastal areas are the most densely-populated areas in the world. Consequently water demand is high, posing great pressure on fresh water resources. Climatic change and its direct impacts on meteorological variables (e.g. precipitation) and indirect impact on sea level rise, as well as anthropogenic pressures (e.g. groundwater abstraction), are strong drivers causing groundwater salinisation and subsequently affecting coastal wetlands salinity with adverse effects on the corresponding ecosystems. Coastal zones are a difficult hydrologic environment to represent with a mathematical model due to the large number of contributing hydrologic processes and variable-density flow conditions. Simulation of sea level rise and tidal effects on aquifer salinisation and accurate prediction of interactions between coastal waters, groundwater and neighbouring wetlands requires the use of integrated surface water-groundwater models. In the past few decades several computer codes have been developed to simulate coupled surface and groundwater flow. In these numerical models surface water flow is usually described by the 1-D Saint Venant equations (e.g. Swain and Wexler, 1996) or the 2D shallow water equations (e.g. Liang et al., 2007). Further simplified equations, such as the diffusion and kinematic wave approximations to the Saint Venant equations, are also employed for the description of 2D overland flow and 1D stream flow (e.g. Gunduz and Aral, 2005). However, for coastal bays, estuaries and wetlands it is often desirable to solve the 3D shallow water equations to simulate surface water flow. This is the case e.g. for wind-driven flows or density-stratified flows. Furthermore, most integrated models are based on the assumption of constant fluid density and therefore their applicability to coastal regions is questionable. Thus, most of the existing codes are not well-suited to represent surface water-groundwater interactions in coastal areas. To this end, the 3D integrated surface water-groundwater model IRENE (Spanoudaki et al., 2009; Spanoudaki, 2010) has been modified in order to simulate surface water-groundwater flow and salinity interactions in the coastal zone. IRENE, in its original form, couples the 3D, non-steady state Navier-Stokes equations, after Reynolds averaging and with the assumption of hydrostatic pressure distribution, to the equations describing 3D saturated groundwater flow of constant density. A semi-implicit finite difference scheme is used to solve the surface water flow equations, while a fully implicit finite difference scheme is used for the groundwater equations. Pollution interactions are simulated by coupling the advection-diffusion equation describing the fate and transport of contaminants introduced in a 3D turbulent flow field to the partial differential equation describing the fate and transport of contaminants in 3D transient groundwater flow systems. The model has been further developed to include the effects of density variations on surface water and groundwater flow, while the already built-in solute transport capabilities are used to simulate salinity interactions. Initial results show that IRENE can accurately predict surface water-groundwater flow and salinity interactions in coastal areas. Important research issues that can be investigated using IRENE include: (a) sea level rise and tidal effects on aquifer salinisation and the configuration of the saltwater wedge, (b) the effects of surface water-groundwater interaction on salinity increase of coastal wetlands and (c) the estimation of the location and magnitude of groundwater discharge to coasts. Acknowledgement The work presented in this paper has been funded by the Greek State Scholarships Foundation (IKY), Fellowships of Excellence for Postdoctoral Studies (Siemens Program), 'A simulation-optimization model for assessing the best practices for the protection of surface water and groundwater in the coastal zone', (2013 - 2015). References Gunduz, O. and Aral, M.M. (2005). River networks and groundwater flow: a simultaneous solution of a coupled system. Journal of Hydrology 301 (1-4), 216-234. Liang, D., Falconer, R.A. and Lin, B. (2007). Coupling surface and subsurface flows in a depth-averaged flood wave model. Journal of Hydrology 337, 147-158. Spanoudaki, K., Stamou, A.I. and Nanou-Giannarou, A. (2009). Development and verification of a 3-D integrated surface water-groundwater model. Journal of Hydrology, 375 (3-4), 410-427. Spanoudaki, K. (2010). Integrated numerical modelling of surface water groundwater systems (in Greek). Ph.D. Thesis, National Technical University of Athens, Greece. Swain, E.D. and Wexler, E.J. (1996). A coupled surface water and groundwater flow model (Modbranch) for simulation of stream-aquifer interaction. United States Geological Survey, Techniques of Water Resources Investigations (Book 6, Chapter A6).

Adhesive contact between a rigid spherical indenter and an elastic multi-layer coated substrate

PubMed Central

Stan, Gheorghe; Adams, George G.

2016-01-01

In this work the frictionless, adhesive contact between a rigid spherical indenter and an elastic multi-layer coated half-space was investigated by means of an integral transform formulation. The indented multi-layer coats were considered as made of isotropic layers that are perfectly bonded to each other and to an isotropic substrate. The adhesive interaction between indenter and contacting surface was treated as Maugis-type adhesion to provide general applicability within the entire range of adhesive interactions. By using a transfer matrix method, the stress-strain equations of the system were reduced to two coupled integral equations for the stress distribution under the indenter and the ratio between the adhesion radius and the contact radius, respectively. These resulting integral equations were solved through a numerical collocation technique, with solutions for the load dependencies of the contact radius and indentation depth for various values of the adhesion parameter and layer composition. The method developed here can be used to calculate the force-distance response of adhesive contacts on various inhomogeneous half-spaces that can be modeled as multi-layer coated half-spaces. PMID:27574338

Isogeometric Kirchhoff-Love shell formulations for biological membranes

PubMed Central

Tepole, Adrián Buganza; Kabaria, Hardik; Bletzinger, Kai-Uwe; Kuhl, Ellen

2015-01-01

Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis. PMID:26251556

A Martian global groundwater model

NASA Technical Reports Server (NTRS)

Howard, Alan D.

1991-01-01

A global groundwater flow model was constructed for Mars to study hydrologic response under a variety of scenarios, improving and extending earlier simple cross sectional models. The model is capable of treating both steady state and transient flow as well as permeability that is anisotropic in the horizontal dimensions. A single near surface confining layer may be included (representing in these simulations a coherent permafrost layer). Furthermore, in unconfined flow, locations of complete saturation and seepage are determined. The flow model assumes that groundwater gradients are sufficiently low that DuPuit conditions are satisfied and the flow component perpendicular to the ground surface is negligible. The flow equations were solved using a finite difference method employing 10 deg spacing of latitude and longitude.

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Ochs, Harry T., III

1988-01-01

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

Anomalous sea surface structures as an object of statistical topography

NASA Astrophysics Data System (ADS)

Klyatskin, V. I.; Koshel, K. V.

2015-06-01

By exploiting ideas of statistical topography, we analyze the stochastic boundary problem of emergence of anomalous high structures on the sea surface. The kinematic boundary condition on the sea surface is assumed to be a closed stochastic quasilinear equation. Applying the stochastic Liouville equation, and presuming the stochastic nature of a given hydrodynamic velocity field within the diffusion approximation, we derive an equation for a spatially single-point, simultaneous joint probability density of the surface elevation field and its gradient. An important feature of the model is that it accounts for stochastic bottom irregularities as one, but not a single, perturbation. Hence, we address the assumption of the infinitely deep ocean to obtain statistic features of the surface elevation field and the squared elevation gradient field. According to the calculations, we show that clustering in the absolute surface elevation gradient field happens with the unit probability. It results in the emergence of rare events such as anomalous high structures and deep gaps on the sea surface almost in every realization of a stochastic velocity field.

Two volume integral equations for the inhomogeneous and anisotropic forward problem in electroencephalography

NASA Astrophysics Data System (ADS)

Rahmouni, Lyes; Mitharwal, Rajendra; Andriulli, Francesco P.

2017-11-01

This work presents two new volume integral equations for the Electroencephalography (EEG) forward problem which, differently from the standard integral approaches in the domain, can handle heterogeneities and anisotropies of the head/brain conductivity profiles. The new formulations translate to the quasi-static regime some volume integral equation strategies that have been successfully applied to high frequency electromagnetic scattering problems. This has been obtained by extending, to the volume case, the two classical surface integral formulations used in EEG imaging and by introducing an extra surface equation, in addition to the volume ones, to properly handle boundary conditions. Numerical results corroborate theoretical treatments, showing the competitiveness of our new schemes over existing techniques and qualifying them as a valid alternative to differential equation based methods.

Comparison of total body water estimates from O-18 and bioelectrical response prediction equations

NASA Technical Reports Server (NTRS)

Barrows, Linda H.; Inners, L. Daniel; Stricklin, Marcella D.; Klein, Peter D.; Wong, William W.; Siconolfi, Steven F.

1993-01-01

Identification of an indirect, rapid means to measure total body water (TBW) during space flight may aid in quantifying hydration status and assist in countermeasure development. Bioelectrical response testing and hydrostatic weighing were performed on 27 subjects who ingested O-18, a naturally occurring isotope of oxygen, to measure true TBW. TBW estimates from three bioelectrical response prediction equations and fat-free mass (FFM) were compared to TBW measured from O-18. A repeated measures MANOVA with post-hoc Dunnett's Test indicated a significant (p less than 0.05) difference between TBW estimates from two of the three bioelectrical response prediction equations and O-18. TBW estimates from FFM and the Kushner & Schoeller (1986) equation yielded results that were similar to those given by O-18. Strong correlations existed between each prediction method and O-18; however, standard errors, identified through regression analyses, were higher for the bioelectrical response prediction equations compared to those derived from FFM. These findings suggest (1) the Kushner & Schoeller (1986) equation may provide a valid measure of TBW, (2) other TBW prediction equations need to be identified that have variability similar to that of FFM, and (3) bioelectrical estimates of TBW may prove valuable in quantifying hydration status during space flight.

Feasibility of detecting near-surface feature with Rayleigh-wave diffraction

USGS Publications Warehouse

Xia, J.; Nyquist, Jonathan E.; Xu, Y.; Roth, M.J.S.; Miller, R.D.

2007-01-01

Detection of near-surfaces features such as voids and faults is challenging due to the complexity of near-surface materials and the limited resolution of geophysical methods. Although multichannel, high-frequency, surface-wave techniques can provide reliable shear (S)-wave velocities in different geological settings, they are not suitable for detecting voids directly based on anomalies of the S-wave velocity because of limitations on the resolution of S-wave velocity profiles inverted from surface-wave phase velocities. Therefore, we studied the feasibility of directly detecting near-surfaces features with surface-wave diffractions. Based on the properties of surface waves, we have derived a Rayleigh-wave diffraction traveltime equation. We also have solved the equation for the depth to the top of a void and an average velocity of Rayleigh waves. Using these equations, the depth to the top of a void/fault can be determined based on traveltime data from a diffraction curve. In practice, only two diffraction times are necessary to define the depth to the top of a void/fault and the average Rayleigh-wave velocity that generates the diffraction curve. We used four two-dimensional square voids to demonstrate the feasibility of detecting a void with Rayleigh-wave diffractions: a 2??m by 2??m with a depth to the top of the void of 2??m, 4??m by 4??m with a depth to the top of the void of 7??m, and 6??m by 6??m with depths to the top of the void 12??m and 17??m. We also modeled surface waves due to a vertical fault. Rayleigh-wave diffractions were recognizable for all these models after FK filtering was applied to the synthetic data. The Rayleigh-wave diffraction traveltime equation was verified by the modeled data. Modeling results suggested that FK filtering is critical to enhance diffracted surface waves. A real-world example is presented to show how to utilize the derived equation of surface-wave diffractions. ?? 2006 Elsevier B.V. All rights reserved.

Optimization of cutting parameters in CNC turning of stainless steel 304 with TiAlN nano coated carbide cutting tool

NASA Astrophysics Data System (ADS)

Durga Prasada Rao, V.; Harsha, N.; Raghu Ram, N. S.; Navya Geethika, V.

2018-02-01

In this work, turning was performed to optimize the surface finish or roughness (Ra) of stainless steel 304 with uncoated and coated carbide tools under dry conditions. The carbide tools were coated with Titanium Aluminium Nitride (TiAlN) nano coating using Physical Vapour Deposition (PVD) method. The machining parameters, viz., cutting speed, depth of cut and feed rate which show major impact on Ra are considered during turning. The experiments are designed as per Taguchi orthogonal array and machining process is done accordingly. Then second-order regression equations have been developed on the basis of experimental results for Ra in terms of machining parameters used. Regarding the effect of machining parameters, an upward trend is observed in Ra with respect to feed rate, and as cutting speed increases the Ra value increased slightly due to chatter and vibrations. The adequacy of response variable (Ra) is tested by conducting additional experiments. The predicted Ra values are found to be a close match of their corresponding experimental values of uncoated and coated tools. The corresponding average % errors are found to be within the acceptable limits. Then the surface roughness equations of uncoated and coated tools are set as the objectives of optimization problem and are solved by using Differential Evolution (DE) algorithm. Also the tool lives of uncoated and coated tools are predicted by using Taylor’s tool life equation.

The dynamic-response characteristics of a 35 degree swept-wing airplane as determined from flight measurements

NASA Technical Reports Server (NTRS)

Triplett, William C; Brown, Stuart C; Smith, G Allan

1955-01-01

The longitudinal and lateral-directional dynamic-response characteristics of a 35 degree swept-wing fighter-type airplane determined from flight measurements are presented and compared with predictions based on theoretical studies and wind-tunnel data. Flights were made at an altitude of 35,000 feet covering the Mach number range of 0.50 to 1.04. A limited amount of lateral-directional data were also obtained at 10,000 feet. The flight consisted essentially of recording transient responses to pilot-applied pulsed motions of each of the three primary control surfaces. These transient data were converted into frequency-response form by means of the Fourier transformation and compared with predicted responses calculated from the basic equations. Experimentally determined transfer functions were used for the evaluation of the stability derivatives that have the greatest effect on the dynamic response of the airplane. The values of these derivatives, in most cases, agreed favorably with predictions over the Mach number range of the test.

Nonlinear vibration of double-walled boron nitride and carbon nanopeapods under multi-physical fields with consideration of surface stress effects

NASA Astrophysics Data System (ADS)

Ghorbanpour Arani, A.; Sabzeali, M.; BabaAkbar Zarei, H.

2017-12-01

In this study, the nonlinear thermo-electro vibrations of double-walled boron nitride nanopeapods (DWBNNPPs) and double-walled carbon nanopeapods (DWCNPPs) under magnetic field embedded in an elastic medium is investigated. DWBNNPPs are made of piezoelectric and smart materials therefore, electric field is effective on them; meanwhile, DWCNPPs are made of carbon thus, magnetic field can be useful to control them. The Pasternak model is used to simulate the effects of elastic medium which surrounds the system. Nanotubes are modeled with assumption of the Euler-Bernoulli beam (EBB) theory and the surface effects are considered to achieve accurate response of the system. Moreover, interaction between two layers is modeled by van der Waals (vdW) forces. The equations of motion are derived using the energy method and the Hamilton principle. Then the governing equations are solved by using Galerkin's method and incremental harmonic balance method (IHBM). The influences of various parameters such as the magnetic field, different types of DWCNPPs and DWBNNPPs, elastic medium, existence of fullerene and surface effect on the vibration behavior of the system are investigated. The results demonstrate that DWBNNPPs have more influence on the frequency of the system than DWCNPPs. In addition, the presence of fullerene in nanotubes has a negative impact on the frequency behavior of revisionthe system.

A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method.

PubMed

Renteria Marquez, I A; Bolborici, V

2017-05-01

This manuscript presents a method to model in detail the piezoelectric traveling wave rotary ultrasonic motor (PTRUSM) stator response under the action of DC and AC voltages. The stator is modeled with a discrete two dimensional system of equations using the finite volume method (FVM). In order to obtain accurate results, a model of the stator bridge is included into the stator model. The model of the stator under the action of DC voltage is presented first, and the results of the model are compared versus a similar model using the commercial finite element software COMSOL Multiphysics. One can observe that there is a difference of less than 5% between the displacements of the stator using the proposed model and the one with COMSOL Multiphysics. After that, the model of the stator under the action of AC voltages is presented. The time domain analysis shows the generation of the traveling wave in the stator surface. One can use this model to accurately calculate the stator surface velocities, elliptical motion of the stator surface and the amplitude and shape of the stator traveling wave. A system of equations discretized with the finite volume method can easily be transformed into electrical circuits, because of that, FVM may be a better choice to develop a model-based control strategy for the PTRUSM. Copyright © 2017 Elsevier B.V. All rights reserved.

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

PubMed Central

Kurihara, Eru; Hay, Todd A.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2011-01-01

Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability. PMID:22088009

Influence of Wall Porosity and Surfaces Roughness on the Steady Performance of an Externally Pressurized Hydrostatic Conical Bearing Lubricated by a Rabinowitsch Fluid

NASA Astrophysics Data System (ADS)

Walicka, A.; Walicki, E.; Jurczak, P.; Falicki, J.

2017-08-01

In the paper, the influence of both the bearing surfaces roughness as well as porosity of one bearing surface on the pressure distribution and load-carrying capacity of a curvilinear, externally pressurized, thrust bearing is discussed. The equations of motion of a pseudo-plastic Rabinowitsch fluid are used to derive the Reynolds equation. After general considerations on the flow in a bearing clearance and in a porous layer using the Morgan-Cameron approximation and Christensen theory of hydrodynamic lubrication with rough bearing surfaces the modified Reynolds equation is obtained. The analytical solution is presented; as a result one obtains the formulae expressing the pressure distribution and load-carrying capacity. Thrust radial and conical bearings, externally pressurized, are considered as numerical examples.

Mathematical and computational studies of equilibrium capillary free surfaces

NASA Technical Reports Server (NTRS)

Albright, N.; Chen, N. F.; Concus, P.; Finn, R.

1977-01-01

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated.

Strongly anomalous diffusion in sheared magnetic configurations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vanden Eijnden, E.; Balescu, R.

1996-03-01

The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface {ital x}=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface {ital x}=0. Due to the shear, the diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly non-Gaussian. The reference surface acts likemore » an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of the first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded that the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium. {copyright} {ital 1996 American Institute of Physics.}« less

A General Theory of Unsteady Compressible Potential Aerodynamics

NASA Technical Reports Server (NTRS)

Morino, L.

1974-01-01

The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the potential is obtained for both supersonic and subsonic flow. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface, sigma, of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface sigma. For the important practical case of small harmonic oscillation around a rest position, the equation reduces to a two-dimensional Fredholm integral equation of second-type. It is shown that this equation reduces properly to the lifting surface theories as well as other classical mathematical formulas. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings.

Effect of surface bilayer charges on the magnetic field around ionic channels

NASA Astrophysics Data System (ADS)

Gomes Soares, Marília Amável; Cortez, Celia Martins; Oliveira Cruz, Frederico Alan de; Silva, Dilson

2017-01-01

In this work, we present a physic-mathematical model for representing the ion transport through membrane channels, in special Na+ and K+-channels, and discuss the influence of surface bilayer charges on the magnetic field behavior around the ionic current. The model was composed of a set of equations, including: a nonlinear differential Poisson-Boltzmann equation which usually allows to estimate the surface potentials and electric potential profile across membrane; equations for the ionic flux through channel and the ionic current density based on Armstrong's model for Na+ and K+ permeability and other Physics concepts; and a magnetic field expression derived from the classical Ampère equation. Results from computational simulations using the finite element method suggest that the ionic permeability is strongly dependent of surface bilayer charges, the current density through a K+-channel is very less sensible to temperature changes than the current density through a Na+- channel, active Na+-channels do not directly interfere with the K+-channels around, and vice-versa, since the magnetic perturbation generated by an active channel is of short-range.

