A practical application of the geometrical theory on fibered manifolds to an autonomous bicycle motion in mechanical system with nonholonomic constraints

NASA Astrophysics Data System (ADS)

Haddout, Soufiane

2018-01-01

The equations of motion of a bicycle are highly nonlinear and rolling of wheels without slipping can only be expressed by nonholonomic constraint equations. A geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by O. Krupková (Rossi) in 1990's. Her approach is suitable for study of all kinds of mechanical systems-without restricting to Lagrangian, time-independent, or regular ones, and is applicable to arbitrary constraints (holonomic, semiholonomic, linear, nonlinear or general nonholonomic). The goal of this paper is to apply Krupková's geometric theory of nonholonomic mechanical systems to study a concrete problem in nonlinear nonholonomic dynamics, i.e., autonomous bicycle. The dynamical model is preserved in simulations in its original nonlinear form without any simplifying. The results of numerical solutions of constrained equations of motion, derived within the theory, are in good agreement with measurements and thus they open the possibility of direct application of the theory to practical situations.

Verification of a Constraint Force Equation Methodology for Modeling Multi-Body Stage Separation

NASA Technical Reports Server (NTRS)

Tartabini, Paul V.; Roithmayr, Carlos; Toniolo, Matthew D.; Karlgaard, Christopher; Pamadi, Bandu N.

2008-01-01

This paper discusses the verification of the Constraint Force Equation (CFE) methodology and its implementation in the Program to Optimize Simulated Trajectories II (POST2) for multibody separation problems using three specially designed test cases. The first test case involves two rigid bodies connected by a fixed joint; the second case involves two rigid bodies connected with a universal joint; and the third test case is that of Mach 7 separation of the Hyper-X vehicle. For the first two cases, the POST2/CFE solutions compared well with those obtained using industry standard benchmark codes, namely AUTOLEV and ADAMS. For the Hyper-X case, the POST2/CFE solutions were in reasonable agreement with the flight test data. The CFE implementation in POST2 facilitates the analysis and simulation of stage separation as an integral part of POST2 for seamless end-to-end simulations of launch vehicle trajectories.

Connection forces in deformable multibody dynamics

NASA Technical Reports Server (NTRS)

Shabana, A. A.; Chang, C. W.

1989-01-01

In the dynamic formulation of holonomic and nonholonomic systems based on D'Alembert-Lagrange equation, the forces of constraints are maintained in the dynamic equations by introducing auxiliary variables, called Lagrange multipliers. This approach introduces a set of generalized reaction forces associated with the system generalized coordinates. Different sets of variables can be used as generalized coordinates and accordingly, the generalized reactions associated with these generalized coordinates may not be the actual reaction forces at the joints. In rigid body dynamics, the generalized reaction forces and the actual reaction forces at the joints represent equipollent systems of forces since they produce the same total forces and moments at and about any point on the rigid body. This is not, however, the case in deformable body analyses wherein the generalized reaction forces depend on the system generalized reference and elastic coordinates. In this paper, a method for determining the actual reaction forces at the joints from the generalized reaction forces in deformable multibody systems is presented.

A vector-dyadic development of the equations of motion for N-coupled rigid bodies and point masses

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1974-01-01

The equations of motion are derived, in vector-dyadic format, for a topological tree of coupled rigid bodies, point masses, and symmetrical momentum wheels. These equations were programmed, and form the basis for the general-purpose digital computer program N-BOD. A complete derivation of the equations of motion is included along with a description of the methods used for kinematics, constraint elimination, and for the inclusion of nongyroscope forces and torques acting external or internal to the system.

The Langevin equation

NASA Astrophysics Data System (ADS)