Extraction of skin-friction fields from surface flow visualizations as an inverse problem

NASA Astrophysics Data System (ADS)

Liu, Tianshu

2013-12-01

Extraction of high-resolution skin-friction fields from surface flow visualization images as an inverse problem is discussed from a unified perspective. The surface flow visualizations used in this study are luminescent oil-film visualization and heat-transfer and mass-transfer visualizations with temperature- and pressure-sensitive paints (TSPs and PSPs). The theoretical foundations of these global methods are the thin-oil-film equation and the limiting forms of the energy- and mass-transport equations at a wall, which are projected onto the image plane to provide the relationships between a skin-friction field and the relevant quantities measured by using an imaging system. Since these equations can be re-cast in the same mathematical form as the optical flow equation, they can be solved by using the variational method in the image plane to extract relative or normalized skin-friction fields from images. Furthermore, in terms of instrumentation, essentially the same imaging system for measurements of luminescence can be used in these surface flow visualizations. Examples are given to demonstrate the applications of these methods in global skin-friction diagnostics of complex flows.

Release from or through a wax matrix system. I. Basic release properties of the wax matrix system.

PubMed

Yonezawa, Y; Ishida, S; Sunada, H

2001-11-01

Release properties from a wax matrix tablet was examined. To obtain basic release properties, the wax matrix tablet was prepared from a physical mixture of drug and wax powder (hydrogenated caster oil) at a fixed mixing ratio. Properties of release from the single flat-faced surface or curved side surface of the wax matrix tablet were examined. The applicability of the square-root time law and of Higuchi equations was confirmed. The release rate constant obtained as g/min(1/2) changed with the release direction. However, the release rate constant obtained as g/cm2 x min(1/2) was almost the same. Hence it was suggested that the release property was almost the same and the wax matrix structure was uniform independent of release surface or direction at a fixed mixing ratio. However, these equations could not explain the entire release process. The applicability of a semilogarithmic equation was not as good compared with the square-root time law or Higuchi equation. However, it was revealed that the semilogarithmic equation was available to simulate the entire release process, even though the fit was somewhat poor. Hence it was suggested that the semilogarithmic equation was sufficient to describe the release process. The release rate constant was varied with release direction. However, these release rate constants were expressed by a function of the effective surface area and initial amount, independent of the release direction.

More exact solutions of the constant astigmatism equation

NASA Astrophysics Data System (ADS)

Hlaváč, Adam

2018-01-01

By using Bäcklund transformation for the sine-Gordon equation, new periodic exact solutions of the constant astigmatism equation zyy +(1 / z) xx + 2 = 0 are generated from a seed which corresponds to Lipschitz surfaces of constant astigmatism.

Weak hydrological sensitivity to temperature change over land, independent of climate forcing

NASA Astrophysics Data System (ADS)

Samset, Bjorn H.

2017-04-01

As the global surface temperature changes, so will patterns and rates of precipitation. Theoretically, these changes can be understood in terms of changes to the energy balance of the atmosphere, caused by introducing drivers of climate change such as greenhouse gases, aerosols and altered insolation. Climate models, however, disagree strongly in their prediction of precipitation changes, both for historical and future emission pathways, and per degree of surface warming in idealized experiments. The latter value, often termed the apparent hydrological sensitivity, has also been found to differ substantially between climate drivers. Here, we present the global and regional hydrological sensitivity (HS) to surface temperature changes, for perturbations to CO2, CH4, sulfate and black carbon concentrations, and solar irradiance. Based on results from 10 climate models participating in the Precipitation Driver and Response Model Intercomparison Project (PDRMIP), we show how modeled global mean precipitation increases by 2-3 % per kelvin of global mean surface warming, independent of driver, when the effects of rapid adjustments are removed. Previously reported differences in response between drivers are therefore mainly ascribable to rapid atmospheric adjustment processes. All models show a sharp contrast in behavior over land and over ocean, with a strong surface temperature driven (slow) ocean HS of 3-5 %/K, while the slow land HS is only 0-2 %/K. Separating the response into convective and large-scale cloud processes, we find larger inter-model differences, in particular over land regions. Large-scale precipitation changes are most relevant at high latitudes, while the equatorial HS is dominated by convective precipitation changes. Black carbon stands out as the driver with the largest inter-model slow HS variability, and also the strongest contrast between a weak land and strong sea response. Convective precipitation in the Arctic and large scale precipitation around the Equator are found to be topics where further model investigations and observational constraints may provide rapid improvements to modelling of the precipitation response to future, CO2 dominated climate change.

Development of cookies made with cocoyam, fermented sorghum and germinated pigeon pea flour blends using response surface methodology.

PubMed

Okpala, Laura C; Okoli, Eric C

2014-10-01

Cookies were produced from blends of cocoyam, fermented sorghum and germinated pigeon pea flours. The study was carried out to evaluate the effects of varying the proportions of these components on the sensory and protein quality of the cookies. The sensory attributes studied were colour, taste, texture, crispness and general acceptability while the protein quality indices were biological value (BV) and net protein utilization (NPU). Mixture response surface methodology was used to model the sensory and protein quality with single, binary and ternary combinations of germinated pigeon pea, fermented sorghum and cocoyam flours. Results showed that BV and NPU of most of the cookies were above minimum acceptable levels. With the exception of cookies containing high levels of pigeon pea flour, cookies had acceptable sensory scores. Increase in pigeon pea flour resulted in increase in the BV and NPU. Regression equations suggested that the ternary blends produced the highest increase in all the sensory attributes (with the exception of colour).

Optimisation on processing parameters for minimising warpage on side arm using response surface methodology (RSM) and particle swarm optimisation (PSO)

NASA Astrophysics Data System (ADS)

Rayhana, N.; Fathullah, M.; Shayfull, Z.; Nasir, S. M.; Hazwan, M. H. M.; Sazli, M.; Yahya, Z. R.

2017-09-01

This study presents the application of optimisation method to reduce the warpage of side arm part. Autodesk Moldflow Insight software was integrated into this study to analyse the warpage. The design of Experiment (DOE) for Response Surface Methodology (RSM) was constructed and by using the equation from RSM, Particle Swarm Optimisation (PSO) was applied. The optimisation method will result in optimised processing parameters with minimum warpage. Mould temperature, melt temperature, packing pressure, packing time and cooling time was selected as the variable parameters. Parameters selection was based on most significant factor affecting warpage stated by previous researchers. The results show that warpage was improved by 28.16% for RSM and 28.17% for PSO. The warpage improvement in PSO from RSM is only by 0.01 %. Thus, the optimisation using RSM is already efficient to give the best combination parameters and optimum warpage value for side arm part. The most significant parameters affecting warpage are packing pressure.

Optimization of isolation of cellulose from orange peel using sodium hydroxide and chelating agents.

PubMed

Bicu, Ioan; Mustata, Fanica

2013-10-15

Response surface methodology was used to optimize cellulose recovery from orange peel using sodium hydroxide (NaOH) as isolation reagent, and to minimize its ash content using ethylenediaminetetraacetic acid (EDTA) as chelating agent. The independent variables were NaOH charge, EDTA charge and cooking time. Other two constant parameters were cooking temperature (98 °C) and liquid-to-solid ratio (7.5). The dependent variables were cellulose yield and ash content. A second-order polynomial model was used for plotting response surfaces and for determining optimum cooking conditions. The analysis of coefficient values for independent variables in the regression equation showed that NaOH and EDTA charges were major factors influencing the cellulose yield and ash content, respectively. Optimum conditions were defined by: NaOH charge 38.2%, EDTA charge 9.56%, and cooking time 317 min. The predicted cellulose yield was 24.06% and ash content 0.69%. A good agreement between the experimental values and the predicted was observed. Copyright © 2013 Elsevier Ltd. All rights reserved.

[Optimization of calcium alginate floating microspheres loading aspirin by artificial neural networks and response surface methodology].

PubMed

Zhang, An-yang; Fan, Tian-yuan

2010-04-18

To investigate the preparation and optimization of calcium alginate floating microspheres loading aspirin. A model was used to predict the in vitro release of aspirin and optimize the formulation by artificial neural networks (ANNs) and response surface methodology (RSM). The amounts of the material in the formulation were used as inputs, while the release and floating rate of the microspheres were used as outputs. The performances of ANNs and RSM were compared. ANNs were more accurate in prediction. There was no significant difference between ANNs and RSM in optimization. Approximately 90% of the optimized microspheres could float on the artificial gastric juice over 4 hours. 42.12% of aspirin was released in 60 min, 60.97% in 120 min and 78.56% in 240 min. The release of the drug from the microspheres complied with Higuchi equation. The aspirin floating microspheres with satisfying in vitro release were prepared successfully by the methods of ANNs and RSM.

Optimization by response surface methodology of lutein recovery from paprika leaves using accelerated solvent extraction.

PubMed

Kang, Jae-Hyun; Kim, Suna; Moon, BoKyung

2016-08-15

In this study, we used response surface methodology (RSM) to optimize the extraction conditions for recovering lutein from paprika leaves using accelerated solvent extraction (ASE). The lutein content was quantitatively analyzed using a UPLC equipped with a BEH C18 column. A central composite design (CCD) was employed for experimental design to obtain the optimized combination of extraction temperature (°C), static time (min), and solvent (EtOH, %). The experimental data obtained from a twenty sample set were fitted to a second-order polynomial equation using multiple regression analysis. The adjusted coefficient of determination (R(2)) for the lutein extraction model was 0.9518, and the probability value (p=0.0000) demonstrated a high significance for the regression model. The optimum extraction conditions for lutein were temperature: 93.26°C, static time: 5 min, and solvent: 79.63% EtOH. Under these conditions, the predicted extraction yield of lutein was 232.60 μg/g. Copyright © 2016 Elsevier Ltd. All rights reserved.

An enhanced trend surface analysis equation for regional-residual separation of gravity data

NASA Astrophysics Data System (ADS)

Obasi, A. I.; Onwuemesi, A. G.; Romanus, O. M.

2016-12-01

Trend surface analysis is a geological term for a mathematical technique which separates a given map set into a regional component and a local component. This work has extended the steps for the derivation of the constants in the trend surface analysis equation from the popularly known matrix and simultaneous form to a more simplified and easily achievable format. To achieve this, matrix inversion was applied to the existing equations and the outcome was tested for suitability using a large volume of gravity data set acquired from the Anambra Basin, south-eastern Nigeria. Tabulation of the field data set was done using the Microsoft Excel spread sheet, while gravity maps were generated from the data set using Oasis Montaj software. A comparison of the residual gravity map produced using the new equations with its software derived counterpart has shown that the former has a higher enhancing capacity than the latter. This equation has shown strong suitability for application in the separation of gravity data sets into their regional and residual components.

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

NASA Technical Reports Server (NTRS)

Anderson, O. L.

1984-01-01

Zonal concepts are utilized to delineate regions of application of three-dimensional boundary layer (DBL) theory. The zonal approach requires three distinct analyses. A modified version of the 3-DBL code named TABLET is used to analyze the boundary layer flow. This modified code solves the finite difference form of the compressible 3-DBL equations in a nonorthogonal surface coordinate system which includes coriolis forces produced by coordinate rotation. These equations are solved using an efficient, implicit, fully coupled finite difference procedure. The nonorthogonal surface coordinate system is calculated using a general analysis based on the transfinite mapping of Gordon which is valid for any arbitrary surface. Experimental data is used to determine the boundary layer edge conditions. The boundary layer edge conditions are determined by integrating the boundary layer edge equations, which are the Euler equations at the edge of the boundary layer, using the known experimental wall pressure distribution. Starting solutions along the inflow boundaries are estimated by solving the appropriate limiting form of the 3-DBL equations.

Data dependence for the amplitude equation of surface waves

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2016-04-01

We consider the amplitude equation for nonlinear surface wave solutions of hyperbolic conservation laws. This is an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. For example, this equation describes the propagation of nonlinear Rayleigh waves (Hamilton et al. in J Acoust Soc Am 97:891-897, 1995), surface waves on current-vortex sheets in incompressible MHD (Alì and Hunter in Q Appl Math 61(3):451-474, 2003; Alì et al. in Stud Appl Math 108(3):305-321, 2002) and on the incompressible plasma-vacuum interface (Secchi in Q Appl Math 73(4):711-737, 2015). The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables was shown in Hunter (J Hyperbolic Differ Equ 3(2):247-267, 2006), Secchi (Q Appl Math 73(4):711-737, 2015). In the present paper we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard.

Strong collective attraction in colloidal clusters on a liquid-air interface.

PubMed

Pergamenshchik, V M

2009-01-01

It is shown that in a cluster of many colloids, trapped at a liquid-air interface, the well-known vertical-force-induced pairwise logarithmic attraction changes to a strongly enhanced power-law attraction. In large two-dimensional clusters, the attraction energy scales as the inverse square of the distance between colloids. The enhancement is given by the ratio eta = (square of the capillary length) / (interface surface area per colloid) and can be as large as 10;{5} . This explains why a very small vertical force on colloids, which is too weak to bring two of them together, can stabilize many-body structures on a liquid-air interface. The profile of a cluster is shown to consist of a large slow collective envelope modulated by a fast low-amplitude perturbation due to individual colloids. A closed equation for the slow envelope, which incorporates an arbitrary power-law repulsion between colloids, is derived. For example, this equation is solved for a large circular cluster with the hard-core colloid repulsion. It is suggested that the predicted effect is responsible for mysterious stabilization of colloidal structures observed in experiments on a surface of isotropic liquid and nematic liquid crystal.

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

NASA Astrophysics Data System (ADS)

Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

2015-12-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

Optimal Fermentation Conditions of Hyaluronidase Inhibition Activity on Asparagus cochinchinensis Merrill by Weissella cibaria.

PubMed

Kim, Minji; Kim, Won-Baek; Koo, Kyoung Yoon; Kim, Bo Ram; Kim, Doohyun; Lee, Seoyoun; Son, Hong Joo; Hwang, Dae Youn; Kim, Dong Seob; Lee, Chung Yeoul; Lee, Heeseob

2017-04-28

This study was conducted to evaluate the hyaluronidase (HAase) inhibition activity of Asparagus cochinchinesis (AC) extracts following fermentation by Weissella cibaria through response surface methodology. To optimize the HAase inhibition activity, a central composite design was introduced based on four variables: the concentration of AC extract ( X 1 : 1-5%), amount of starter culture ( X 2 : 1-5%), pH ( X 3 : 4-8), and fermentation time ( X 4 : 0-10 days). The experimental data were fitted to quadratic regression equations, the accuracy of the equations was analyzed by ANOVA, and the regression coefficients for the surface quadratic model of HAase inhibition activity in the fermented AC extract were estimated by the F test and the corresponding p values. The HAase inhibition activity indicated that fermentation time was most significant among the parameters within the conditions tested. To validate the model, two different conditions among those generated by the Design Expert program were selected. Under both conditions, predicted and experimental data agreed well. Moreover, the content of protodioscin (a well-known compound related to anti-inflammation activity) was elevated after fermentation of the AC extract at the optimized fermentation condition.

New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows

PubMed Central

Li, Zhilin; Lai, Ming-Chih

2012-01-01

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena. PMID:23795308

Model for the dynamic responses of taste receptor cells to salty stimuli. I. Function of lipid bilayer membranes.

PubMed Central

Naito, M; Fuchikami, N; Sasaki, N; Kambara, T

1991-01-01

The dynamic response of the lipid bilayer membrane is studied theoretically using a microscopic model of the membrane. The time courses of membrane potential variations due to monovalent salt stimulation are calculated explicitly under various conditions. A set of equations describing the time evolution of membrane surface potential and diffusion potential is derived and solved numerically. It is shown that a rather simple membrane such as lipid bilayer has functions capable of reproducing the following properties of dynamic response observed in gustatory receptor potential. Initial transient depolarization does not occur under Ringer adaptation but does under water. It appears only for comparatively rapid flows of stimuli, the peak height of transient response is expressed by a power function of the flow rate, and the membrane potential gradually decreases after reaching its peak under long and strong stimulation. The dynamic responses in the present model arise from the differences between the time dependences in the surface potential phi s and the diffusion potential phi d across a membrane. Under salt stimulation phi d cannot immediately follow the variation in phi s because of the delay due to the charging up of membrane capacitance. It is suggested that lipid bilayer in the apical membrane is the most probable agency producing the initial phasic response to the stimulation. PMID:1873461

Excitation of propagating magnetization waves by microstrip antennas

NASA Astrophysics Data System (ADS)

Dmitriev, V. F.; Kalinikos, B. A.

1988-11-01

We discuss the self-consistent theory of excitation of dipole-exchange magnetization waves by microstrip antennas in a metal-dielectric-ferrite-dielectric-metal stratified structure, magnetized under an arbitrary angle to the surface. Spin-wave Green's functions are derived, describing the response of the spin-system to a spatially inhomogeneous varying magnetic field. The radiative resistance of microstrip antenna is calculated. In this case the distribution of surface current density in the antenna is found on the basis of the analytic solution of a singular integral equation. The nature of the effect of metallic screens and redistributed surface current densities in the antenna on the frequency dependence of the resistive radiation is investigated. Approximate relations are obtained, convenient for practical calculations of radiative resistance of microstrip antennas both in a free and in a screened ferromagnetic film. The theoretical calculations are verified by data of experiments carried out on monocrystalline films of iron-yttrium garnet.

Simulation of Earthquake-Generated Sea-Surface Deformation

NASA Astrophysics Data System (ADS)

Vogl, Chris; Leveque, Randy

2016-11-01

Earthquake-generated tsunamis can carry with them a powerful, destructive force. One of the most well-known, recent examples is the tsunami generated by the Tohoku earthquake, which was responsible for the nuclear disaster in Fukushima. Tsunami simulation and forecasting, a necessary element of emergency procedure planning and execution, is typically done using the shallow-water equations. A typical initial condition is that using the Okada solution for a homogeneous, elastic half-space. This work focuses on simulating earthquake-generated sea-surface deformations that are more true to the physics of the materials involved. In particular, a water layer is added on top of the half-space that models the seabed. Sea-surface deformations are then simulated using the Clawpack hyperbolic PDE package. Results from considering the water layer both as linearly elastic and as "nearly incompressible" are compared to that of the Okada solution.

The evolution equation for the flame surface density in turbulent premixed combustion

NASA Technical Reports Server (NTRS)

Trouve, Arnaud

1993-01-01

The mean reaction rate in flamelet models for turbulent premixed combustion depends on two basic quantities: a mean chemical rate, called the flamelet speed, and the flame surface density. Our previous work had been primarily focused on the problem of the structure and topology of turbulent premixed flames, and it was then determined that the flamelet speed, when space-averaged, is only weakly sensitive to the turbulent flow field. Consequently, the flame surface density is the key quantity that conveys most of the effects of the turbulence on the rate of energy release. In flamelet models, this quantity is obtained via a modeled transport equation called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact but unclosed formulation for the turbulent Sigma-equation. In the exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the turbulent flame stretch as well as the flame surface density is not available from experiments, and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the alternative approach to get basic information on these fundamental quantities. In the present work, three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, our objective is to extract the turbulent flame stretch from the DNS data base and then perform extensive comparisons with flamelet models. Thanks to the detailed information produced by the DNS-based analysis, it is expected that this type of comparison will not only underscore the shortcomings of current models, but also suggest ways to improve them.

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

Unsteady Convection Flow and Heat Transfer over a Vertical Stretching Surface

PubMed Central

Cai, Wenli; Su, Ning; Liu, Xiangdong

2014-01-01

This paper investigates the effect of thermal radiation on unsteady convection flow and heat transfer over a vertical permeable stretching surface in porous medium, where the effects of temperature dependent viscosity and thermal conductivity are also considered. By using a similarity transformation, the governing time-dependent boundary layer equations for momentum and thermal energy are first transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by the numerical shooting technique with fourth-fifth order Runge-Kutta scheme. Numerical results show that as viscosity variation parameter increases both the absolute value of the surface friction coefficient and the absolute value of the surface temperature gradient increase whereas the temperature decreases slightly. With the increase of viscosity variation parameter, the velocity decreases near the sheet surface but increases far away from the surface of the sheet in the boundary layer. The increase in permeability parameter leads to the decrease in both the temperature and the absolute value of the surface friction coefficient, and the increase in both the velocity and the absolute value of the surface temperature gradient. PMID:25264737

Unsteady convection flow and heat transfer over a vertical stretching surface.