Pomeau, Yves; Piasecki, Jarosław

2017-11-01

The existence of atoms has been long predicted by philosophers and scientists. The development of thermodynamics and of the statistical interpretation of its concepts at the end of the nineteenth century and in the early years of the twentieth century made it possible to bridge the gap of scales between the macroscopic world and the world of atoms. Einstein and Smoluchowski showed in 1905 and 1906 that the Brownian motion of particles of measurable size is a manifestation of the motion of atoms in fluids. Their derivation was completely different from each other. Langevin showed in 1908 how to put in a coherent framework the subtle effect of the randomness of the atomic world, responsible for the fluctuating force driving the motion of the Brownian particle and the viscosity of the "macroscopic" flow taking place around the same Brownian particle. Whereas viscous forces were already well understood at this time, the "Langevin" force appears there for the first time: it represents the fluctuating part of the interaction between the Brownian particle and the surrounding fluid. We discuss the derivation by Einstein and Smoluchowski as well as a previous paper by Sutherland on the diffusion coefficient of large spheres. Next we present Langevin's short note and explain the fundamental splitting into a random force and a macroscopic viscous force. This brings us to discuss various points, like the kind of constraints on Langevin-like equations. We insist in particular on the one arising from the time-reversal symmetry of the equilibrium fluctuations. Moreover, we discuss another constraint, raised first by Lorentz, which implies that, if the Brownian particle is not very heavy, the viscous force cannot be taken as the standard Stokes drag on an object moving at uniform speed. Lastly, we examine the so-called Langevin-Heisenberg and/or Langevin-Schrödinger equation used in quantum mechanics.

Integrating viscoelastic mass spring dampers into position-based dynamics to simulate soft tissue deformation in real time

PubMed Central

Lu, Yuhua; Liu, Qian

2018-01-01

We propose a novel method to simulate soft tissue deformation for virtual surgery applications. The method considers the mechanical properties of soft tissue, such as its viscoelasticity, nonlinearity and incompressibility; its speed, stability and accuracy also meet the requirements for a surgery simulator. Modifying the traditional equation for mass spring dampers (MSD) introduces nonlinearity and viscoelasticity into the calculation of elastic force. Then, the elastic force is used in the constraint projection step for naturally reducing constraint potential. The node position is enforced by the combined spring force and constraint conservative force through Newton's second law. We conduct a comparison study of conventional MSD and position-based dynamics for our new integrating method. Our approach enables stable, fast and large step simulation by freely controlling visual effects based on nonlinearity, viscoelasticity and incompressibility. We implement a laparoscopic cholecystectomy simulator to demonstrate the practicality of our method, in which liver and gallbladder deformation can be simulated in real time. Our method is an appropriate choice for the development of real-time virtual surgery applications. PMID:29515870

Integrating viscoelastic mass spring dampers into position-based dynamics to simulate soft tissue deformation in real time.

PubMed

Xu, Lang; Lu, Yuhua; Liu, Qian

2018-02-01

We propose a novel method to simulate soft tissue deformation for virtual surgery applications. The method considers the mechanical properties of soft tissue, such as its viscoelasticity, nonlinearity and incompressibility; its speed, stability and accuracy also meet the requirements for a surgery simulator. Modifying the traditional equation for mass spring dampers (MSD) introduces nonlinearity and viscoelasticity into the calculation of elastic force. Then, the elastic force is used in the constraint projection step for naturally reducing constraint potential. The node position is enforced by the combined spring force and constraint conservative force through Newton's second law. We conduct a comparison study of conventional MSD and position-based dynamics for our new integrating method. Our approach enables stable, fast and large step simulation by freely controlling visual effects based on nonlinearity, viscoelasticity and incompressibility. We implement a laparoscopic cholecystectomy simulator to demonstrate the practicality of our method, in which liver and gallbladder deformation can be simulated in real time. Our method is an appropriate choice for the development of real-time virtual surgery applications.

Hemispheric symmetry of the Earth's Energy Balance as a fundamental constraint on the Earth's climate

NASA Astrophysics Data System (ADS)

Stephens, G. L.; Webster, P. J.; OBrien, D. M.

2013-12-01

We currently lack a quantitative understanding of how the Earth's energy balance and the poleward energy transport adjust to different forcings that determine climate change. Currently, there are no constraints that guide this understanding. We will demonstrate that the Earth's energy balance exhibits a remarkable symmetry about the equator, and that this symmetry is a necessary condition of a steady state climate. Our analysis points to clouds as the principal agent that highly regulates this symmetry and sets the steady state. The existence of this thermodynamic steady-state constraint on climate and the symmetry required to sustain it leads to important inferences about the synchronous nature of climate changes between hemispheres, offering for example insights on mechanisms that can sustain global ice ages forced by asymmetric hemispheric solar radiation variations or how climate may respond to increases in greenhouse gas concentration. Further inferences regarding cloud effects on climate can also be deduced without resorting to the complex and intricate processes of cloud formation, whose representation continues to challenge the climate modeling community. The constraint suggests cloud feedbacks must be negative buffering the system against change. We will show that this constraint doesn't exist in the current CMIP5 model experiments and the lack of such a constraint suggests there is insufficient buffering in models in response to external forcings

Study of flutter related computational procedures for minimum weight structural sizing of advanced aircraft, supplemental data

NASA Technical Reports Server (NTRS)

Oconnell, R. F.; Hassig, H. J.; Radovcich, N. A.

1975-01-01

Computational aspects of (1) flutter optimization (minimization of structural mass subject to specified flutter requirements), (2) methods for solving the flutter equation, and (3) efficient methods for computing generalized aerodynamic force coefficients in the repetitive analysis environment of computer-aided structural design are discussed. Specific areas included: a two-dimensional Regula Falsi approach to solving the generalized flutter equation; method of incremented flutter analysis and its applications; the use of velocity potential influence coefficients in a five-matrix product formulation of the generalized aerodynamic force coefficients; options for computational operations required to generate generalized aerodynamic force coefficients; theoretical considerations related to optimization with one or more flutter constraints; and expressions for derivatives of flutter-related quantities with respect to design variables.

A general-purpose approach to computer-aided dynamic analysis of a flexible helicopter

NASA Technical Reports Server (NTRS)

Agrawal, Om P.

1988-01-01

A general purpose mathematical formulation is described for dynamic analysis of a helicopter consisting of flexible and/or rigid bodies that undergo large translations and rotations. Rigid body and elastic sets of generalized coordinates are used. The rigid body coordinates define the location and the orientation of a body coordinate frame (global frame) with respect to an inertial frame. The elastic coordinates are introduced using a finite element approach in order to model flexible components. The compatibility conditions between two adjacent elements in a flexible body are imposed using a Boolean matrix, whereas the compatibility conditions between two adjacent bodies are imposed using the Lagrange multiplier approach. Since the form of the constraint equations depends upon the type of kinematic joint and involves only the generalized coordinates of the two participating elements, then a library of constraint elements can be developed to impose the kinematic constraint in an automated fashion. For the body constraints, the Lagrange multipliers yield the reaction forces and torques of the bodies at the joints. The virtual work approach is used to derive the equations of motion, which are a system of differential and algebraic equations that are highly nonlinear. The formulation presented is general and is compared with hard-wired formulations commonly used in helicopter analysis.

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

Unseren, M.A.

A rigid body model for the entire system which accounts for the load distribution scheme proposed in Part 1 as well as for the dynamics of the manipulators and the kinematic constraints is derived in the joint space. A technique is presented for expressing the object dynamics in terms of the joint variables of both manipulators which leads to a positive definite and symmetric inertia matrix. The model is then transformed to obtain reduced order equations of motion and a separate set of equations which govern the behavior of the internal contact forces. The control architecture is applied to themore » model which results in the explicit decoupling of the position and internal contact force-controlled degrees of freedom (DOF).« less

On the Direct Assimilation of Along-track Sea Surface Height Observations into a Free-surface Ocean Model Using a Weak Constraints Four Dimensional Variational (4dvar) Method

NASA Astrophysics Data System (ADS)

Ngodock, H.; Carrier, M.; Smith, S. R.; Souopgui, I.; Martin, P.; Jacobs, G. A.

2016-02-01

The representer method is adopted for solving a weak constraints 4dvar problem for the assimilation of ocean observations including along-track SSH, using a free surface ocean model. Direct 4dvar assimilation of SSH observations along the satellite tracks requires that the adjoint model be integrated with Dirac impulses on the right hand side of the adjoint equations for the surface elevation equation. The solution of this adjoint model will inevitably include surface gravity waves, and it constitutes the forcing for the tangent linear model (TLM) according to the representer method. This yields an analysis that is contaminated by gravity waves. A method for avoiding the generation of the surface gravity waves in the analysis is proposed in this study; it consists of removing the adjoint of the free surface from the right hand side (rhs) of the free surface mode in the TLM. The information from the SSH observations will still propagate to all other variables via the adjoint of the balance relationship between the barotropic and baroclinic modes, resulting in the correction to the surface elevation. Two assimilation experiments are carried out in the Gulf of Mexico: one with adjoint forcing included on the rhs of the TLM free surface equation, and the other without. Both analyses are evaluated against the assimilated SSH observations, SSH maps from Aviso and independent surface drifters, showing that the analysis that did not include adjoint forcing in the free surface is more accurate. This study shows that when a weak constraint 4dvar approach is considered for the assimilation of along-track SSH observations using a free surface model, with the aim of correcting the mesoscale circulation, an independent model error should not be assigned to the free surface.