PubMed

Cai, Wenli; Su, Ning; Liu, Xiangdong

2014-01-01

This paper investigates the effect of thermal radiation on unsteady convection flow and heat transfer over a vertical permeable stretching surface in porous medium, where the effects of temperature dependent viscosity and thermal conductivity are also considered. By using a similarity transformation, the governing time-dependent boundary layer equations for momentum and thermal energy are first transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by the numerical shooting technique with fourth-fifth order Runge-Kutta scheme. Numerical results show that as viscosity variation parameter increases both the absolute value of the surface friction coefficient and the absolute value of the surface temperature gradient increase whereas the temperature decreases slightly. With the increase of viscosity variation parameter, the velocity decreases near the sheet surface but increases far away from the surface of the sheet in the boundary layer. The increase in permeability parameter leads to the decrease in both the temperature and the absolute value of the surface friction coefficient, and the increase in both the velocity and the absolute value of the surface temperature gradient.

Aerodynamics Via Acoustics: Application of Acoustic Formulas for Aerodynamic Calculations

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.

1986-01-01

Prediction of aerodynamic loads on bodies in arbitrary motion is considered from an acoustic point of view, i.e., in a frame of reference fixed in the undisturbed medium. An inhomogeneous wave equation which governs the disturbance pressure is constructed and solved formally using generalized function theory. When the observer is located on the moving body surface there results a singular linear integral equation for surface pressure. Two different methods for obtaining such equations are discussed. Both steady and unsteady aerodynamic calculations are considered. Two examples are presented, the more important being an application to propeller aerodynamics. Of particular interest for numerical applications is the analytical behavior of the kernel functions in the various integral equations.

An explicit asymptotic model for the surface wave in a viscoelastic half-space based on applying Rabotnov's fractional exponential integral operators

NASA Astrophysics Data System (ADS)

Wilde, M. V.; Sergeeva, N. V.

2018-05-01

An explicit asymptotic model extracting the contribution of a surface wave to the dynamic response of a viscoelastic half-space is derived. Fractional exponential Rabotnov's integral operators are used for describing of material properties. The model is derived by extracting the principal part of the poles corresponding to the surface waves after applying Laplace and Fourier transforms. The simplified equations for the originals are written by using power series expansions. Padè approximation is constructed to unite short-time and long-time models. The form of this approximation allows to formulate the explicit model using a fractional exponential Rabotnov's integral operator with parameters depending on the properties of surface wave. The applicability of derived models is studied by comparing with the exact solutions of a model problem. It is revealed that the model based on Padè approximation is highly effective for all the possible time domains.

Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.

2009-09-01

Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.

Computer Implementation of the Bounding Surface Plasticity Model for Cohesive Soils.

DTIC Science & Technology

1983-12-01

Contract # DACA 39-79-M-0059), the Civil Engineering Laboratory, Naval Construction Battalion Center (Re: Orders N62583-80-M-R478, N62583-81-M- R320, N62#74...correspondinga a expression in the equation of "Modification 5" (Section 1) is treated in a similar fashion. In general, this arbitrary action does not...Contract # DACA 39-79-M-0059), April 1980. 3. Dafalias, Y.F., L.R. Herrmann and J.S. DeNatale, "Prediction of the Response of the Natural Clays X and Y

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Study of photoinduced absorption by the method of modified laser photothermal radiometry

NASA Astrophysics Data System (ADS)

Skvortsov, L. A.; Maksimov, E. M.; Tuchkov, A. A.

2008-10-01

The application of the method of modified laser photothermal radiometry for studying the photoinduced absorption in thin films is considered. The sensitivity of the method is estimated. The mechanism of induced near-IR absorption in titanium dioxide films is proposed and the nature of surface defects responsible for this process is explained. It is shown that kinetic equations describing monomolecular recombination are consistent with the experimental dependences for the thermal activation energy of defects equal to 0.17±0.04 eV.

Finite-surface method for the Maxwell equations with corner singularities

NASA Technical Reports Server (NTRS)

Vinokur, Marcel; Yarrow, Maurice

1994-01-01

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

Stress intensity factors for surface and corner cracks emanating from a wedge-loaded hole

NASA Technical Reports Server (NTRS)

Zhao, W.; Sutton, M. A.; Shivakumar, K. N.; Newman, J. C., Jr.

1994-01-01

To assist analysis of riveted lap joints, stress intensity factors are determined for surface and corner cracks emanating from a wedge-loaded hole by using a 3-D weight function method in conjunction with a 3-D finite element method. A stress intensity factor equation for surface cracks is also developed to provide a closed-form solution. The equation covers commonly-encountered geometrical ranges and retains high accuracy over the entire range.

Development of Phaleria macrocarpa (Scheff.) Boerl Fruits Using Response Surface Methodology Focused on Phenolics, Flavonoids and Antioxidant Properties.

PubMed

Mohamed Mahzir, Khurul Ain; Abd Gani, Siti Salwa; Hasanah Zaidan, Uswatun; Halmi, Mohd Izuan Effendi

2018-03-22

In this study, the optimal conditions for the extraction of antioxidants from the Buah Mahkota Dewa fruit ( Phaleria macrocarpa) was determined by using Response Surface Methodology (RSM). The optimisation was applied using a Central Composite Design (CCD) to investigate the effect of three independent variables, namely extraction temperature (°C), extraction time (minutes) and extraction solvent to-feed ratio (% v / v ) on four responses: free radical scavenging activity (DPPH), ferric ion reducing power assay (FRAP), total phenolic content (TPC) and total flavonoid content (TFC). The optimal conditions for the antioxidants extraction were found to be 64 °C extraction temperature, 66 min extraction time and 75% v / v solvent to-feed ratio giving the highest percentage yields of DPPH, FRAP, TPC and TFC of 86.85%, 7.47%, 292.86 mg/g and 3.22 mg/g, respectively. Moreover, the data were subjected to Response Surface Methodology (RSM) and the results showed that the polynomial equations for all models were significant, did not show lack of fit, and presented adjusted determination coefficients ( R ²) above 99%, proving that the yield of phenolic, flavonoid and antioxidants activities obtained experimentally were close to the predicted values and the suitability of the model employed in RSM to optimise the extraction conditions. Hence, in this study, the fruit from P. macrocarpa could be considered to have strong antioxidant ability and can be used in various cosmeceutical or medicinal applications.

Conformal dynamics of precursors to fracture

NASA Astrophysics Data System (ADS)

Barra, F.; Herrera, M.; Procaccia, I.

2003-09-01

An exact integro-differential equation for the conformal map from the unit circle to the boundary of an evolving cavity in a stressed 2-dimensional solid is derived. This equation provides an accurate description of the dynamics of precursors to fracture when surface diffusion is important. The solution predicts the creation of sharp grooves that eventually lead to material failure via rapid fracture. Solutions of the new equation are demonstrated for the dynamics of an elliptical cavity and the stability of a circular cavity under biaxial stress, including the effects of surface stress.

The Dugdale model for the compact specimen

NASA Technical Reports Server (NTRS)

Mall, S.; Newman, J. C., Jr.

1983-01-01

Plastic zone size and crack tip opening displacement (CTOD) equations were developed. Boundary collocation analyses were used to analyze the compact specimen subjected to various loading conditions (pin loads, concentrated forces, and uniform pressure acting on the crack surface). Stress intensity factor and crack surface displacement equations for some of these loadings were developed and used to obtain the Dugdale model. The results from the equations for plastic zone size and CTOD agreed well with numerical values calculated by Terada for crack length to width ratios greater than 0.4.

Channel surface plasmons in a continuous and flat graphene sheet

NASA Astrophysics Data System (ADS)

Chaves, A. J.; Peres, N. M. R.; da Costa, D. R.; Farias, G. A.

2018-05-01

We derive an integral equation describing surface-plasmon polaritons in graphene deposited on a substrate with a planar surface and a dielectric protrusion in the opposite surface of the dielectric slab. We show that the problem is mathematically equivalent to the solution of a Fredholm equation, which we solve exactly. In addition, we show that the dispersion relation of the channel surface plasmons is determined by the geometric parameters of the protrusion alone. We also show that such a system supports both even and odd modes. We give the electrostatic potential and the intensity plot of the electrostatic field, which clearly show the transverse localized nature of the surface plasmons in a continuous and flat graphene sheet.

Prediction of health effects of cross-border atmospheric pollutants using an aerosol forecast model.

PubMed

Onishi, Kazunari; Sekiyama, Tsuyoshi Thomas; Nojima, Masanori; Kurosaki, Yasunori; Fujitani, Yusuke; Otani, Shinji; Maki, Takashi; Shinoda, Masato; Kurozawa, Youichi; Yamagata, Zentaro

2018-08-01

Health effects of cross-border air pollutants and Asian dust are of significant concern in Japan. Currently, models predicting the arrival of aerosols have not investigated the association between arrival predictions and health effects. We investigated the association between subjective health symptoms and unreleased aerosol data from the Model of Aerosol Species in the Global Atmosphere (MASINGAR) acquired from the Japan Meteorological Agency, with the objective of ascertaining if these data could be applied to predicting health effects. Subjective symptom scores were collected via self-administered questionnaires and, along with modeled surface aerosol concentration data, were used to conduct a risk evaluation using generalized estimating equations between October and November 2011. Altogether, 29 individuals provided 1670 responses. Spearman's correlation coefficients were determined for the relationship between the proportion of the participants reporting the maximum score of two or more for each symptom and the surface concentrations for each considered aerosol species calculated using MASINGAR; the coefficients showed significant intermediate correlations between surface sulfate aerosol concentration and respiratory, throat, and fever symptoms (R = 0.557, 0.454, and 0.470, respectively; p < 0.01). In the general estimation equation (logit link) analyses, a significant linear association of surface sulfate aerosol concentration, with an endpoint determined by reported respiratory symptom scores of two or more, was observed (P trend = 0.001, odds ratio [OR] of the highest quartile [Q4] vs. the lowest [Q1] = 5.31, 95% CI = 2.18 to 12.96), with adjustment for potential confounding. The surface sulfate aerosol concentration was also associated with throat and fever symptoms. In conclusion, our findings suggest that modeled data are potentially useful for predicting health risks of cross-border aerosol arrivals. Copyright © 2018 Elsevier Ltd. All rights reserved.

Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Ratliff, Daniel J.

2018-04-01

The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Stability analysis of nanoscale surface patterns in stressed solids

NASA Astrophysics Data System (ADS)

Kostyrko, Sergey A.; Shuvalov, Gleb M.

2018-05-01

Here, we use the theory of surface elasticity to extend the morphological instability analysis of stressed solids developed in the works of Asaro, Tiller, Grinfeld, Srolovitz and many others. Within the framework of Gurtin-Murdoch model, the surface phase is assumed to be a negligibly thin layer with the elastic properties which differ from those of the bulk material. We consider the mass transport mechanism driven by the variation of surface and bulk energy along undulated surface of stressed solid. The linearized surface evolution equation is derived in the case of plane strain conditions and describes the amplitude change of surface perturbations with time. A parametric analysis of this equation leads to the definition of critical conditions which depend on undulation wavelength, residual surface stress, applied loading, surface and bulk elastic constants and predict the surface morphological stability.

Analysis of wave propagation and wavefront sensing in target-in-the-loop beam control systems

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeri V.

2004-10-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual intensity function (MIF) for the backscattered (returned) wave. The resulting evolution equation for the MIF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation of the transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.

A boundary integral approach in primitive variables for free surface flows

NASA Astrophysics Data System (ADS)

Casciola, C.; Piva, R.

The boundary integral formulation, very efficient for free surface potential flows, was considered for its possible extension to rotational flows either inviscid or viscous. We first analyze a general formulation for unsteady Navier-Stokes equations in primitive variables, which reduces to a representation for the Euler equations in the limiting case of Reynolds infinity. A first simplified model for rotational flows, obtained by decoupling kinematics and dynamics, reduces the integral equations to a known kinematical form whose mathematical and numerical properties have been studied. The dynamics equations to complete the model are obtained for the free surface and the wake. A simple and efficient scheme for the study of the non linear evolution of the wave system and its interaction with the body wake is presented. A steady state version for the calculation of the wave resistance is also reported. A second model was proposed for the simulation of rotational separated regions, by coupling the integral equations in velocity with an integral equation for the vorticity at the body boundary. The same procedure may be extended to include the diffusion of the vorticity in the flowfield. The vortex shedding from a cylindrical body in unsteady motion is discussed, as a first application of the model.

Theoretical study of the design of a catalyst for para to ortho hydrogen conversion

NASA Technical Reports Server (NTRS)

Coffman, Robert E.

1992-01-01

The theory of Petzinger and Scalapino (1973) was thoroughly reviewed, and all of the basic equations for paramagnetic para to ortho hydrogen catalysis re-derived. There are only a few minor phase errors and errors of omission in the description of the theory. Three models (described by Petzinger and Scalapino) for the rate of para to ortho H2 catalysis were worked out, and uniform agreement obtained to within a constant factor of 2 pi. The analytical methods developed in the course of this study were then extended to two new models, which more adequately describe the process of surface catalysis including transfer of hydrogen molecules onto and off of the surface. All five equations for the para to ortho catalytic rate of conversion are described. The two new equations describe the catalytic rate for these models: H2 on the surface is a 2-D gas with lifetime tau; and H2 on the surface is a 2-D liquid undergoing Brownian motion (diffusion) with surface lifetime tau.

Identification of Spurious Signals from Permeable Ffowcs Williams and Hawkings Surfaces

NASA Technical Reports Server (NTRS)

Lopes, Leonard V.; Boyd, David D., Jr.; Nark, Douglas M.; Wiedemann, Karl E.

2017-01-01

Integral forms of the permeable surface formulation of the Ffowcs Williams and Hawkings (FW-H) equation often require an input in the form of a near field Computational Fluid Dynamics (CFD) solution to predict noise in the near or far field from various types of geometries. The FW-H equation involves three source terms; two surface terms (monopole and dipole) and a volume term (quadrupole). Many solutions to the FW-H equation, such as several of Farassat's formulations, neglect the quadrupole term. Neglecting the quadrupole term in permeable surface formulations leads to inaccuracies called spurious signals. This paper explores the concept of spurious signals, explains how they are generated by specifying the acoustic and hydrodynamic surface properties individually, and provides methods to determine their presence, regardless of whether a correction algorithm is employed. A potential approach based on the equivalent sources method (ESM) and the sensitivity of Formulation 1A (Formulation S1A) is also discussed for the removal of spurious signals.

The Minimum-Mass Surface Density of the Solar Nebula using the Disk Evolution Equation

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2005-01-01

The Hayashi minimum-mass power law representation of the pre-solar nebula (Hayashi 1981, Prog. Theo. Phys.70,35) is revisited using analytic solutions of the disk evolution equation. A new cumulative-planetary-mass-model (an integrated form of the surface density) is shown to predict a smoother surface density compared with methods based on direct estimates of surface density from planetary data. First, a best-fit transcendental function is applied directly to the cumulative planetary mass data with the surface density obtained by direct differentiation. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the planetary data. The latter model indicates a decay rate of r -1/2 in the inner disk followed by a rapid decay which results in a sharper outer boundary than predicted by the minimum mass model. The model is shown to be a good approximation to the finite-size early Solar Nebula and by extension to extra solar protoplanetary disks.

MULTISCALE MODELS OF TAXIS-DRIVEN PATTERNING IN BACTERIAL POPULATIONS

PubMed Central

XUE, CHUAN; OTHMER, HANS G.

2009-01-01

Spatially-distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants. In the past decade a great deal has been learned about signal transduction, metabolism and movement in E. coli and other bacteria, but translating the individual-level behavior into population-level dynamics is still a challenging problem. However, this is a necessary step because it is computationally impractical to use a strictly cell-based model to understand patterning in growing populations, since the total number of cells may reach 1012 - 1014 in some experiments. In the past phenomenological equations such as the Patlak-Keller-Segel equations have been used in modeling the cell movement that is involved in the formation of such patterns, but the question remains as to how the microscopic behavior can be correctly described by a macroscopic equation. Significant progress has been made for bacterial species that employ a “run-and-tumble” strategy of movement, in that macroscopic equations based on simplified schemes for signal transduction and turning behavior have been derived [14, 15]. Here we extend previous work in a number of directions: (i) we allow for time-dependent signals, which extends the applicability of the equations to natural environments, (ii) we use a more general turning rate function that better describes the biological behavior, and (iii) we incorporate the effect of hydrodynamic forces that arise when cells swim in close proximity to a surface. We also develop a new approach to solving the moment equations derived from the transport equation that does not involve closure assumptions. Numerical examples show that the solution of the lowest-order macroscopic equation agrees well with the solution obtained from a Monte Carlo simulation of cell movement under a variety of temporal protocols for the signal. We also apply the method to derive equations of chemotactic movement that are governed by multiple chemotactic signals. PMID:19784399

Minimization of deviations of gear real tooth surfaces determined by coordinate measurements

NASA Technical Reports Server (NTRS)

Litvin, F. L.; Kuan, C.; Wang, J.-C.; Handschuh, R. F.; Masseth, J.; Maruyama, N.

1992-01-01

The deviations of a gear's real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method was developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine-tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

The Scattering of Partially Coherent Electromagnetic Beam Illumination from Statistically Rough Surfaces

DTIC Science & Technology

2014-06-19

scattering research performed by the radio - frequency /microwave and visible/near-infrared communities for synthetic aperture radar and remote...Rough Surfaces with Arbitrary Slope and Frequency ,” IEEE Trans. Antennas Propag. 28, 11 - 21 (1980). 76. E. Bahar, “Full-Wave Solutions for the...equations ..................................................................................... 11 2.2.1 Electric-field integral equations

Pressure Distribution in a Squeeze Film Spherical Bearing with Rough Surfaces Lubricated by an Ellis Fluid

NASA Astrophysics Data System (ADS)

Jurczak, P.; Falicki, J.

2016-08-01

In this paper, the solution to a problem of pressure distribution in a curvilinear squeeze film spherical bearing is considered. The equations of motion of an Ellis pseudo-plastic fluid are presented. Using Christensen's stochastic model of rough surfaces, different forms of Reynolds equation for various types of surface roughness pattern are obtained. The analytical solutions of these equations for the cases of externally pressurized bearing and squeeze film bearing are presented. Analytical solutions for the film pressure are found for the longitudinal and circumferential roughness patterns. As a result the formulae expressing pressure distribution in the clearance of bearing lubricated by an Ellis fluid was obtained. The numerical considerations for a spherical bearing are given in detail.

Slip effect on stagnation point flow past a stretching surface with the presence of heat generation/absorption and Newtonian heating

NASA Astrophysics Data System (ADS)

Mohamed, Muhammad Khairul Anuar; Noar, Nor Aida Zuraimi Md; Ismail, Zulkhibri; Kasim, Abdul Rahman Mohd; Sarif, Norhafizah Md; Salleh, Mohd Zuki; Ishak, Anuar

2017-08-01

Present study solved numerically the velocity slip effect on stagnation point flow past a stretching surface with the presence of heat generation/absorption and Newtonian heating. The governing equations which in the form of partial differential equations are transformed to ordinary differential equations before being solved numerically using the Runge-Kutta-Fehlberg method in MAPLE. The numerical solution is obtained for the surface temperature, heat transfer coefficient, reduced skin friction coefficient as well as the temperature and velocity profiles. The flow features and the heat transfer characteristic for the pertinent parameter such as Prandtl number, stretching parameter, heat generation/absorption parameter, velocity slip parameter and conjugate parameter are analyzed and discussed.

Einstein-Weyl spaces and third-order differential equations

NASA Astrophysics Data System (ADS)

Tod, K. P.