Development of Constraint Force Equation Methodology for Application to Multi-Body Dynamics Including Launch Vehicle Stage Seperation

NASA Technical Reports Server (NTRS)

Pamadi, Bandu N.; Toniolo, Matthew D.; Tartabini, Paul V.; Roithmayr, Carlos M.; Albertson, Cindy W.; Karlgaard, Christopher D.

2016-01-01

The objective of this report is to develop and implement a physics based method for analysis and simulation of multi-body dynamics including launch vehicle stage separation. The constraint force equation (CFE) methodology discussed in this report provides such a framework for modeling constraint forces and moments acting at joints when the vehicles are still connected. Several stand-alone test cases involving various types of joints were developed to validate the CFE methodology. The results were compared with ADAMS(Registered Trademark) and Autolev, two different industry standard benchmark codes for multi-body dynamic analysis and simulations. However, these two codes are not designed for aerospace flight trajectory simulations. After this validation exercise, the CFE algorithm was implemented in Program to Optimize Simulated Trajectories II (POST2) to provide a capability to simulate end-to-end trajectories of launch vehicles including stage separation. The POST2/CFE methodology was applied to the STS-1 Space Shuttle solid rocket booster (SRB) separation and Hyper-X Research Vehicle (HXRV) separation from the Pegasus booster as a further test and validation for its application to launch vehicle stage separation problems. Finally, to demonstrate end-to-end simulation capability, POST2/CFE was applied to the ascent, orbit insertion, and booster return of a reusable two-stage-to-orbit (TSTO) vehicle concept. With these validation exercises, POST2/CFE software can be used for performing conceptual level end-to-end simulations, including launch vehicle stage separation, for problems similar to those discussed in this report.

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

Unseren, M.A.

The report reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restricts the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for themore » closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.« less

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

Unseren, M.A.

The paper reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restrict the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for themore » closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.« less

Dynamic Behavior of Wind Turbine by a Mixed Flexible-Rigid Multi-Body Model

NASA Astrophysics Data System (ADS)

Wang, Jianhong; Qin, Datong; Ding, Yi

A mixed flexible-rigid multi-body model is presented to study the dynamic behavior of a horizontal axis wind turbine. The special attention is given to flexible body: flexible rotor is modeled by a newly developed blade finite element, support bearing elasticities, variations in the number of teeth in contact as well as contact tooth's elasticities are mainly flexible components in the power train. The couple conditions between different subsystems are established by constraint equations. The wind turbine model is generated by coupling models of rotor, power train and generator with constraint equations together. Based on this model, an eigenproblem analysis is carried out to show the mode shape of rotor and power train at a few natural frequencies. The dynamic responses and contact forces among gears under constant wind speed and fixed pitch angle are analyzed.

Stick-slip chaos in a mechanical oscillator with dry friction

NASA Astrophysics Data System (ADS)

Kousaka, Takuji; Asahara, Hiroyuki; Inaba, Naohiko

2018-03-01

This study analyzes a forced mechanical dynamical system with dry friction that can generate chaotic stick-slip vibrations. We find that the dynamics proposed by Yoshitake et al. [Trans. Jpn. Soc. Mech. Eng. C 61, 768 (1995)] can be expressed as a nonautonomous constraint differential equation owing to the static friction force. The object is constrained to the surface of a moving belt by a static friction force from when it sticks to the surface until the force on the object exceeds the maximal static friction force. We derive a 1D Poincaré return map from the constrained mechanical system, and prove numerically that this 1D map has an absolutely continuous invariant measure and a positive Lyapunov exponent, providing strong evidence for chaos.

ROCOPT: A user friendly interactive code to optimize rocket structural components

NASA Technical Reports Server (NTRS)

Rule, William K.

1989-01-01

ROCOPT is a user-friendly, graphically-interfaced, microcomputer-based computer program (IBM compatible) that optimizes rocket components by minimizing the structural weight. The rocket components considered are ring stiffened truncated cones and cylinders. The applied loading is static, and can consist of any combination of internal or external pressure, axial force, bending moment, and torque. Stress margins are calculated by means of simple closed form strength of material type equations. Stability margins are determined by approximate, orthotropic-shell, closed-form equations. A modified form of Powell's method, in conjunction with a modified form of the external penalty method, is used to determine the minimum weight of the structure subject to stress and stability margin constraints, as well as user input constraints on the structural dimensions. The graphical interface guides the user through the required data prompts, explains program options and graphically displays results for easy interpretation.

Computational strategies in the dynamic simulation of constrained flexible MBS

NASA Technical Reports Server (NTRS)

Amirouche, F. M. L.; Xie, M.