2000-08-01

The three-dimensional null-surface formalism of Tanimoto [M. Tanimoto, "On the null surface formalism," Report No. gr-qc/9703003 (1997)] and Forni et al. [Forni et al., "Null surfaces formation in 3D," J. Math Phys. (submitted)] are extended to describe Einstein-Weyl spaces, following Cartan [E. Cartan, "Les espaces généralisées et l'integration de certaines classes d'equations différentielles," C. R. Acad. Sci. 206, 1425-1429 (1938); "La geometria de las ecuaciones diferenciales de tercer order," Rev. Mat. Hispano-Am. 4, 1-31 (1941)]. In the resulting formalism, Einstein-Weyl spaces are obtained from a particular class of third-order differential equations. Some examples of the construction which include some new Einstein-Weyl spaces are given.

Dissolution process analysis using model-free Noyes-Whitney integral equation.

PubMed

Hattori, Yusuke; Haruna, Yoshimasa; Otsuka, Makoto

2013-02-01

Drug dissolution process of solid dosages is theoretically described by Noyes-Whitney-Nernst equation. However, the analysis of the process is demonstrated assuming some models. Normally, the model-dependent methods are idealized and require some limitations. In this study, Noyes-Whitney integral equation was proposed and applied to represent the drug dissolution profiles of a solid formulation via the non-linear least squares (NLLS) method. The integral equation is a model-free formula involving the dissolution rate constant as a parameter. In the present study, several solid formulations were prepared via changing the blending time of magnesium stearate (MgSt) with theophylline monohydrate, α-lactose monohydrate, and crystalline cellulose. The formula could excellently represent the dissolution profile, and thereby the rate constant and specific surface area could be obtained by NLLS method. Since the long time blending coated the particle surface with MgSt, it was found that the water permeation was disturbed by its layer dissociating into disintegrant particles. In the end, the solid formulations were not disintegrated; however, the specific surface area gradually increased during the process of dissolution. The X-ray CT observation supported this result and demonstrated that the rough surface was dominant as compared to dissolution, and thus, specific surface area of the solid formulation gradually increased. Copyright © 2012 Elsevier B.V. All rights reserved.

A Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Parsakhoo, Zahra; Shao, Yaping

2017-04-01

Near-surface turbulent mixing has considerable effect on surface fluxes, cloud formation and convection in the atmospheric boundary layer (ABL). Its quantifications is however a modeling and computational challenge since the small eddies are not fully resolved in Eulerian models directly. We have developed a Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer based on the Ito Stochastic Differential Equation (SDE) for air parcels (particles). Due to the complexity of the mixing in the ABL, we find that linear Ito SDE cannot represent convections properly. Three strategies have been tested to solve the problem: 1) to make the deterministic term in the Ito equation non-linear; 2) to change the random term in the Ito equation fractional, and 3) to modify the Ito equation by including Levy flights. We focus on the third strategy and interpret mixing as interaction between at least two stochastic processes with different Lagrangian time scales. The model is in progress to include the collisions among the particles with different characteristic and to apply the 3D model for real cases. One application of the model is emphasized: some land surface patterns are generated and then coupled with the Large Eddy Simulation (LES).

Dynamic analysis of flexible rotor-bearing systems using a modal approach

NASA Technical Reports Server (NTRS)

Choy, K. C.; Gunter, E. J.; Barrett, L. E.

1978-01-01

The generalized dynamic equations of motion were obtained by the direct stiffness method for multimass flexible rotor-bearing systems. The direct solution of the equations of motion is illustrated on a simple 3-mass system. For complex rotor-bearing systems, the direct solution of the equations becomes very difficult. The transformation of the equations of motion into modal coordinates can greatly simplify the computation for the solution. The use of undamped and damped system mode shapes in the transformation are discussed. A set of undamped critical speed modes is used to transform the equations of motion into a set of coupled modal equations of motion. A rapid procedure for computing stability, steady state unbalance response, and transient response of the rotor-bearing system is presented. Examples of the application of this modal approach are presented. The dynamics of the system is further investigated with frequency spectrum analysis of the transient response.

Titan's Atmospheric Dynamics and Meteorology

NASA Technical Reports Server (NTRS)

Flasar, F. M.; Baines, K. H.; Bird, M. K.; Tokano, T.; West, R. A.

2008-01-01

Titan, after Venus, is the second example of an atmosphere with a global cyclostrophic circulation in the solar system, but a circulation that has a strong seasonal modulation in the middle atmosphere. Direct measurement of Titan's winds, particularly observations tracking the Huygens probe at 10degS, indicate that the zonal winds are generally in the sense of the satellites rotation. They become cyclostrophic approx. 35 km above the surface and generally increase with altitude, with the exception of a sharp minimum centered near 75 km, where the wind velocity decreases to nearly zero. Zonal winds derived from the temperature field retrieved from Cassini measurements, using the thermal wind equation, indicate a strong winter circumpolar vortex, with maximum winds at mid northern latitudes of 190 ms-' near 300 km. Above this level, the vortex decays. Curiously, the zonal winds and temperatures are symmetric about a pole that is offset from the surface pole by approx.4 degrees. The cause of this is not well understood, but it may reflect the response of a cyclostrophic circulation to the offset between the equator, where the distance to the rotation axis is greatest, and the solar equator. The mean meridional circulation can be inferred from the temperature field and the meridional distribution of organic molecules and condensates and hazes. Both the warm temperatures in the north polar region near 400 km and the enhanced concentration of several organic molecules suggests subsidence there during winter and early spring. Stratospheric condensates are localized at high northern latitudes, with a sharp cut-off near 50degN. Titan's winter polar vortex appears to share many of the same characteristics of winter vortices on Earth-the ozone holes. Global mapping of temperatures, winds, and composition in he troposphere, by contrast, is incomplete. The few suitable discrete clouds that have bee found for tracking indicate smaller velocities than aloft, consistent with the Huygens measurements. At low latitudes the zonal winds near the surface appear not to be westward as on Earth, but eastward. Because the net zonal-mean time-averaged torq exerted by the surface on the atmosphere should vanish, this implies westward flow o part of the surface; the question is where. The latitude contrast in tropospheric temperatures, deduced from radio occultations at low, mid, and high latitudes, is small approx.5 K at the tropopause and approx.3 K at the surface.

The sagitta and lens thickness: the exact solution and a matrix approximation for lenses with toric, spherical, and cylindrical surfaces.

PubMed

Harris, W F

1989-03-01

The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.

A finite-element analysis for steady and oscillatory supersonic flows around complex configurations

NASA Technical Reports Server (NTRS)

Morino, L.; Chen, L. T.

1974-01-01

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, sigma sub i, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element, and this yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements, sigma sub i. The results obtained using the above formulation are compared with existing analytical and experimental results.

A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis.

PubMed

MacDonald, G; Mackenzie, J A; Nolan, M; Insall, R H

2016-03-15

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

Dirac equation on a curved surface

NASA Astrophysics Data System (ADS)

Brandt, F. T.; Sánchez-Monroy, J. A.

2016-09-01

The dynamics of Dirac particles confined to a curved surface is examined employing the thin-layer method. We perform a perturbative expansion to first-order and split the Dirac field into normal and tangential components to the surface. In contrast to the known behavior of second order equations like Schrödinger, Maxwell and Klein-Gordon, we find that there is no geometric potential for the Dirac equation on a surface. This implies that the non-relativistic limit does not commute with the thin-layer method. Although this problem can be overcome when second-order terms are retained in the perturbative expansion, this would preclude the decoupling of the normal and tangential degrees of freedom. Therefore, we propose to introduce a first-order term which rescues the non-relativistic limit and also clarifies the effect of the intrinsic and extrinsic curvatures on the dynamics of the Dirac particles.

Field-Induced and Thermal Electron Currents from Earthed Spherical Emitters

NASA Astrophysics Data System (ADS)

Holgate, J. T.; Coppins, M.

2017-04-01

The theories of electron emission from planar surfaces are well understood, but they are not suitable for describing emission from spherical surfaces; their incorrect application to highly curved, nanometer-scale surfaces can overestimate the emitted current by several orders of magnitude. This inaccuracy is of particular concern for describing modern nanoscale electron sources, which continue to be modeled using the planar equations. In this paper, the field-induced and thermal currents are treated in a unified way to produce Fowler-Nordheim-type and Richardson-Schottky-type equations for the emitted current density from earthed nanoscale spherical surfaces. The limits of applicability of these derived expressions are considered along with the energy spectra of the emitted electrons. Within the relevant limits of validity, these equations are shown to reproduce the results of precise numerical calculations of the emitted current densities. The methods used here are adaptable to other one-dimensional emission problems.

The prediction of the noise of supersonic propellers in time domain - New theoretical results

NASA Technical Reports Server (NTRS)

Farassat, F.

1983-01-01

In this paper, a new formula for the prediction of the noise of supersonic propellers is derived in the time domain which is superior to the previous formulations in several respects. The governing equation is based on the Ffowcs Williams-Hawkings (FW-H) equation with the thickness source term replaced by an equivalent loading source term derived by Isom (1975). Using some results of generalized function theory and simple four-dimensional space-time geometry, the formal solution of the governing equation is manipulated to a form requiring only the knowledge of blade surface pressure data and geometry. The final form of the main result of this paper consists of some surface and line integrals. The surface integrals depend on the surface pressure, time rate of change of surface pressure, and surface pressure gradient. These integrals also involve blade surface curvatures. The line integrals which depend on local surface pressure are along the trailing edge, the shock traces on the blade, and the perimeter of the airfoil section at the inner radius of the blade. The new formulation is for the full blade surface and does not involve any numerical observer time differentiation. The method of implementation on a computer for numerical work is also discussed.

Item Response Theory Equating Using Bayesian Informative Priors.

ERIC Educational Resources Information Center

de la Torre, Jimmy; Patz, Richard J.

This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from…

Empirical Sampling Distributions of Equating Coefficients for Graded and Nominal Response Instruments.

ERIC Educational Resources Information Center

Baker, Frank B.

1997-01-01

Examined the sampling distributions of equating coefficients produced by the characteristic curve method for tests using graded and nominal response scoring using simulated data. For both models and across all three equating situations, the sampling distributions were generally bell-shaped and peaked, and occasionally had a small degree of…

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics: Building Blocks for a Higher Order Method

DTIC Science & Technology

2006-09-30

equation known as the Kadomtsev - Petviashvili (KP) equation ): (ηt + coηx +αηηx + βη )x +γηyy = 0 (4) where γ = co / 2 . The KdV equation ...using the spectral formulation of the Kadomtsev - Petviashvili equation , a standard equation for nonlinear, shallow water wave dynamics that is a... Petviashvili and nonlinear Schroedinger equations and higher order corrections have been developed as prerequisites to coding the Boussinesq and Euler

Modeling 2D and 3D periodic nanostructuring of materials with ultrafast laser pulses (Conference Presentation)

NASA Astrophysics Data System (ADS)

Colombier, Jean-Philippe; Rudenko, Anton; Bévillon, Emile; Zhang, Hao; Itina, Tatiana E.; Stoian, Razvan

2017-03-01

Generation of periodic arrangements of matter on materials irradiated by laser fields of uniform and isotropic energy distribution is a key issue in controlling laser structuring processes below the diffractive limit. Using three-dimensional finite-difference time-domain methods, we evaluate energy deposition patterns below a material's rough surface [1] and in bulk dielectric materials containing randomly distributed nano-inhomogeneities [2]. We show that both surface and volume patterns can be attributed to spatially ordered electromagnetic solutions of linear and nonlinear Maxwell equations. In particular, simulations revealed that anisotropic energy deposition results from the coherent superposition of the incident and the inhomogeneity-scattered light waves. Transient electronic response is also analyzed by kinetic equations of free electron excitation/relaxation processes for dielectrics and by ab initio calculations for metals. They show that for nonplasmonic metals, ultrafast carrier excitation can drastically affect electronic structures, driving a transient surface plasmonic state with high consequences for optical resonances generation [3]. Comparing condition formations of 2D laser-induced periodic surface structures (LIPSS) and 3D self-organized nanogratings, we will discuss the role of collective scattering of nanoroughness and the feedback-driven growth of the nanostructures. [1] H. Zhang, J.P. Colombier, C. Li, N. Faure, G. Cheng, and R. Stoian, Physical Review B 92, 174109 (2015). [2] A. Rudenko, J.P. Colombier, and T.E. Itina, Physical Review B 93 (7), 075427 (2016). [3] E. Bévillon, J.P. Colombier, V. Recoules, H. Zhang, C. Li and R. Stoian, Physical Review B 93 (16), 165416 (2016).

Ultrashort laser-matter interaction at moderate intensities: two-temperature relaxation, foaming of stretched melt, and freezing of evolving nanostructures

NASA Astrophysics Data System (ADS)

Inogamov, Nail A.; Zhakhovsky, Vasily V.; Petrov, Yurii V.; Khokhlov, Viktor A.; Ashitkov, Sergey I.; Migdal, Kirill P.; Ilnitsky, Denis K.; Emirov, Yusuf N.; Khishchenko, Konstantin V.; Komarov, Pavel S.; Shepelev, Vadim V.; Agranat, Mikhail B.; Anisimov, Sergey I.; Oleynik, Ivan I.; Fortov, Vladimir E.

2013-11-01

Interaction of ultrashort laser pulse with metals is considered. Ultrafast heating in our range of absorbed fluences Fabs > 10 mJjcm2 transfers matter into two-temperature (2T) state and induces expressed thermomechani­ cal response. To analyze our case, where 2T, thermomechanical, and multidimensional (formation of surface structures) effects are significant, we use density functional theory (DFT), solutions of kinetic equations in τ- approximation, 2T-hydrodynamics, and molecular dynamics simulations. We have studied transition from light absorption in a skin layer to 2T state, and from 2T stage to hydrodynamical motions. We describe (i) formation of very peculiar (superelasticity) acoustic wave irradiated from the laser heated surface layer and (ii) rich com­ plex of surface phenomena including fast melting, nucleation of seed bubbles in hydrodynamically stretched fluid, evolution of vapor-liquid mixture into very spatially extended foam, mechanical breaking of liquid membranes in foam (foam disintegration), strong surface tension oscillations driven by breaking of membranes, non-equilibrium freezing of overcooled molten metals, transition to nano-domain solid, and formation of surface nanostructures.

Surface mine planning and design implications and theory of a visual environmental quality predictive model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burley, J.B.

1999-07-01

Surface mine planners and designers are searching for scientifically based tools to assist in the pre-mine planning and post-mine development or surface mine sites. In this study, the author presents a science based visual and environmental quality predictive model useful in preparing and assessing landscape treatments for surface mine sites. The equation explains 67 percent of respondent preference, with an overall p-value for the equation >0.0001 and a p-value >0.05 for each regressor. Regressors employed in the equation include an environmental quality index, foreground vegetation, distant nonvegetation, people, vehicles, utilities, foreground flowers, foreground erosion, wildlife, landscape openness, landscape mystery, andmore » noosphericness (a measure of human disturbance). The equation can be explained with an Intrusion/Neutral Modifier/Temporal Enhancement Theory which suggests that human intrusions upon other humans results in landscape of low preference and which also suggests that landscape containing natural and special temporal features such as wildlife and flowers can enhance the value of a landscape scene. This research supports the importance of visual barriers such as berms and vegetation screens during mining operations and supports public perceptions concerning many types of industrial activities. In addition, the equation can be applied to study post-mining landscape development plans to maximize the efficiency and effectiveness of landscape treatments.« less

Prediction of seismic collapse risk of steel moment frame mid-rise structures by meta-heuristic algorithms

NASA Astrophysics Data System (ADS)

Jough, Fooad Karimi Ghaleh; Şensoy, Serhan

2016-12-01

Different performance levels may be obtained for sideway collapse evaluation of steel moment frames depending on the evaluation procedure used to handle uncertainties. In this article, the process of representing modelling uncertainties, record to record (RTR) variations and cognitive uncertainties for moment resisting steel frames of various heights is discussed in detail. RTR uncertainty is used by incremental dynamic analysis (IDA), modelling uncertainties are considered through backbone curves and hysteresis loops of component, and cognitive uncertainty is presented in three levels of material quality. IDA is used to evaluate RTR uncertainty based on strong ground motion records selected by the k-means algorithm, which is favoured over Monte Carlo selection due to its time saving appeal. Analytical equations of the Response Surface Method are obtained through IDA results by the Cuckoo algorithm, which predicts the mean and standard deviation of the collapse fragility curve. The Takagi-Sugeno-Kang model is used to represent material quality based on the response surface coefficients. Finally, collapse fragility curves with the various sources of uncertainties mentioned are derived through a large number of material quality values and meta variables inferred by the Takagi-Sugeno-Kang fuzzy model based on response surface method coefficients. It is concluded that a better risk management strategy in countries where material quality control is weak, is to account for cognitive uncertainties in fragility curves and the mean annual frequency.

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing

NASA Astrophysics Data System (ADS)

Vorontsov, Mikhail A.; Kolosov, Valeriy

2005-01-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing.

PubMed

Vorontsov, Mikhail A; Kolosov, Valeriy

2005-01-01

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.

A new deflection solution and application of a fiber Bragg grating-based inclinometer for monitoring internal displacements in slopes

NASA Astrophysics Data System (ADS)

Zheng, Yong; Huang, Da; Shi, Lin

2018-05-01

Landslide monitoring is critical for predicting the stability of slopes to ensure the safety of life and property. Considering the potential advantages of fiber Bragg gratings (FBGs), such as immunity to electromagnetic interference, resistance to hostile environments, light weight, and high measurement precision and real time response, a self-designed, FBG-based in situ inclinometer combining a traditional inclinometer and FBG technology was designed to monitor the inner deformation of a slope. In practical landslide monitoring, the inclinometer can be regarded as a cantilever beam with one end fixed. Based on the deflection curve equation of a normal beam and the composite Simpson integral equation, a theoretical deflection equation of the FBG-based inclinometer versus longitudinal strain was established. A FBG-based inclinometer was fabricated and calibrated in the laboratory and a calibration strain sensitivity coefficient was obtained. The results of calibration tests show that the displacements measured by dial indicators are in good agreement with the theoretical displacements calculated using the proposed equation. A series of FBG-based inclinometers were installed into three vertical boreholes located at different points on the profile of an actual reinforced slope. The in situ monitoring results show that the FBG-based inclinometer can effectively capture the real-time internal displacements and potential sliding surface of the slope, proving the validity of the proposed theoretical equation as well the reliability and practicality of the proposed FBG-based inclinometer in engineering applications.

Improved AFM Mapping of ICF Target Surfaces

NASA Astrophysics Data System (ADS)

Olson, D. K.; Drake, T.; Frey, D.; Huang, H.; Stephens, R. B.

2003-10-01

Targets for Inertial Confinement Fusion (ICF) research are made from spherical shells with very strict requirements on surface smoothness. Hydrodynamic instabilities are amplified by the presence of surface defects, greatly reducing the gain of ICF targets. Sub-micron variations in the surface can be examined using an Atomic Force Microscope. The current sphere mapping assembly at General Atomics is designed to trace near the equator of a rotating sphere under the AFM head. Spheres are traced on three mutually orthogonal planes. The ˜10 mm piezo-electric actuator range limits how far off the equator we can scan spheres of millimeter diameter. Because only a small fraction of the target's surface can be covered, localized high-mode defects are difficult to detect. In order to meet the needs of ICF research, we need to scan more surface area of the sphere with the AFM. By integrating an additional stepping motor to the sphere mapping assembly, we will be able to recenter the piezo driver of the AFM while mapping. This additional ability allows us to increase the amount of the sphere's surface we are able to scan with the AFM by extending the range of the AFM from the sphere's equator.

Pinning and gas oversaturation imply stable single surface nanobubbles.