1993-01-01

This research focuses on the computational dynamics of flexible constrained multibody systems. At first a recursive mapping formulation of the kinematical expressions in a minimum dimension as well as the matrix representation of the equations of motion are presented. The method employs Kane's equation, FEM, and concepts of continuum mechanics. The generalized active forces are extended to include the effects of high temperature conditions, such as creep, thermal stress, and elastic-plastic deformation. The time variant constraint relations for rolling/contact conditions between two flexible bodies are also studied. The constraints for validation of MBS simulation of gear meshing contact using a modified Timoshenko beam theory are also presented. The last part deals with minimization of vibration/deformation of the elastic beam in multibody systems making use of time variant boundary conditions. The above methodologies and computational procedures developed are being implemented in a program called DYAMUS.

Constrained multibody system dynamics: An automated approach

NASA Technical Reports Server (NTRS)

Kamman, J. W.; Huston, R. L.

1982-01-01

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

Dark matter phenomenology of SM and enlarged Higgs sectors extended with vector-like leptons

NASA Astrophysics Data System (ADS)

Angelescu, Andrei; Arcadi, Giorgio

2017-07-01

We will investigate the scenario in which the Standard Model (SM) Higgs sector and its two-doublet extension (called the Two Higgs Doublet Model or 2HDM) are the "portal" for the interactions between the Standard Model and a fermionic Dark Matter (DM) candidate. The latter is the lightest stable neutral particle of a family of vector-like leptons (VLLs). We will provide an extensive overview of this scenario combining the constraints coming purely from DM phenomenology with more general constraints like Electroweak Precision Test (EWPT) as well as with collider searches. In the case that the new fermionic sector interacts with the SM Higgs sector, constraints from DM phenomenology force the new states to lie above the TeV scale. This requirement is relaxed in the case of 2HDM. Nevertheless, strong constraints coming from EWPTs and the Renormalization Group Equations (RGEs) limit the impact of VLFs on collider phenomenology.

Dark matter phenomenology of SM and enlarged Higgs sectors extended with vector-like leptons.

PubMed

Angelescu, Andrei; Arcadi, Giorgio

2017-01-01

We will investigate the scenario in which the Standard Model (SM) Higgs sector and its two-doublet extension (called the Two Higgs Doublet Model or 2HDM) are the "portal" for the interactions between the Standard Model and a fermionic Dark Matter (DM) candidate. The latter is the lightest stable neutral particle of a family of vector-like leptons (VLLs). We will provide an extensive overview of this scenario combining the constraints coming purely from DM phenomenology with more general constraints like Electroweak Precision Test (EWPT) as well as with collider searches. In the case that the new fermionic sector interacts with the SM Higgs sector, constraints from DM phenomenology force the new states to lie above the TeV scale. This requirement is relaxed in the case of 2HDM. Nevertheless, strong constraints coming from EWPTs and the Renormalization Group Equations (RGEs) limit the impact of VLFs on collider phenomenology.

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.

Initial conditions of inhomogeneous universe and the cosmological constant problem

NASA Astrophysics Data System (ADS)

Totani, Tomonori

2016-06-01

Deriving the Einstein field equations (EFE) with matter fluid from the action principle is not straightforward, because mass conservation must be added as an additional constraint to make rest-frame mass density variable in reaction to metric variation. This can be avoided by introducing a constraint 0δ(√-g) = to metric variations δ gμν, and then the cosmological constant Λ emerges as an integration constant. This is a removal of one of the four constraints on initial conditions forced by EFE at the birth of the universe, and it may imply that EFE are unnecessarily restrictive about initial conditions. I then adopt a principle that the theory of gravity should be able to solve time evolution starting from arbitrary inhomogeneous initial conditions about spacetime and matter. The equations of gravitational fields satisfying this principle are obtained, by setting four auxiliary constraints on δ gμν to extract six degrees of freedom for gravity. The cost of achieving this is a loss of general covariance, but these equations constitute a consistent theory if they hold in the special coordinate systems that can be uniquely specified with respect to the initial space-like hypersurface when the universe was born. This theory predicts that gravity is described by EFE with non-zero Λ in a homogeneous patch of the universe created by inflation, but Λ changes continuously across different patches. Then both the smallness and coincidence problems of the cosmological constant are solved by the anthropic argument. This is just a result of inhomogeneous initial conditions, not requiring any change of the fundamental physical laws in different patches.