PubMed

Lohse, Detlef; Zhang, Xuehua

2015-03-01

Surface nanobubbles are experimentally known to survive for days at hydrophobic surfaces immersed in gas-oversaturated water. This is different from bulk nanobubbles, which are pressed out by the Laplace pressure against any gas oversaturation and dissolve in submilliseconds, as derived by Epstein and Plesset [J. Chem. Phys. 18, 1505 (1950)]. Pinning of the contact line has been speculated to be the reason for the stability of the surface nanobubbles. Building on an exact result by Popov [Phys. Rev. E 71, 036313 (2005)] on coffee stain evaporation, here we confirm this speculation by an exact calculation for single surface nanobubbles. It is based only on (i) the diffusion equation, (ii) Laplace pressure, and (iii) Henry's equation, i.e., fluid dynamical equations which are all known to be valid down to the nanometer scale. The crucial parameter is the gas oversaturation ζ of the liquid. At the stable equilibrium, the gas overpressures due to this oversaturation and the Laplace pressure balance. The theory predicts how the contact angle of the pinned bubble depends on ζ and the surface nanobubble's footprint lateral extension L. It also predicts an upper lateral extension threshold for stable surface nanobubbles to exist.

A numerical study of electromagnetic scattering from ocean like surfaces

NASA Technical Reports Server (NTRS)

Lentz, R. R.

1972-01-01

The integral equations describing electromagnetic scattering from one dimensional conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometric optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root mean square surface roughness is less than one-tenth of a wavelength.

Improved atmosphere-ocean coupled modeling in the tropics for climate prediction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Minghua

2015-01-01

We investigated the initial development of the double ITCZ in the Community Climate System Model (CCSM Version 3) in the central Pacific. Starting from a resting initial condition of the ocean in January, the model developed a warm bias of sea-surface temperature (SST) in the central Pacific from 5oS to 10oS in the first three months. We found this initial bias to be caused by excessive surface shortwave radiation that is also present in the standalone atmospheric model. The initial bias is further amplified by biases in both surface latent heat flux and horizontal heat transport in the upper ocean.more » These biases are caused by the responses of surface winds to SST bias and the thermocline structure to surface wind curls. We also showed that the warming biases in surface solar radiation and latent heat fluxes are seasonally offset by cooling biases from reduced solar radiation after the austral summer due to cloud responses and in the austral fall due to enhanced evaporation when the maximum SST is closest to the equator. The warming biases from the dynamic heat transport by ocean currents however stay throughout all seasons once they are developed, which are eventually balanced by enhanced energy exchange and penetration of solar radiation below the mixed layer. Our results also showed that the equatorial cold tongue develops after the warm biases in the south central Pacific, and the overestimation of surface shortwave radiation recurs in the austral summer in each year.« less

An Elliptic PDE Approach for Shape Characterization

PubMed Central

Haidar, Haissam; Bouix, Sylvain; Levitt, James; McCarley, Robert W.; Shenton, Martha E.; Soul, Janet S.

2009-01-01

This paper presents a novel approach to analyze the shape of anatomical structures. Our methodology is rooted in classical physics and in particular Poisson's equation, a fundamental partial differential equation [1]. The solution to this equation and more specifically its equipotential surfaces display properties that are useful for shape analysis. We present a numerical algorithm to calculate the length of streamlines formed by the gradient field of the solution to this equation for 2D and 3D objects. The length of the streamlines along the equipotential surfaces was used to build a new function which can characterize the shape of objects. We illustrate our method on 2D synthetic and natural shapes as well as 3D medical data. PMID:17271986

A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen

2012-01-01

In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

An evolving effective stress approach to anisotropic distortional hardening

DOE PAGES

Lester, B. T.; Scherzinger, W. M.

2018-03-11

A new yield surface with an evolving effective stress definition is proposed for consistently and efficiently describing anisotropic distortional hardening. Specifically, a new internal state variable is introduced to capture the thermodynamic evolution between different effective stress definitions. The corresponding yield surface and evolution equations of the internal variables are derived from thermodynamic considerations enabling satisfaction of the second law. A closest point projection return mapping algorithm for the proposed model is formulated and implemented for use in finite element analyses. Finally, select constitutive and larger scale boundary value problems are solved to explore the capabilities of the model andmore » examine the impact of distortional hardening on constitutive and structural responses. Importantly, these simulations demonstrate the tractability of the proposed formulation in investigating large-scale problems of interest.« less

An evolving effective stress approach to anisotropic distortional hardening

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lester, B. T.; Scherzinger, W. M.

A new yield surface with an evolving effective stress definition is proposed for consistently and efficiently describing anisotropic distortional hardening. Specifically, a new internal state variable is introduced to capture the thermodynamic evolution between different effective stress definitions. The corresponding yield surface and evolution equations of the internal variables are derived from thermodynamic considerations enabling satisfaction of the second law. A closest point projection return mapping algorithm for the proposed model is formulated and implemented for use in finite element analyses. Finally, select constitutive and larger scale boundary value problems are solved to explore the capabilities of the model andmore » examine the impact of distortional hardening on constitutive and structural responses. Importantly, these simulations demonstrate the tractability of the proposed formulation in investigating large-scale problems of interest.« less

Equilibria Configurations for Epitaxial Crystal Growth with Adatoms

NASA Astrophysics Data System (ADS)

Caroccia, Marco; Cristoferi, Riccardo; Dietrich, Laurent

2018-05-01

The behavior of a surface energy F}(E,u)} , where E is a set of finite perimeter and u\\in L^1(partial^{*} E, R_+) , is studied. These energies have been recently considered in the context of materials science to derive a new model in crystal growth that takes into account the effect of atoms, the freely diffusing on the surface (called adatoms), which are responsible for morphological evolution through an attachment and detachment process. Regular critical points, the existence and uniqueness of minimizers are discussed and the relaxation of F in a general setting under the L 1 convergence of sets and the vague convergence of measures is characterized. This is part of an ongoing project aimed at an analytical study of diffuse interface approximations of the associated evolution equations.

Study of the heat transfer in solids using infrared photothermal radiometry and simulation by COMSOL Multiphysics.

PubMed

Suarez, V; Hernández Wong, J; Nogal, U; Calderón, A; Rojas-Trigos, J B; Juárez, A G; Marín, E

2014-01-01

It is reported the study of the heat transfer through a homogeneous and isotropic solid exited by square periodic light beam on its front surface. For this, we use the Infrared Photothermal Radiometry in order to obtain the evolution of the temperature difference on the rear surface of three samples, silicon, copper and wood, as a function of the exposure time. Also, we solved the heat transport equation for this problem with the boundary conditions congruent with the physical situation, by means of numerical simulation based in finite element analysis. Our results show a good agreement between the experimental and numerical simulated results, which demonstrate the utility of this methodology for the study of the thermal response of solids. Copyright © 2013 Elsevier Ltd. All rights reserved.

Equations for estimating loblolly pine branch and foliage weight and surface area distributions

Treesearch

V. Clark Baldwin; Kelly D. Peterson; Harold E. Burkhatt; Ralph L. Amateis; Phillip M. Dougherty

1996-01-01

Equations to predict foliage weight and surface area, and their vertical and horizontal distributions, within the crowns of unthinned loblolly pine (Pinus tueduL.) trees are presented. A right-truncated Weibull function was used for describing vertical foliage distributions. This function ensures that all of the foliage located between the tree tip and the foliage base...

Numerical Study of Nonlinear Structures of Locally Excited Marangoni Convection in the Long-Wave Approximation

NASA Astrophysics Data System (ADS)

Wertgeim, Igor I.

2018-02-01

We investigate stationary and non-stationary solutions of nonlinear equations of the long-wave approximation for the Marangoni convection caused by a localized source of heat or a surface active impurity (surfactant) in a thin horizontal layer of a viscous incompressible fluid with a free surface. The distribution of heat or concentration flux is determined by the uniform vertical gradient of temperature or impurity concentration, distorted by the imposition of a slightly inhomogeneous heating or of surfactant, localized in the horizontal plane. The lower boundary of the layer is considered thermally insulated or impermeable, whereas the upper boundary is free and deformable. The equations obtained in the long-wave approximation are formulated in terms of the amplitudes of the temperature distribution or impurity concentration, deformation of the surface, and vorticity. For a simplification of the problem, a sequence of nonlinear equations is obtained, which in the simplest form leads to a nonlinear Schrödinger equation with a localized potential. The basic state of the system, its dependence on the parameters and stability are investigated. For stationary solutions localized in the region of the surface tension inhomogeneity, domains of parameters corresponding to different spatial patterns are delineated.

Probabilistic Design of a Wind Tunnel Model to Match the Response of a Full-Scale Aircraft

NASA Technical Reports Server (NTRS)

Mason, Brian H.; Stroud, W. Jefferson; Krishnamurthy, T.; Spain, Charles V.; Naser, Ahmad S.

2005-01-01

approach is presented for carrying out the reliability-based design of a plate-like wing that is part of a wind tunnel model. The goal is to design the wind tunnel model to match the stiffness characteristics of the wing box of a flight vehicle while satisfying strength-based risk/reliability requirements that prevents damage to the wind tunnel model and fixtures. The flight vehicle is a modified F/A-18 aircraft. The design problem is solved using reliability-based optimization techniques. The objective function to be minimized is the difference between the displacements of the wind tunnel model and the corresponding displacements of the flight vehicle. The design variables control the thickness distribution of the wind tunnel model. Displacements of the wind tunnel model change with the thickness distribution, while displacements of the flight vehicle are a set of fixed data. The only constraint imposed is that the probability of failure is less than a specified value. Failure is assumed to occur if the stress caused by aerodynamic pressure loading is greater than the specified strength allowable. Two uncertain quantities are considered: the allowable stress and the thickness distribution of the wind tunnel model. Reliability is calculated using Monte Carlo simulation with response surfaces that provide approximate values of stresses. The response surface equations are, in turn, computed from finite element analyses of the wind tunnel model at specified design points. Because the response surface approximations were fit over a small region centered about the current design, the response surfaces were refit periodically as the design variables changed. Coarse-grained parallelism was used to simultaneously perform multiple finite element analyses. Studies carried out in this paper demonstrate that this scheme of using moving response surfaces and coarse-grained computational parallelism reduce the execution time of the Monte Carlo simulation enough to make the design problem tractable. The results of the reliability-based designs performed in this paper show that large decreases in the probability of stress-based failure can be realized with only small sacrifices in the ability of the wind tunnel model to represent the displacements of the full-scale vehicle.

Asymptotic research of transonic gas flows

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Tamarova, Yuliya A.

2017-12-01

The article is dedicated to the development asymptotic theory of gas flowing at speed next to sound velocity, particularly of gas transonic flows, i.e. the flows, containing both, subsonic and supersonic areas. The main issue, when styding such flows, are nonlinearity and combined type of equations, describing the transonic flow. Based on asymptotic nonlinear equation obtained in the article, the gas transonic flows is studied, considering transverse disturbance with respect to the main flow. The asymptotic conditions at shock-wave front and conditions on the streamlined surface are found. Moreover, the equation of sound surface and asymptotic formula defining the pressure are recorded. Several exact particular solutions of such equation are given, and their application to solve several tasks of transonic aerodynamics is indicated. Specifically, the polynomial form solution describing gas axisymmetric flows in Laval nozzles with constant acceleration in direction of the nozzle's axis and flow swirling is obtained. The solutions describing the unsteady flow along the channels between spinning surfaces are presented. The asymptotic equation is obtained, describing the flow, appearing during non-separated and separated flow past, closely approximated to cylindrical one. Specific solutions are given, based on which the examples of steady flow are formed.

Cosmological applications of singular hypersurfaces in general relativity

NASA Astrophysics Data System (ADS)

Laguna-Castillo, Pablo

Three applications to cosmology of surface layers, based on Israel's formalism of singular hypersurfaces and thin shells in general relativity, are presented. Einstein's field equations are analyzed in the presence of a bubble nucleated in vacuum phase transitions within the context of the old inflationary universe scenario. The evolution of a bubble with vanishing surface energy density is studied. It is found that such bubbles lead to a worm-hole matching. Next, the observable four-dimensional universe is considered as a singular hypersurface of discontinuity embedded in a five-dimensional Kaluza-Klein cosmology. It is possible to rewrite the projected five-dimensional Einstein equations on the surface layer in a similar way to the four-dimensional Robertson-Walker cosmology equations. Next, a model is described for an infinite-length, straight U(1) cosmic string as a cylindrical, singular shell enclosing a region of false vacuum. A set of equations is introduced which are required to develop a three-dimensional computer code whose purpose is to study the process of intercommuting cosmic strings with the inclusion of gravitational effects. The outcome is evolution and constraint equations for the gravitational, scalar and gauge field of two initially separated, perpendicular, cosmic strings.

The Kadomtsev-Petviashvili equation under rapid forcing

NASA Astrophysics Data System (ADS)

Moroz, Irene M.

1997-06-01

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data.

Using Automated Essay Scores as an Anchor When Equating Constructed Response Writing Tests

ERIC Educational Resources Information Center

Almond, Russell G.

2014-01-01

Assessments consisting of only a few extended constructed response items (essays) are not typically equated using anchor test designs as there are typically too few essay prompts in each form to allow for meaningful equating. This article explores the idea that output from an automated scoring program designed to measure writing fluency (a common…

Generalized Path Analysis and Generalized Simultaneous Equations Model for Recursive Systems with Responses of Mixed Types

ERIC Educational Resources Information Center

Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang

2006-01-01

This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…

Nonlinear reflection and refraction of ultrashort light pulses at the surfaces of resonant media and phase memory effects

NASA Astrophysics Data System (ADS)

Vlasov, R. A.; Gadomskii, O. H.; Gadomskaia, I. V.; Samartsev, V. V.

1986-06-01

The method of integrodifferential equations related to the optical Bloch equations is used to study the nonlinear reflection (or refraction) of a scanning laser beam at the surface of a resonant medium excited by traveling and standing surface electromagnetic waves at resonant frequency. The effect of the phase memory of surface atoms on the pulsed action of fields with space-time resolution is taken into account. The reversal of the scanning beam from the excited surface with phase conjugation of the wave front is considered. In addition, the spectrum of the nonlinear surface polaritons is analyzed as a function of the area of the exciting pulse and the penetration depth of polaritons in the resonant optical medium.

The Aqua-planet Experiment (APE): Response to Changed Meridional SST Profile

NASA Technical Reports Server (NTRS)

Williamson, David L.; Blackburn, Michael; Nakajima, Kensuke; Ohfuchi, Wataru; Takahashi, Yoshiyuki O.; Hayashi, Yoshi-Yuki; Nakamura, Hisashi; Ishiwatari, Masaki; Mcgregor, John L.; Borth, Hartmut;

Computational tools for fitting the Hill equation to dose-response curves.

PubMed

Gadagkar, Sudhindra R; Call, Gerald B

2015-01-01

Many biological response curves commonly assume a sigmoidal shape that can be approximated well by means of the 4-parameter nonlinear logistic equation, also called the Hill equation. However, estimation of the Hill equation parameters requires access to commercial software or the ability to write computer code. Here we present two user-friendly and freely available computer programs to fit the Hill equation - a Solver-based Microsoft Excel template and a stand-alone GUI-based "point and click" program, called HEPB. Both computer programs use the iterative method to estimate two of the Hill equation parameters (EC50 and the Hill slope), while constraining the values of the other two parameters (the minimum and maximum asymptotes of the response variable) to fit the Hill equation to the data. In addition, HEPB draws the prediction band at a user-defined confidence level, and determines the EC50 value for each of the limits of this band to give boundary values that help objectively delineate sensitive, normal and resistant responses to the drug being tested. Both programs were tested by analyzing twelve datasets that varied widely in data values, sample size and slope, and were found to yield estimates of the Hill equation parameters that were essentially identical to those provided by commercial software such as GraphPad Prism and nls, the statistical package in the programming language R. The Excel template provides a means to estimate the parameters of the Hill equation and plot the regression line in a familiar Microsoft Office environment. HEPB, in addition to providing the above results, also computes the prediction band for the data at a user-defined level of confidence, and determines objective cut-off values to distinguish among response types (sensitive, normal and resistant). Both programs are found to yield estimated values that are essentially the same as those from standard software such as GraphPad Prism and the R-based nls. Furthermore, HEPB also has the option to simulate 500 response values based on the range of values of the dose variable in the original data and the fit of the Hill equation to that data. Copyright © 2014. Published by Elsevier Inc.

Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

DTIC Science & Technology

1971-06-01

the Equilibrium Solution . 7 Hamilton-Jacobi-Bellman Partial Differential Equations ............. .............. 9 Influence Function Differential...Linearly .......... ............ 18 Problem Statement .......... ............ 18 Formulation of LJB Equations, Influence Function Equations and the TPBVP...19 Control Lawe . . .. ...... ........... 21 Conditions for Influence Function Continuity along Singular Surfaces

Modulation of a methane Bunsen flame by upstream perturbations

NASA Astrophysics Data System (ADS)

de Souza, T. Cardoso; Bastiaans, R. J. M.; De Goey, L. P. H.; Geurts, B. J.

2017-04-01

In this paper the effects of an upstream spatially periodic modulation acting on a turbulent Bunsen flame are investigated using direct numerical simulations of the Navier-Stokes equations coupled with the flamelet generated manifold (FGM) method to parameterise the chemistry. The premixed Bunsen flame is spatially agitated with a set of coherent large-scale structures of specific wave-number, K. The response of the premixed flame to the external modulation is characterised in terms of time-averaged properties, e.g. the average flame height ⟨H⟩ and the flame surface wrinkling ⟨W⟩. Results show that the flame response is notably selective to the size of the length scales used for agitation. For example, both flame quantities ⟨H⟩ and ⟨W⟩ present an optimal response, in comparison with an unmodulated flame, when the modulation scale is set to relatively low wave-numbers, 4π/L ≲ K ≲ 6π/L, where L is a characteristic scale. At the agitation scales where the optimal response is observed, the average flame height, ⟨H⟩, takes a clearly defined minimal value while the surface wrinkling, ⟨W⟩, presents an increase by more than a factor of 2 in comparison with the unmodulated reference case. Combined, these two response quantities indicate that there is an optimal scale for flame agitation and intensification of combustion rates in turbulent Bunsen flames.

Surface transport processes in charged porous media

DOE PAGES

Gabitto, Jorge; Tsouris, Costas

2017-03-03

Surface transport processes are important in chemistry, colloidal sciences, engineering, biology, and geophysics. Natural or externally produced charges on surfaces create electrical double layers (EDLs) at the solid-liquid interface. The existence of the EDLs produces several complex processes including bulk and surface transport of ions. In this work, a model is presented to simulate bulk and transport processes in homogeneous porous media comprising big pores. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A volume averaging technique is used to derive the averaged transport equations inmore » the limit of thin electrical double layers. Description of the EDL between the electrolyte solution and the charged wall is accomplished using the Gouy-Chapman-Stern (GCS) model. The surface transport terms enter into the average equations due to the use of boundary conditions for diffuse interfaces. Two extra surface transports terms appear in the closed average equations. One is a surface diffusion term equivalent to the transport process in non-charged porous media. The second surface transport term is a migration term unique to charged porous media. The effective bulk and transport parameters for isotropic porous media are calculated solving the corresponding closure problems.« less

Influence of surface conductivity on the apparent zeta potential of calcite.

PubMed

Li, Shuai; Leroy, Philippe; Heberling, Frank; Devau, Nicolas; Jougnot, Damien; Chiaberge, Christophe

2016-04-15

Zeta potential is a physicochemical parameter of particular importance in describing the surface electrical properties of charged porous media. However, the zeta potential of calcite is still poorly known because of the difficulty to interpret streaming potential experiments. The Helmholtz-Smoluchowski (HS) equation is widely used to estimate the apparent zeta potential from these experiments. However, this equation neglects the influence of surface conductivity on streaming potential. We present streaming potential and electrical conductivity measurements on a calcite powder in contact with an aqueous NaCl electrolyte. Our streaming potential model corrects the apparent zeta potential of calcite by accounting for the influence of surface conductivity and flow regime. We show that the HS equation seriously underestimates the zeta potential of calcite, particularly when the electrolyte is diluted (ionic strength ⩽ 0.01 M) because of calcite surface conductivity. The basic Stern model successfully predicted the corrected zeta potential by assuming that the zeta potential is located at the outer Helmholtz plane, i.e. without considering a stagnant diffuse layer at the calcite-water interface. The surface conductivity of calcite crystals was inferred from electrical conductivity measurements and computed using our basic Stern model. Surface conductivity was also successfully predicted by our surface complexation model. Copyright © 2016 Elsevier Inc. All rights reserved.

Surface transport processes in charged porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gabitto, Jorge; Tsouris, Costas

Surface transport processes are important in chemistry, colloidal sciences, engineering, biology, and geophysics. Natural or externally produced charges on surfaces create electrical double layers (EDLs) at the solid-liquid interface. The existence of the EDLs produces several complex processes including bulk and surface transport of ions. In this work, a model is presented to simulate bulk and transport processes in homogeneous porous media comprising big pores. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A volume averaging technique is used to derive the averaged transport equations inmore » the limit of thin electrical double layers. Description of the EDL between the electrolyte solution and the charged wall is accomplished using the Gouy-Chapman-Stern (GCS) model. The surface transport terms enter into the average equations due to the use of boundary conditions for diffuse interfaces. Two extra surface transports terms appear in the closed average equations. One is a surface diffusion term equivalent to the transport process in non-charged porous media. The second surface transport term is a migration term unique to charged porous media. The effective bulk and transport parameters for isotropic porous media are calculated solving the corresponding closure problems.« less

Modeling electrokinetics in ionic liquids: General

DOE PAGES

Wang, Chao; Bao, Jie; Pan, Wenxiao; ...

2017-04-01

Using direct numerical simulations, we provide a thorough study regarding the electrokinetics of ionic liquids. In particular, modified Poisson–Nernst–Planck equations are solved to capture the crowding and overscreening effects characteristic of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the modified Poisson-Nernst-Planck equations are coupled with Navier–Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel charged surfaces, charging dynamics in a nanopore, capacitance of electric double-layer capacitors, electroosmotic flow in a nanochannel, electroconvective instability on a plane ion-selective surface, and electroconvective flow on amore » curved ionselective surface. Lastly, we also discuss how crowding and overscreening and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.« less

Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-12-01

In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.

Three-variable solution in the (2+1)-dimensional null-surface formulation

NASA Astrophysics Data System (ADS)

Harriott, Tina A.; Williams, J. G.

2018-04-01

The null-surface formulation of general relativity (NSF) describes gravity by using families of null surfaces instead of a spacetime metric. Despite the fact that the NSF is (to within a conformal factor) equivalent to general relativity, the equations of the NSF are exceptionally difficult to solve, even in 2+1 dimensions. The present paper gives the first exact (2+1)-dimensional solution that depends nontrivially upon all three of the NSF's intrinsic spacetime variables. The metric derived from this solution is shown to represent a spacetime whose source is a massless scalar field that satisfies the general relativistic wave equation and the Einstein equations with minimal coupling. The spacetime is identified as one of a family of (2+1)-dimensional general relativistic spacetimes discovered by Cavaglià.

Complex-valued derivative propagation method with approximate Bohmian trajectories: Application to electronic nonadiabatic dynamics

NASA Astrophysics Data System (ADS)

Wang, Yu; Chou, Chia-Chun

2018-05-01

The coupled complex quantum Hamilton-Jacobi equations for electronic nonadiabatic transitions are approximately solved by propagating individual quantum trajectories in real space. Equations of motion are derived through use of the derivative propagation method for the complex actions and their spatial derivatives for wave packets moving on each of the coupled electronic potential surfaces. These equations for two surfaces are converted into the moving frame with the same grid point velocities. Excellent wave functions can be obtained by making use of the superposition principle even when nodes develop in wave packet scattering.

Double diffusive conjugate heat transfer: Part III

NASA Astrophysics Data System (ADS)

Soudagar, Manzoor Elahi M.; Azeem

2018-05-01

The placement of a small solid wall towards cold surface of square porous cavity affects the heat transfer behavior of porous region due to restriction of fluid motion in the region occupied by solid wall. An investigation of heat transfer is carried out to understand the fluid flow and heat transfer behavior in porous cavity by solving the governing partial differential equations. Galerkin's approach is used to convert the partial differential equations into algebraic form of equations by applying finite element method. The heat transfer increases for solid towards right surface as compared to the case of solid at center of cavity.

Equating Multidimensional Tests under a Random Groups Design: A Comparison of Various Equating Procedures

ERIC Educational Resources Information Center

Lee, Eunjung

2013-01-01

The purpose of this research was to compare the equating performance of various equating procedures for the multidimensional tests. To examine the various equating procedures, simulated data sets were used that were generated based on a multidimensional item response theory (MIRT) framework. Various equating procedures were examined, including…

Comparison of Kernel Equating and Item Response Theory Equating Methods

ERIC Educational Resources Information Center

Meng, Yu

2012-01-01

The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeon, Sangmin; Desikan, Ramya; Thundat, Thomas George

Young's equation, which is commonly used for determining the contact angle of liquid drops on a solid surface, ignores the vertical component of the surface energy. Although this force is extremely small and its effect on the solid can be ignored, it plays a significant role for flexible surfaces such as microcantilevers. A gold-coated silicon microcantilever and a dodecanethiol coated silicon microcantilever were used to detect real-time formation of nanobubbles on their surfaces when exposed to air-rich water. As air nanobubbles form on the surfaces of the cantilever, the cantilever undergoes bending, and we relate this to the vertical componentmore » of surface energy in Young's equation. This implies that the vertical component of the surface tension should be considered for flexible solid surfaces, and the formation of nanobubbles should be avoided when cantilevers are used as sensors to avoid artifacts.« less

A computer program for fitting smooth surfaces to an aircraft configuration and other three dimensional geometries

NASA Technical Reports Server (NTRS)

Craidon, C. B.

1975-01-01

A computer program that uses a three-dimensional geometric technique for fitting a smooth surface to the component parts of an aircraft configuration is presented. The resulting surface equations are useful in performing various kinds of calculations in which a three-dimensional mathematical description is necessary. Programs options may be used to compute information for three-view and orthographic projections of the configuration as well as cross-section plots at any orientation through the configuration. The aircraft geometry input section of the program may be easily replaced with a surface point description in a different form so that the program could be of use for any three-dimensional surface equations.

Skinfold Prediction Equations Fail to Provide an Accurate Estimate of Body Composition in Elite Rugby Union Athletes of Caucasian and Polynesian Ethnicity.

PubMed

Zemski, Adam J; Broad, Elizabeth M; Slater, Gary J

2018-01-01

Body composition in elite rugby union athletes is routinely assessed using surface anthropometry, which can be utilized to provide estimates of absolute body composition using regression equations. This study aims to assess the ability of available skinfold equations to estimate body composition in elite rugby union athletes who have unique physique traits and divergent ethnicity. The development of sport-specific and ethnicity-sensitive equations was also pursued. Forty-three male international Australian rugby union athletes of Caucasian and Polynesian descent underwent surface anthropometry and dual-energy X-ray absorptiometry (DXA) assessment. Body fat percent (BF%) was estimated using five previously developed equations and compared to DXA measures. Novel sport and ethnicity-sensitive prediction equations were developed using forward selection multiple regression analysis. Existing skinfold equations provided unsatisfactory estimates of BF% in elite rugby union athletes, with all equations demonstrating a 95% prediction interval in excess of 5%. The equations tended to underestimate BF% at low levels of adiposity, whilst overestimating BF% at higher levels of adiposity, regardless of ethnicity. The novel equations created explained a similar amount of variance to those previously developed (Caucasians 75%, Polynesians 90%). The use of skinfold equations, including the created equations, cannot be supported to estimate absolute body composition. Until a population-specific equation is established that can be validated to precisely estimate body composition, it is advocated to use a proven method, such as DXA, when absolute measures of lean and fat mass are desired, and raw anthropometry data routinely to derive an estimate of body composition change.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

Capillary waves in the subcritical nonlinear Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kozyreff, G.

2010-01-15

We expand recent results on the nonlinear Schroedinger equation with cubic-quintic nonlinearity to show that some solutions are described by the Bernoulli equation in the presence of surface tension. As a consequence, capillary waves are predicted and found numerically at the interface between regions of large and low amplitude.

Comparison of Numerical Approaches to a Steady-State Landscape Equation

NASA Astrophysics Data System (ADS)

Bachman, S.; Peckham, S.

2008-12-01

A mathematical model of an idealized fluvial landscape has been developed, in which a land surface will evolve to preserve dendritic channel networks as the surface is lowered. The physical basis for this model stems from the equations for conservation of mass for water and sediment. These equations relate the divergence of the 2D vector fields showing the unit-width discharge of water and sediment to the excess rainrate and tectonic uplift on the land surface. The 2D flow direction is taken to be opposite to the water- surface gradient vector. These notions are combined with a generalized Manning-type flow resistance formula and a generalized sediment transport law to give a closed mathematical system that can, in principle, be solved for all variables of interest: discharge of water and sediment, land surface height, vertically- averaged flow velocity, water depth, and shear stress. The hydraulic geometry equations (Leopold et. al, 1964, 1995) are used to incorporate width, depth, velocity, and slope of river channels as powers of the mean-annual river discharge. Combined, they give the unit- width discharge of the stream as a power, γ, of the water surface slope. The simplified steady-state model takes into account three components among those listed above: conservation of mass for water, flow opposite the gradient, and a slope-discharge exponent γ = -1 to reflect mature drainage networks. The mathematical representation of this model appears as a second-order hyperbolic partial differential equation (PDE) where the diffusivity is inversely proportional to the square of the local surface slope. The highly nonlinear nature of this PDE has made it very difficult to solve both analytically and numerically. We present simplistic analytic solutions to this equation which are used to test the validity of the numerical algorithms. We also present three such numerical approaches which have been used in solving the differential equation. The first is based on a nonlinear diffusion filtering technique (Welk et. al, 2007) that has been applied successfully in the context of image processing. The second uses a Ritz finite element approach to the Euler-Lagrange formulation of the PDE in which an eighth degree polynomial is solved whose coefficients are locally dependent on slope and elevation. Lastly, we show a variant to the diffusion filtering approach in which a single-stage Runge-Kutta method is used to iterate a time-derivative to steady- state. The relative merits and drawbacks of these approaches are discussed, as well as stability and consistency requirements.

A double expansion method for the frequency response of finite-length beams with periodic parameters

NASA Astrophysics Data System (ADS)

Ying, Z. G.; Ni, Y. Q.

2017-03-01

A double expansion method for the frequency response of finite-length beams with periodic distribution parameters is proposed. The vibration response of the beam with spatial periodic parameters under harmonic excitations is studied. The frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non-periodic functions. The procedure of the double expansion method includes the following two main steps: first, the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the Floquet-Bloch theorem, and the period-parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients; second, the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions, and the linear differential equations are converted into algebraic equations according to the Galerkin method. The expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined. The proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively. The modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method. The proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis. Numerical results on the frequency response of the finite-length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics, including the parameter-excited modal resonance, doubling-peak frequency response and remarkable reduction of the maximum frequency response for certain parametric wave number and wave amplitude. The results have the potential application to structural vibration control.

Development, optimization, and in vitro characterization of dasatinib-loaded PEG functionalized chitosan capped gold nanoparticles using Box-Behnken experimental design.

PubMed

Adena, Sandeep Kumar Reddy; Upadhyay, Mansi; Vardhan, Harsh; Mishra, Brahmeshwar

2018-03-01

The purpose of this research study was to develop, optimize, and characterize dasatinib loaded polyethylene glycol (PEG) stabilized chitosan capped gold nanoparticles (DSB-PEG-Ch-GNPs). Gold (III) chloride hydrate was reduced with chitosan and the resulting nanoparticles were coated with thiol-terminated PEG and loaded with dasatinib (DSB). Plackett-Burman design (PBD) followed by Box-Behnken experimental design (BBD) were employed to optimize the process parameters. Polynomial equations, contour, and 3D response surface plots were generated to relate the factors and responses. The optimized DSB-PEG-Ch-GNPs were characterized by FTIR, XRD, HR-SEM, EDX, TEM, SAED, AFM, DLS, and ZP. The results of the optimized DSB-PEG-Ch-GNPs showed particle size (PS) of 24.39 ± 1.82 nm, apparent drug content (ADC) of 72.06 ± 0.86%, and zeta potential (ZP) of -13.91 ± 1.21 mV. The responses observed and the predicted values of the optimized process were found to be close. The shape and surface morphology studies showed that the resulting DSB-PEG-Ch-GNPs were spherical and smooth. The stability and in vitro drug release studies confirmed that the optimized formulation was stable at different conditions of storage and exhibited a sustained drug release of the drug of up to 76% in 48 h and followed Korsmeyer-Peppas release kinetic model. A process for preparing gold nanoparticles using chitosan, anchoring PEG to the particle surface, and entrapping dasatinib in the chitosan-PEG surface corona was optimized.

The validation and application of a rotor acoustic prediction computer program

NASA Technical Reports Server (NTRS)

Gallman, Judith M.

1990-01-01

An essential prerequisite to reducing the acoustic detectability of military rotorcraft is a better understanding of main rotor noise which is the major contributor to the overall noise. A simple, yet accurate, Rotor Acoustic Prediction Program (RAPP) was developed to advance the understanding of main rotor noise. This prediction program uses the Ffowcs Williams and Hawkings (FW-H) equation. The particular form of the FW-H equation used is well suited for the coupling of the measured blade surface pressure to the prediction of acoustic pressure. The FW-H equation is an inhomogeneous wave equation that is valid in all space and governs acoustic pressure generated by thin moving bodies. The nonhomogeneous terms describe mass displacement due to surface motion and forces due to local surface stresses, such as viscous stress and pressure distribution on the surface. This paper examines two of the four types of main rotor noise: BVI noise and low-frequency noise. Blade-vortex interaction noise occurs when a tip vortex, previously shed by a rotor blade, passes close enough to a rotor blade to cause large variations in the blade surface pressures. This event is most disturbing when it happens on the advancing side of the rotor disk. Low-frequency noise includes hover and low to moderate speed forward flight. For these flight conditions, the low frequency components of the acoustic signal dominate.

Minimal area surfaces dual to Wilson loops and the Mathieu equation

DOE PAGES

Huang, Changyu; He, Yifei; Kruczenski, Martin

2016-08-11

The AdS/CFT correspondence relates Wilson loops in N=4 SYM to minimal area surfaces in AdS 5 × S 5 space. Recently, a new approach to study minimal area surfaces in AdS 3 c AdS 5 was discussed based on a Schroedinger equation with a periodic potential determined by the Schwarzian derivative of the shape of the Wilson loop. Here we use the Mathieu equation, a standard example of a periodic potential, to obtain a class of Wilson loops such that the area of the dual minimal area surface can be computed analytically in terms of eigenvalues of such equation. Asmore » opposed to previous examples, these minimal surfaces have an umbilical point (where the principal curvatures are equal) and are invariant under λ-deformations. In various limits they reduce to the single and multiple wound circular Wilson loop and to the regular light-like polygons studied by Alday and Maldacena. In this last limit, the periodic potential becomes a series of deep wells each related to a light-like segment. Small corrections are described by a tight-binding approximation. In the circular limit they are well approximated by an expansion developed by A. Dekel. In the particular case of no umbilical points they reduce to a previous solution proposed by J. Toledo. The construction works both in Euclidean and Minkowski signature of AdS 3.« less

Physical evaluation of a maize-based extruded snack with curry powder.

PubMed

Christofides, Vassilis; Ainsworth, Paul; Ibanoğlu, Senol; Gomes, Frances

2004-02-01

Response surface methodology was used to analyze the effect of screw speed (200-280 rpm), feed moisture (13.0-17.0%, wet basis), and curry powder (6.0-9.0%) on the bulk density, lateral expansion, and firmness of maize-based extruded snack with curry powder. Regression equations describing the effect of each variable on the responses were obtained. Responses were most affected by changes in feed moisture followed by screw speed and curry powder (p < 0.05). Lateral expansion increased linearly as the amount of curry powder added was increased whereas a quadratic increase was obtained in lateral expansion with decreasing feed moisture. The firmness of samples was increased with an increase in feed moisture. The bulk density of samples was increased with increasing feed moisture and screw speeds. Radial expansion was found to be a better index to measure the physical properties of the extruded product indicated by a higher correlation coefficient.

An Experimental Investigation into the Optimal Processing Conditions for the CO2 Laser Cladding of 20 MnCr5 Steel Using Taguchi Method and ANN

NASA Astrophysics Data System (ADS)

Mondal, Subrata; Bandyopadhyay, Asish.; Pal, Pradip Kumar

2010-10-01

This paper presents the prediction and evaluation of laser clad profile formed by means of CO2 laser applying Taguchi method and the artificial neural network (ANN). Laser cladding is one of the surface modifying technologies in which the desired surface characteristics of any component can be achieved such as good corrosion resistance, wear resistance and hardness etc. Laser is used as a heat source to melt the anti-corrosive powder of Inconel-625 (Super Alloy) to give a coating on 20 MnCr5 substrate. The parametric study of this technique is also attempted here. The data obtained from experiments have been used to develop the linear regression equation and then to develop the neural network model. Moreover, the data obtained from regression equations have also been used as supporting data to train the neural network. The artificial neural network (ANN) is used to establish the relationship between the input/output parameters of the process. The established ANN model is then indirectly integrated with the optimization technique. It has been seen that the developed neural network model shows a good degree of approximation with experimental data. In order to obtain the combination of process parameters such as laser power, scan speed and powder feed rate for which the output parameters become optimum, the experimental data have been used to develop the response surfaces.

Seismic gradiometry using ambient seismic noise in an anisotropic Earth

NASA Astrophysics Data System (ADS)

de Ridder, S. A. L.; Curtis, A.

2017-05-01

We introduce a wavefield gradiometry technique to estimate both isotropic and anisotropic local medium characteristics from short recordings of seismic signals by inverting a wave equation. The method exploits the information in the spatial gradients of a seismic wavefield that are calculated using dense deployments of seismic arrays. The application of the method uses the surface wave energy in the ambient seismic field. To estimate isotropic and anisotropic medium properties we invert an elliptically anisotropic wave equation. The spatial derivatives of the recorded wavefield are evaluated by calculating finite differences over nearby recordings, which introduces a systematic anisotropic error. A two-step approach corrects this error: finite difference stencils are first calibrated, then the output of the wave-equation inversion is corrected using the linearized impulse response to the inverted velocity anomaly. We test the procedure on ambient seismic noise recorded in a large and dense ocean bottom cable array installed over Ekofisk field. The estimated azimuthal anisotropy forms a circular geometry around the production-induced subsidence bowl. This conforms with results from studies employing controlled sources, and with interferometry correlating long records of seismic noise. Yet in this example, the results were obtained using only a few minutes of ambient seismic noise.

Capillary instability of elliptic liquid jets

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Dolatabadi, Ali

2011-08-01

Instability of a liquid jet issuing from an elliptic nozzle in Rayleigh mode is investigated and its behavior is compared with a circular jet. Mathematical solution of viscous free-surface flow for asymmetric geometry is complicated if 3-D analytical solutions are to be obtained. Hence, one-dimensional Cosserat (directed curve) equations are used which can be assumed as a low order form of Navier-Stokes equations for slender jets. Linear solution is performed using perturbation method. Temporal dispersion equation is derived to find the most unstable wavelength responsible for the jet breakup. The obtained results for a circular jet (i.e., an ellipse with an aspect ratio of one) are compared with the classical results of Rayleigh and Weber for inviscid and viscous cases, respectively. It is shown that in the Rayleigh regime, which is the subject of this research, symmetric perturbations are unstable while asymmetric perturbations are stable. Consequently, spatial analysis is performed and the variation of growth rate under the effect of perturbation frequencies for various jet velocities is demonstrated. Results reveal that in comparison with a circular jet, the elliptic jet is more unstable. Furthermore, among liquid jets with elliptical cross sections, those with larger ellipticities have a larger instability growth rate.

Incompressible material point method for free surface flow

NASA Astrophysics Data System (ADS)

Zhang, Fan; Zhang, Xiong; Sze, Kam Yim; Lian, Yanping; Liu, Yan

2017-02-01

To overcome the shortcomings of the weakly compressible material point method (WCMPM) for modeling the free surface flow problems, an incompressible material point method (iMPM) is proposed based on operator splitting technique which splits the solution of momentum equation into two steps. An intermediate velocity field is first obtained by solving the momentum equations ignoring the pressure gradient term, and then the intermediate velocity field is corrected by the pressure term to obtain a divergence-free velocity field. A level set function which represents the signed distance to free surface is used to track the free surface and apply the pressure boundary conditions. Moreover, an hourglass damping is introduced to suppress the spurious velocity modes which are caused by the discretization of the cell center velocity divergence from the grid vertexes velocities when solving pressure Poisson equations. Numerical examples including dam break, oscillation of a cubic liquid drop and a droplet impact into deep pool show that the proposed incompressible material point method is much more accurate and efficient than the weakly compressible material point method in solving free surface flow problems.

A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions.

PubMed

Yang, S A

2002-10-01

This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method.

Computational flow development for unsteady viscous flows: Foundation of the numerical method

NASA Technical Reports Server (NTRS)

Bratanow, T.; Spehert, T.

1978-01-01

A procedure is presented for effective consideration of viscous effects in computational development of high Reynolds number flows. The procedure is based on the interpretation of the Navier-Stokes equations as vorticity transport equations. The physics of the flow was represented in a form suitable for numerical analysis. Lighthill's concept for flow development for computational purposes was adapted. The vorticity transport equations were cast in a form convenient for computation. A statement for these equations was written using the method of weighted residuals and applying the Galerkin criterion. An integral representation of the induced velocity was applied on the basis of the Biot-Savart law. Distribution of new vorticity, produced at wing surfaces over small computational time intervals, was assumed to be confined to a thin region around the wing surfaces.

Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

NASA Astrophysics Data System (ADS)

Di Nucci, Carmine

2018-05-01

This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.

Dust transportation in bounday layers on complex areas

NASA Astrophysics Data System (ADS)

Karelsky, Kirill; Petrosyan, Arakel

2017-04-01

This presentation is aimed at creating and realization of new physical model of impurity transfer (solid particles and heavy gases) in areas with non-flat and/or nonstationary boundaries. The main idea of suggested method is to use non-viscous equations for solid particles transport modeling in the vicinity of complex boundary. In viscous atmosphere with as small as one likes coefficient of molecular viscosity, the non-slip boundary condition on solid surface must be observed. This postulates the reduction of velocity to zero at a solid surface. It is unconditionally in this case Prandtle hypothesis must be observed: for rather wide range of conditions in the surface neighboring layers energy dissipation of atmosphere flows is comparable by magnitude with manifestation of inertia forces. That is why according to Prandtle hypothesis in atmosphere movement characterizing by a high Reynolds number the boundary layer is forming near a planet surface, within which the required transition from zero velocities at the surface to magnitudes at the external boundary of the layer that are quite close to ones in ideal atmosphere flow. In that layer fast velocity gradients cause viscous effects to be comparable in magnitude with inertia forces influence. For conditions considered essential changes of hydrodynamic fields near solid boundary caused not only by nonslip condition but also by a various relief of surface: mountains, street canyons, individual buildings. Transport of solid particles, their ascent and precipitation also result in dramatic changes of meteorological fields. As dynamic processes of solid particles transfer accompanying the flow past of complex relief surface by wind flows is of our main interest we are to use equations of non-viscous hydrodynamic. We should put up with on the one hand idea of high wind gradients in the boundary layer and on the other hand disregard of molecular viscosity in two-phase atmosphere equations. We deal with describing high field gradients with the aid of scheme viscosity of numerical algorithm used to model near-surface phenomena. This idea is implemented in the model of ideal gas equations with variable equation of state describing particulates transportation within boundary layer with obstacles.

Double diffusion in arbitrary porous cavity: Part II

NASA Astrophysics Data System (ADS)

Ahamad, N. Ameer; Kamangar, Sarfaraz; Salman Ahmed N., J.; Soudagar, Manzoor Elahi M.; Khan, T. M. Yunus

2017-07-01

Heat and mass transfer in porous medium is one of the fundamental topics of interest. The present article is dedicated to study the effect of a small block placed at center of left vertical surface of the cavity. The block is maintained at isothermal temperature That three of its edges attached with porous medium. The left surface of cavity is maintained at highest concentration and right surface at lowest concentration. The right surface of cavity is at cold isothermal temperature Tc. Governing equations are converted into matrix form of equations with the help of finite element method and solved iteratively by using a computer code generated in MATLAB.

Voltera's Solution of the Wave Equation as Applied to Three-Dimensional Supersonic Airfoil Problems

NASA Technical Reports Server (NTRS)

Heslet, Max A; Lomax, Harvard; Jones, Arthur L

1947-01-01

A surface integral is developed which yields solutions of the linearized partial differential equation for supersonic flow. These solutions satisfy boundary conditions arising in wing theory. Particular applications of this general method are made, using acceleration potentials, to flat surfaces and to uniformly loaded lifting surfaces. Rectangular and trapezoidal plan forms are considered along with triangular forms adaptable to swept-forward and swept-back wings. The case of the triangular plan form in sideslip is also included. Emphasis is placed on the systematic application of the method to the lifting surfaces considered and on the possibility of further application.

Modeling of multiple equilibria in the self-aggregation of di-n-decyldimethylammonium chloride/octaethylene glycol monododecyl ether/cyclodextrin ternary systems.

PubMed

Leclercq, Loïc; Lubart, Quentin; Aubry, Jean-Marie; Nardello-Rataj, Véronique

2013-05-28

The surface tension equations of binary surfactant mixtures (di-n-decyldimethylammonium chloride and octaethylene glycol monododecyl ether) are established by combining the Szyszkowski equation of surfactant solutions, the ideal or nonideal mixing theory, and the phase separation model. For surfactant mixtures, the surface tension at the air-water interface is calculated using nonideal theory due to synergism between the two adsorbed surfactant types. The incorporation of cyclodextrin complexation model to the surface tension equations gives a robust model for the description of the surface tension isotherms of binary, ternary, and more complex systems involving numerous inclusion complexes. The surface tension data obtained experimentally shows excellent agreement with the theoretical model below and above the formation of micelles. The strong synergistic effect observed between the two surfactants is disrupted by the presence of CDs, leading to ideal behavior of ternary systems. Indeed, depending on the nature of the cyclodextrin (i.e., α, β, or γ), which allows a tuning of the cavity size, the binding constants with the surfactants are modified as well as the surface properties due to strong modification of equilibria involved in the ternary mixture.

The Craik-Leibovich Vortex Force as a Skin Effect

NASA Astrophysics Data System (ADS)

Malecha, Ziemowit; Chini, Gregory; Julien, Keith

2013-11-01

The Craik-Leibovich (CL) equations are a surface-wave filtered version of the instantaneous Navier-Stokes equations in which the rectified effects of the surface waves are captured through a so-called ``vortex force'' term: the cross-product of the Stokes, or Lagrangian, mass drift associated with the filtered surface waves and the filtered vorticity vector. For locally generated wind waves, the Stokes drift is very strongly surface confined. In this scenario, the induced body force may be represented as a surface, or skin, effect. Using matched asymptotic analysis in this limit, we derive effective boundary conditions (BCs) for the flow beneath the Stokes drift layer (i.e. in the bulk of the mixed layer). We establish the regime of validity of the resulting formulation by performing linear stability analyses and numerical simulations of both the asymptotic model and the full CL equations for a variety of vertical Stokes drift profiles. The effective BC formulation offers both theoretical and computational advantages, and should be particularly useful for LES of Langmuir turbulence for which the need to resolve very small scale near-surface flow structures imposes severe computational constraints. GPC would like to acknowledge funding from the NSF award 0934827, administered by the Physical Oceanography Program.

Theoretical analysis of shock induced depolarization and current generation in ferroelectrics

NASA Astrophysics Data System (ADS)

Agrawal, Vinamra; Bhattacharya, Kaushik

Ferroelectric generators are used to generate large magnitude current pulse by impacting a polarized ferroelectric material. The impact causes depolarization of the material and at high impact speeds, dielectric breakdown. Depending on the loading conditions and the electromechanical boundary conditions, the current or voltage profiles obtained vary. In this study, we explore the large deformation dynamic response of a ferroelectric material. Using the Maxwell's equations, conservation laws and the second law of thermodynamics, we derive the governing equations for the phase boundary propagation as well as the driving force acting on it. We allow for the phase boundary to contain surface charges which introduces the contribution of curvature of phase boundary in the governing equations and the driving force. This type of analysis accounts for the dielectric breakdown and resulting conduction in the material. Next, we implement the equations derived to solve a one dimensional impact problem on a ferroelectric material under different electrical boundary conditions. The constitutive law is chosen to be piecewise quadratic in polarization and quadratic in the strain. We solve for the current profile generated in short circuit case and for voltage profile in open circuited case. This work was made possible by the financial support of the US Air Force Office of Scientific Research through the Center of Excellence in High Rate Deformation Physics of Heterogeneous Materials (Grant: FA 9550-12-1-0091).

Strong motion from surface waves in deep sedimentary basins

USGS Publications Warehouse

Joyner, W.B.

2000-01-01

It is widely recognized that long-period surface waves generated by conversion of body waves at the boundaries of deep sedimentary basins make an important contribution to strong ground motion. The factors controlling the amplitude of such motion, however, are not widely understood. A study of pseudovelocity response spectra of strong-motion records from the Los Angeles Basin shows that late-arriving surface waves with group velocities of about 1 km/sec dominate the ground motion for periods of 3 sec and longer. The rate of amplitude decay for these waves is less than for the body waves and depends significantly on period, with smaller decay for longer periods. The amplitude can be modeled by the equation log y = f(M, RE) + c + bRB where y is the pseudovelocity response, f(M, RE) is an attenuation relation based on a general strong-motion data set, M is moment magnitude, RE is the distance from the source to the edge of the basin, RB is the distance from the edge of the basin to the recording site, and b and c are parameters fit to the data. The equation gives values larger by as much as a factor of 3 than given by the attenuation relationships based on general strong-motion data sets for the same source-site distance. It is clear that surface waves need to be taken into account in the design of long-period structures in deep sedimentary basins. The ground-motion levels specified by the earthquake provisions of current building codes, in California at least, accommodate the long-period ground motions from basin-edge-generated surface waves for periods of 5 sec and less and earthquakes with moment magnitudes of 7.5 or less located more than 20 km outside the basin. There may be problems at longer periods and for earthquakes located closer to the basin edge. The results of this study suggest that anelastic attenuation may need to be included in attempts to model long-period motion in deep sedimentary basins. To obtain better data on surface waves in the future, operators of strong-motion networks should take special care for the faithful recording of the long-period components of ground motion. It will also be necessary to insure that at least some selected recorders, once triggered, continue to operate for a time sufficient for the surface waves to traverse the basin. With velocities of about 1 km/sec, that time will be as long as 100 sec for a basin the size of the Los Angeles Basin.

Computer-aided design of bevel gear tooth surfaces

NASA Technical Reports Server (NTRS)

Shuo, Hung Chang; Huston, Ronald L.; Coy, John J.

1989-01-01

This paper presents a computer-aided design procedure for generating bevel gears. The development is based on examining a perfectly plastic, cone-shaped gear blank rolling over a cutting tooth on a plane crown rack. The resulting impression on the plastic gear blank is the envelope of the cutting tooth. This impression and envelope thus form a conjugate tooth surface. Equations are presented for the locus of points on the tooth surface. The same procedures are then extended to simulate the generation of a spiral bevel gear. The corresponding governing equations are presented.

Computer aided design of bevel gear tooth surfaces

NASA Technical Reports Server (NTRS)

Chang, S. H.; Huston, R. L.; Coy, J. J.

1989-01-01

This paper presents a computer-aided design procedure for generating bevel gears. The development is based on examining a perfectly plastic, cone-shaped gear blank rolling over a cutting tooth on a plane crown rack. The resulting impression on the plastic gear blank is the envelope of the cutting tooth. This impression and envelope thus form a conjugate tooth surface. Equations are presented for the locus of points on the tooth surface. The same procedures are then extended to simulate the generation of a spiral bevel gear. The corresponding governing equations are presented.

Nonlinear oscillations of inviscid free drops

NASA Technical Reports Server (NTRS)

Patzek, T. W.; Benner, R. E., Jr.; Basaran, O. A.; Scriven, L. E.

1991-01-01

The present analysis of free liquid drops' inviscid oscillations proceeds through solution of Bernoulli's equation to obtain the free surface shape and of Laplace's equation for the velocity potential field. Results thus obtained encompass drop-shape sequences, pressure distributions, particle paths, and the temporal evolution of kinetic and surface energies; accuracy is verified by the near-constant drop volume and total energy, as well as the diminutiveness of mass and momentum fluxes across drop surfaces. Further insight into the nature of oscillations is provided by Fourier power spectrum analyses of mode interactions and frequency shifts.

Estimation of Regional Evapotranspiration Using Remotely Sensed Land Surface Temperature. Part 2: Application of Equilibrium Evaporation Model to Estimate Evapotranspiration by Remote Sensing Technique. [Japan

NASA Technical Reports Server (NTRS)

Kotoda, K.; Nakagawa, S.; Kai, K.; Yoshino, M. M.; Takeda, K.; Seki, K.

1985-01-01

In a humid region like Japan, it seems that the radiation term in the energy balance equation plays a more important role for evapotranspiration then does the vapor pressure difference between the surface and lower atmospheric boundary layer. A Priestley-Taylor type equation (equilibrium evaporation model) is used to estimate evapotranspiration. Net radiation, soil heat flux, and surface temperature data are obtained. Only temperature data obtained by remotely sensed techniques are used.

The method of lines in analyzing solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, John P.

1990-01-01

A semi-numerical method is reviewed for solving a set of coupled partial differential equations subject to mixed and possibly coupled boundary conditions. The line method of analysis is applied to the Navier-Cauchy equations of elastic and elastoplastic equilibrium to calculate the displacement distributions in various, simple geometry bodies containing cracks. The application of this method to the appropriate field equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling of the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The use of this method is illustrated by reviewing and presenting selected solutions of mixed boundary value problems in three dimensional fracture mechanics. These solutions are of great importance in fracture toughness testing, where accurate stress and displacement distributions are required for the calculation of certain fracture parameters. Computations obtained for typical flawed specimens include that for elastic as well as elastoplastic response. Problems in both Cartesian and cylindrical coordinate systems are included. Results are summarized for a finite geometry rectangular bar with a central through-the-thickness or rectangular surface crack under remote uniaxial tension. In addition, stress and displacement distributions are reviewed for finite circular bars with embedded penny-shaped cracks, and rods with external annular or ring cracks under opening mode tension. The results obtained show that the method of lines presents a systematic approach to the solution of some three-dimensional mechanics problems with arbitrary boundary conditions. The advantage of this method over other numerical solutions is that good results are obtained even from the use of a relatively coarse grid.

Causes of plasma column contraction in surface-wave-driven discharges in argon at atmospheric pressure

NASA Astrophysics Data System (ADS)

Ridenti, Marco Antonio; de Amorim, Jayr; Dal Pino, Arnaldo; Guerra, Vasco; Petrov, George

2018-01-01

In this work we compute the main features of a surface-wave-driven plasma in argon at atmospheric pressure in view of a better understanding of the contraction phenomenon. We include the detailed chemical kinetics dynamics of Ar and solve the mass conservation equations of the relevant neutral excited and charged species. The gas temperature radial profile is calculated by means of the thermal diffusion equation. The electric field radial profile is calculated directly from the numerical solution of the Maxwell equations assuming the surface wave to be propagating in the TM00 mode. The problem is considered to be radially symmetrical, the axial variations are neglected, and the equations are solved in a self-consistent fashion. We probe the model results considering three scenarios: (i) the electron energy distribution function (EEDF) is calculated by means of the Boltzmann equation; (ii) the EEDF is considered to be Maxwellian; (iii) the dissociative recombination is excluded from the chemical kinetics dynamics, but the nonequilibrium EEDF is preserved. From this analysis, the dissociative recombination is shown to be the leading mechanism in the constriction of surface-wave plasmas. The results are compared with mass spectrometry measurements of the radial density profile of the ions Ar+ and Ar2+. An explanation is proposed for the trends seen by Thomson scattering diagnostics that shows a substantial increase of electron temperature towards the plasma borders where the electron density is small.

The global strong solutions of Hasegawa-Mima-Charney-Obukhov equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao Hongjun; Zhu Anyou

2005-08-01

The quasigeostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with no dissipation term which was obtained as an asymptotic model from the Euler equations with free surface under a quasigeostrophic velocity field assumption. It is called the Hasegawa-Mima-Charney-Obukhov equation, which also arises from plasmas theory. We use a priori estimates to get the global existence of strong solutions for an Hasegawa-Mima-Charney-Obukhov equation.

Microscopic modeling of gas-surface scattering. I. A combined molecular dynamics-rate equation approach

NASA Astrophysics Data System (ADS)

Filinov, A.; Bonitz, M.; Loffhagen, D.

2018-06-01

A combination of first principle molecular dynamics (MD) simulations with a rate equation model (MD-RE approach) is presented to study the trapping and the scattering of rare gas atoms from metal surfaces. The temporal evolution of the atom fractions that are either adsorbed or scattered into the continuum is investigated in detail. We demonstrate that for this description one has to consider trapped, quasi-trapped and scattering states, and present an energetic definition of these states. The rate equations contain the transition probabilities between the states. We demonstrate how these rate equations can be derived from kinetic theory. Moreover, we present a rigorous way to determine the transition probabilities from a microscopic analysis of the particle trajectories generated by MD simulations. Once the system reaches quasi-equilibrium, the rates converge to stationary values, and the subsequent thermal adsorption/desorption dynamics is completely described by the rate equations without the need to perform further time-consuming MD simulations. As a proof of concept of our approach, MD simulations for argon atoms interacting with a platinum (111) surface are presented. A detailed deterministic trajectory analysis is performed, and the transition rates are constructed. The dependence of the rates on the incidence conditions and the lattice temperature is analyzed. Based on this example, we analyze the time scale of the gas-surface system to approach the quasi-stationary state. The MD-RE model has great relevance for the plasma-surface modeling as it makes an extension of accurate simulations to long, experimentally relevant time scales possible. Its application to the computation of atomic sticking probabilities is given in the second part (paper II).

The Role of Electrical Anisotropy in Modeling and Interpreting Controlled-Source Electromagnetic Responses for Hydraulic Fracture Monitoring

NASA Astrophysics Data System (ADS)

Trevino, S., III; Hickey, M. S.; Everett, M. E.

2017-12-01

Controlled-Source Electromagnetics (CSEM) can be used to monitor the movement and extent of injection fluid during a hydraulic fracture. The response of the fluid to energization by a CSEM source is dependent upon the electrical conductivity difference between the fluid and background geological formation. An important property that must be taken into account when modeling and interpreting CSEM responses is that electrical conductivity may be anisotropic. We study the effect of electrical anisotropy in both the background formation and the fluid-injection zone. First, various properties of the background formation can affect anisotropy including variations in grain size, composition and bedding-plane orientation. In certain formations, such as shale, the horizontal component of the conductivity can be more than an order of magnitude larger than the vertical component. We study this effect by computing differences in surface CSEM responses using the analytic 1-D anisotropic primary solution of a horizontal electric dipole positioned at the surface. Second, during hydraulic fracturing, the injected fluid can create new fractures and infill existing natural fractures. To include the explicit fracture geometry in modeling, a large increase in the number of nodes and computational time is required which may not be feasible. An alternative is to instead model the large-scale fracture geometry as a uniform slab with an appropriate bulk conductivity. Micro-scale fracture geometry may cause preferential fluid propagation in a single direction or plane which can be represented by electrical anisotropy of the slab. To study such effects of bulk anisotropy on CSEM responses we present results from multiple scenarios of surface to surface hydraulic fracture monitoring using 3-D finite element modeling. The model uses Coulomb-gauged potentials to solve Maxwell's equations in the frequency domain and we have updated the code to allow a triaxial electrical conductivity tensor to be specified. By allowing for formation and target electrical anisotropy these modeling results contribute to a better understanding and faster interpretation of field data.

Sample Invariance of the Structural Equation Model and the Item Response Model: A Case Study.

ERIC Educational Resources Information Center

Breithaupt, Krista; Zumbo, Bruno D.

2002-01-01

Evaluated the sample invariance of item discrimination statistics in a case study using real data, responses of 10 random samples of 500 people to a depression scale. Results lend some support to the hypothesized superiority of a two-parameter item response model over the common form of structural equation modeling, at least when responses are…

Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface Potential Trap Model

NASA Astrophysics Data System (ADS)

Wan, Li; Xu, Shixin; Liao, Maijia; Liu, Chun; Sheng, Ping

2014-01-01

In this work, we treat the Poisson-Nernst-Planck (PNP) equations as the basis for a consistent framework of the electrokinetic effects. The static limit of the PNP equations is shown to be the charge-conserving Poisson-Boltzmann (CCPB) equation, with guaranteed charge neutrality within the computational domain. We propose a surface potential trap model that attributes an energy cost to the interfacial charge dissociation. In conjunction with the CCPB, the surface potential trap can cause a surface-specific adsorbed charge layer σ. By defining a chemical potential μ that arises from the charge neutrality constraint, a reformulated CCPB can be reduced to the form of the Poisson-Boltzmann equation, whose prediction of the Debye screening layer profile is in excellent agreement with that of the Poisson-Boltzmann equation when the channel width is much larger than the Debye length. However, important differences emerge when the channel width is small, so the Debye screening layers from the opposite sides of the channel overlap with each other. In particular, the theory automatically yields a variation of σ that is generally known as the "charge regulation" behavior, attendant with predictions of force variation as a function of nanoscale separation between two charged surfaces that are in good agreement with the experiments, with no adjustable or additional parameters. We give a generalized definition of the ζ potential that reflects the strength of the electrokinetic effect; its variations with the concentration of surface-specific and surface-nonspecific salt ions are shown to be in good agreement with the experiments. To delineate the behavior of the electro-osmotic (EO) effect, the coupled PNP and Navier-Stokes equations are solved numerically under an applied electric field tangential to the fluid-solid interface. The EO effect is shown to exhibit an intrinsic time dependence that is noninertial in its origin. Under a step-function applied electric field, a pulse of fluid flow is followed by relaxation to a new ion distribution, owing to the diffusive counter current. We have numerically evaluated the Onsager coefficients associated with the EO effect, L21, and its reverse streaming potential effect, L12, and show that L12=L21 in accordance with the Onsager relation. We conclude by noting some of the challenges ahead.

Evaluation of crystallization behavior on the surface of nifedipine solid dispersion powder using inverse gas chromatography.

PubMed

Miyanishi, Hideo; Nemoto, Takayuki; Mizuno, Masayasu; Mimura, Hisashi; Kitamura, Satoshi; Iwao, Yasunori; Noguchi, Shuji; Itai, Shigeru

2013-02-01

To investigate crystallization behavior on the surface of amorphous solid dispersion powder using inverse gas chromatography (IGC) and to predict the physical stability at temperatures below the glass transition temperature (T (g)). Amorphous solid dispersion powder was prepared by melt-quenching of a mixture of crystalline nifedipine and polyvinylpyrrolidon (PVP) K-30. IGC was conducted by injecting undecane (probe gas) and methane (reference gas) repeatedly to the solid dispersion at temperatures below T (g). Surface crystallization was evaluated by the retention volume change of undecane based on the observation that the surface of the solid dispersion with crystallized nifedipine gives an increased retention volume. On applying the retention volume change to the Hancock-Sharp equation, surface crystallization was found to follow a two-dimensional growth of nuclei mechanism. Estimation of the crystallization rates at temperatures far below T (g) using the Avrami-Erofeev equation and Arrhenius equation showed that, to maintain its quality for at least three years, the solid dispersion should be stored at -20°C (T (g) - 65°C). IGC can be used to evaluate crystallization behavior on the surface of a solid dispersion powder, and, unlike traditional techniques, can also predict the stability of the solid dispersion based on the surface crystallization behavior.

Study of non-spherical bubble oscillations near a surface in a weak acoustic standing wave field.

PubMed

Xi, Xiaoyu; Cegla, Frederic; Mettin, Robert; Holsteyns, Frank; Lippert, Alexander

2014-04-01

The interaction of acoustically driven bubbles with a wall is important in many applications of ultrasound and cavitation, as the close boundary can severely alter the bubble dynamics. In this paper, the non-spherical surface oscillations of bubbles near a surface in a weak acoustic standing wave field are investigated experimentally and numerically. The translation, the volume, and surface mode oscillations of bubbles near a flat glass surface were observed by a high speed camera in a standing wave cell at 46.8 kHz. The model approach is based on a modified Keller-Miksis equation coupled to surface mode amplitude equations in the first order, and to the translation equations. Modifications are introduced due to the adjacent wall. It was found that a bubble's oscillation mode can change in the presence of the wall, as compared to the bubble in the bulk liquid. In particular, the wall shifts the instability pressure thresholds to smaller driving frequencies for fixed bubble equilibrium radii, or to smaller equilibrium radii for fixed excitation frequency. This can destabilize otherwise spherical bubbles, or stabilize bubbles undergoing surface oscillations in the bulk. The bubble dynamics observed in experiment demonstrated the same trend as the theoretical results.

Analysis of surface cracks in finite plates under tension or bending loads

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Raju, I. S.

1979-01-01

Stress-intensity factors calculated with a three-dimensional, finite-element analysis for shallow and deep semielliptical surface cracks in finite elastic isotropic plates subjected to tension or bending loads are presented. A wide range of configuration parameters was investigated. The ratio of crack depth to plate thickness ranged from 0.2 to 0.8 and the ratio of crack depth to crack length ranged from 0.2 to 2.0. The effects of plate width on stress-intensity variations along the crack front was also investigated. A wide-range equation for stress-intensity factors along the crack front as a function of crack depth, crack length, plate thickness, and plate width was developed for tension and bending loads. The equation was used to predict patterns of surface-crack growth under tension or bending fatigue loads. A modified form of the equation was also used to correlate surface-crack fracture data for a brittle epoxy material within + or - 10 percent for a wide range of crack shapes and crack sizes.

Solution of an eigenvalue problem for the Laplace operator on a spherical surface. M.S. Thesis - Maryland Univ.

NASA Technical Reports Server (NTRS)

Walden, H.

1974-01-01

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

A time-domain Kirchhoff formula for the convective acoustic wave equation

NASA Astrophysics Data System (ADS)

Ghorbaniasl, Ghader; Siozos-Rousoulis, Leonidas; Lacor, Chris

2016-03-01

Kirchhoff's integral method allows propagated sound to be predicted, based on the pressure and its derivatives in time and space obtained on a data surface located in the linear flow region. Kirchhoff's formula for noise prediction from high-speed rotors and propellers suffers from the limitation of the observer located in uniform flow, thus requiring an extension to arbitrarily moving media. This paper presents a Kirchhoff formulation for moving surfaces in a uniform moving medium of arbitrary configuration. First, the convective wave equation is derived in a moving frame, based on the generalized functions theory. The Kirchhoff formula is then obtained for moving surfaces in the time domain. The formula has a similar form to the Kirchhoff formulation for moving surfaces of Farassat and Myers, with the presence of additional terms owing to the moving medium effect. The equation explicitly accounts for the influence of mean flow and angle of attack on the radiated noise. The formula is verified by analytical cases of a monopole source located in a moving medium.

The exact calculation of quadrupole sources for some incompressible flows

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.

1988-01-01

This paper is concerned with the application of the acoustic analogy of Lighthill to the acoustic and aerodynamic problems associated with moving bodies. The Ffowcs Williams-Hawkings equation, which is an interpretation of the acoustic analogy for sound generation by moving bodies, manipulates the source terms into surface and volume sources. Quite often in practice the volume sources, or quadrupoles, are neglected for various reasons. Recently, Farassat, Long and others have attempted to use the FW-H equation with the quadrupole source and neglected to solve for the surface pressure on the body. The purpose of this paper is to examine the contribution of the quadrupole source to the acoustic pressure and body surface pressure for some problems for which the exact solution is known. The inviscid, incompressible, 2-D flow, calculated using the velocity potential, is used to calculate the individual contributions of the various surface and volume source terms in the FW-H equation. The relative importance of each of the sources is then assessed.

Evidence of singularities for a family of contour dynamics equations

PubMed Central

Córdoba, Diego; Fontelos, Marco A.; Mancho, Ana M.; Rodrigo, Jose L.

2005-01-01

In this work, we show evidence of the existence of singularities developing in finite time for a class of contour dynamics equations depending on a parameter 0 < α ≤ 1. The limiting case α → 0 corresponds to 2D Euler equations, and α = 1 corresponds to the surface quasi-geostrophic equation. The singularity is point-like, and it is approached in a self-similar manner. PMID:15837929

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

An Equation for Moist Entropy in a Precipitating and Icy Atmosphere

NASA Technical Reports Server (NTRS)

Tao, Wei-Kuo; Simpson, Joanne; Zeng, Xiping

2003-01-01

Moist entropy is nearly conserved in adiabatic motion. It is redistributed rather than created by moist convection. Thus moist entropy and its equation, as a healthy direction, can be used to construct analytical and numerical models for the interaction between tropical convective clouds and large-scale circulations. Hence, an accurate equation of moist entropy is needed for the analysis and modeling of atmospheric convective clouds. On the basis of the consistency between the energy and the entropy equations, a complete equation of moist entropy is derived from the energy equation. The equation expresses explicitly the internal and external sources of moist entropy, including those in relation to the microphysics of clouds and precipitation. In addition, an accurate formula for the surface flux of moist entropy from the underlying surface into the air above is derived. Because moist entropy deals "easily" with the transition among three water phases, it will be used as a prognostic variable in the next generation of cloud-resolving models (e. g. a global cloud-resolving model) for low computational noise. Its equation that is derived in this paper is accurate and complete, providing a theoretical basis for using moist entropy as a prognostic variable in the long-term modeling of clouds and large-scale circulations.

Dynamic coupling of subsurface and seepage flows solved within a regularized partition formulation

NASA Astrophysics Data System (ADS)

Marçais, J.; de Dreuzy, J.-R.; Erhel, J.

2017-11-01

Hillslope response to precipitations is characterized by sharp transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Locally, the transition between these two regimes is triggered by soil saturation. Here we develop an integrative approach to simultaneously solve the subsurface flow, locate the potential fully saturated areas and deduce the generated saturation excess overland flow. This approach combines the different dynamics and transitions in a single partition formulation using discontinuous functions. We propose to regularize the system of partial differential equations and to use classic spatial and temporal discretization schemes. We illustrate our methodology on the 1D hillslope storage Boussinesq equations (Troch et al., 2003). We first validate the numerical scheme on previous numerical experiments without saturation excess overland flow. Then we apply our model to a test case with dynamic transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Our results show that discretization respects mass balance both locally and globally, converges when the mesh or time step are refined. Moreover the regularization parameter can be taken small enough to ensure accuracy without suffering of numerical artefacts. Applied to some hundreds of realistic hillslope cases taken from Western side of France (Brittany), the developed method appears to be robust and efficient.

Modeling of a piezoelectric/piezomagnetic nano energy harvester based on two dimensional theory

NASA Astrophysics Data System (ADS)

Yan, Zhi

2018-01-01

This work presents a two dimensional theory for a piezoelectric/piezomagnetic bilayer nanoplate in coupled extensional and flexural vibrations with both flexoelectric and surface effects. The magneto-electro-elastic (MEE) coupling equations are derived from three-dimensional equations and Kirchhoff plate theory. Based on the developed theory, a piezoelectric/piezomagnetic nano energy harvester is proposed, which can generate electricity under time-harmonic applied magnetic field. The approximate solutions for the mechanical responses and voltage of the energy harvester are obtained using the weighted residual method. Results show that the properties of the proposed energy harvester are size-dependent due to the flexoelectric and surface effects, and such effects are more pronounced when the bilayer thickness is reduced to dozens of nanometers. It is also found that the magnetoelectric coupling coefficient and power density of the energy harvester are sensitive to the load resistance, the thickness fraction of the piezoelectric or the piezomagnetic layer and damping ratios. Moreover, results indicate that the flexoelectric effect could be made use to build a dielectric/piezomagnetic nano energy harvester. This work provides modeling techniques and numerical methods for investigating the size-dependent properties of MEE nanoplate-based energy harvester and could be helpful for designing nano energy harvesters using the principle of flexoelectricity.

A Theoretical Study of Love Wave Sensors Based on ZnO–Glass Layered Structures for Application to Liquid Environments

PubMed Central

Caliendo, Cinzia; Hamidullah, Muhammad

2016-01-01

The propagation of surface acoustic Love modes along ZnO/glass-based structures was modeled and analysed with the goal of designing a sensor able to detect changes in the environmental parameters, such as liquid viscosity changes and minute amounts of mass supported in the viscous liquid medium. Love mode propagation was modeled by numerically solving the system of coupled electro-mechanical field equations and Navier–Stokes equations. The phase and group velocities and the attenuation of the acoustic wave propagating along the 30° tilted c-axis ZnO/glass structure contacting a viscous non-conductive liquid were calculated for different ZnO guiding layer thicknesses, added mass thicknesses, and liquid viscosity and density. The three sensor responses, i.e., the wave phase and group velocity, and attenuation changes are calculated for different environmental parameters and related to the sensor velocity and attenuation sensitivities. The resulted sensitivities to liquid viscosity and added mass were optimized by adjusting the ZnO guiding layer thickness corresponding to a sensitivity peak. The present analysis is valuable for the manufacture and application of the ZnO-glass structure Love wave sensors for the detection of liquid properties, such as viscosity, density and mass anchored to the sensor surface. PMID:27918419

A CORRELATION BETWEEN RADIATION TOLERANCE AND NUCLEAR SURFACE AREA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iversen, S.

1962-09-22

Sparrow and Miksche (Science, 134:282) determined the dose (r/day) required to produce severe growth inhibition in 23 species of plants and found a linear relationship between log nuclear volume and log dose. The following equations hold for 6 species: log nuclear volume - 4.42 -0.82 log dose and log nuclear volume = 1.66 + 0.66 log (DNA content). If all the nuclear DNA is distributed in two peripheral zones, the equations also hold: 2(log nuclear surface area) - 1.33(log nuclear volume) - 2.21 + 0.88 log(DNA content) and 5.88-- 1.09 log dose. For the 23 species, the equation was obtained:more » 2(log nuclear surface area) = 5.41 -- 0.97 log dose. All the slopes are close to the expected value of 1.00. (D.L.C.)« less

DIFFEOMORPHIC SURFACE FLOWS: A NOVEL METHOD OF SURFACE EVOLUTION*

PubMed Central

Zhang, Sirong; Younes, Laurent; Zweck, John; Ratnanather, J. Tilak

2009-01-01

We describe a new class of surface flows, diffeomorphic surface flows, induced by restricting diffeomorphic flows of the ambient Euclidean space to a surface. Different from classical surface PDE flows such as mean curvature flow, diffeomorphic surface flows are solutions of integro-differential equations in a group of diffeomorphisms. They have the potential advantage of being both topology-invariant and singularity free, which can be useful in computational anatomy and computer graphics. We first derive the Euler–Lagrange equation of the elastic energy for general diffeomorphic surface flows, which can be regarded as a smoothed version of the corresponding classical surface flows. Then we focus on diffeomorphic mean curvature flow. We prove the short-time existence and uniqueness of the flow, and study the long-time existence of the flow for surfaces of revolution. We present numerical experiments on synthetic and cortical surfaces from neuroimaging studies in schizophrenia and auditory disorders. Finally we discuss unresolved issues and potential applications. PMID:20016768

The Approach to Equilibrium: Detailed Balance and the Master Equation

ERIC Educational Resources Information Center

Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.

2011-01-01

The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…

The Bernoulli Equation in a Moving Reference Frame

ERIC Educational Resources Information Center

Mungan, Carl E.

2011-01-01

Unlike other standard equations in introductory classical mechanics, the Bernoulli equation is not Galilean invariant. The explanation is that, in a reference frame moving with respect to constrictions or obstacles, those surfaces do work on the fluid, constituting an extra term that needs to be included in the work-energy calculation. A…

Observed variability in the upper layers at the Equator, 90°E in the Indian Ocean during 2001-2008, 1: zonal currents

NASA Astrophysics Data System (ADS)

Rao, R. R.; Horii, T.; Masumoto, Y.; Mizuno, K.

2017-08-01

The observed variability of zonal currents (ZC) at the Equator, 90°E shows a strong seasonal cycle in the near-surface 40-350 m water column with periodic east-west reversals most pronounced at semiannual frequency. Superposed on this, a strong intraseasonal variability of 30-90 day periodicity is also prominently seen in the near-surface layer (40-80 m) almost throughout the year with the only exception of February-March. An eastward flowing equatorial undercurrent (EUC) is present in the depth range of 80-160 m during March-April and October-November. The observed intraseasonal variability in the near-surface layer is primarily determined by the equatorial zonal westerly wind bursts (WWBs) through local frictional coupling between the zonal flow in the surface layer and surface zonal winds and shows large interannual variability. The eastward flowing EUC maintained by the ZPG set up by the east-west slope of the thermocline remotely controlled by the zonal wind (ZW) and zonally propagating wave fields also shows significant interannual variability. This observed variability on interannual time scales appears to be controlled by the corresponding variability in the alongshore winds off the Somalia coast during the preceding boreal winter, the ZW field along the equator, and the associated zonally propagating Kelvin and Rossby waves. The salinity induced vertical stratification observed in the near-surface layer through barrier layer thickness (BLT) effects also shows a significant influence on the ZC field on intraseasonal time scale. Interestingly, among all the 8 years (2001-2008), relatively weaker annual cycle is seen in both ZC in the 40-350 m water column and boreal spring sea surface temperature (SST) only during 2001 and 2008 along the equator caused through propagating wave dynamics.

Item response theory and structural equation modelling for ordinal data: Describing the relationship between KIDSCREEN and Life-H.

PubMed

Titman, Andrew C; Lancaster, Gillian A; Colver, Allan F

2016-10-01

Both item response theory and structural equation models are useful in the analysis of ordered categorical responses from health assessment questionnaires. We highlight the advantages and disadvantages of the item response theory and structural equation modelling approaches to modelling ordinal data, from within a community health setting. Using data from the SPARCLE project focussing on children with cerebral palsy, this paper investigates the relationship between two ordinal rating scales, the KIDSCREEN, which measures quality-of-life, and Life-H, which measures participation. Practical issues relating to fitting models, such as non-positive definite observed or fitted correlation matrices, and approaches to assessing model fit are discussed. item response theory models allow properties such as the conditional independence of particular domains of a measurement instrument to be assessed. When, as with the SPARCLE data, the latent traits are multidimensional, structural equation models generally provide a much more convenient modelling framework. © The Author(s) 2013.