Periodic Forced Response of Structures Having Three-Dimensional Frictional Constraints

NASA Astrophysics Data System (ADS)

CHEN, J. J.; YANG, B. D.; MENQ, C. H.

2000-01-01

Many mechanical systems have moving components that are mutually constrained through frictional contacts. When subjected to cyclic excitations, a contact interface may undergo constant changes among sticks, slips and separations, which leads to very complex contact kinematics. In this paper, a 3-D friction contact model is employed to predict the periodic forced response of structures having 3-D frictional constraints. Analytical criteria based on this friction contact model are used to determine the transitions among sticks, slips and separations of the friction contact, and subsequently the constrained force which consists of the induced stick-slip friction force on the contact plane and the contact normal load. The resulting constrained force is often a periodic function and can be considered as a feedback force that influences the response of the constrained structures. By using the Multi-Harmonic Balance Method along with Fast Fourier Transform, the constrained force can be integrated with the receptance of the structures so as to calculate the forced response of the constrained structures. It results in a set of non-linear algebraic equations that can be solved iteratively to yield the relative motion as well as the constrained force at the friction contact. This method is used to predict the periodic response of a frictionally constrained 3-d.o.f. oscillator. The predicted results are compared with those of the direct time integration method so as to validate the proposed method. In addition, the effect of super-harmonic components on the resonant response and jump phenomenon is examined.

Newton-Euler Dynamic Equations of Motion for a Multi-body Spacecraft

NASA Technical Reports Server (NTRS)

Stoneking, Eric

2007-01-01

The Magnetospheric MultiScale (MMS) mission employs a formation of spinning spacecraft with several flexible appendages and thruster-based control. To understand the complex dynamic interaction of thruster actuation, appendage motion, and spin dynamics, each spacecraft is modeled as a tree of rigid bodies connected by spherical or gimballed joints. The method presented facilitates assembling by inspection the exact, nonlinear dynamic equations of motion for a multibody spacecraft suitable for solution by numerical integration. The building block equations are derived by applying Newton's and Euler's equations of motion to an "element" consisting of two bodies and one joint (spherical and gimballed joints are considered separately). Patterns in the "mass" and L'force" matrices guide assembly by inspection of a general N-body tree-topology system. Straightforward linear algebra operations are employed to eliminate extraneous constraint equations, resulting in a minimum-dimension system of equations to solve. This method thus combines a straightforward, easily-extendable, easily-mechanized formulation with an efficient computer implementation.

A formulation of rotor-airframe coupling for design analysis of vibrations of helicopter airframes

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; Walton, W. C., Jr.

1982-01-01

A linear formulation of rotor airframe coupling intended for vibration analysis in airframe structural design is presented. The airframe is represented by a finite element analysis model; the rotor is represented by a general set of linear differential equations with periodic coefficients; and the connections between the rotor and airframe are specified through general linear equations of constraint. Coupling equations are applied to the rotor and airframe equations to produce one set of linear differential equations governing vibrations of the combined rotor airframe system. These equations are solved by the harmonic balance method for the system steady state vibrations. A feature of the solution process is the representation of the airframe in terms of forced responses calculated at the rotor harmonics of interest. A method based on matrix partitioning is worked out for quick recalculations of vibrations in design studies when only relatively few airframe members are varied. All relations are presented in forms suitable for direct computer implementation.

Bladed disk assemblies; Proceedings of the Eleventh Biennial Conference on Mechanical Vibration and Noise, Boston, MA, Sept. 27-30, 1987

NASA Technical Reports Server (NTRS)

Kielb, R. (Editor); Crawley, E. (Editor); Simonis, J. C. (Editor)

1987-01-01

The present conference on bladed disk assemblies discusses aerodynamic indicial reponse and stability derivatives for a rotor annulus, an analysis of aerodynamically forced turbomachine vibration, the effect of downwash on the nonsteady forces in a turbomachine stage, the vibration of turbomachine blades with root flexibility effects, mistuned bladed disk assembly vibrations, and the model-generation and modal analysis of flexible bladed disk assemblies. Also discussed are the vibration characteristics of a mistuned bladed disk, free and forced vibrations associated with localization phenomena in mistuned assemblies with cyclic symmetry, steam turbine cyclic symmetry through constraint equations, and the interpretation of experimental and theoretical results predicting vibrating turbocharger blade mode shapes.

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

Oscillating scalar fields in extended quintessence

NASA Astrophysics Data System (ADS)

Li, Dan; Pi, Shi; Scherrer, Robert J.

2018-01-01

We study a rapidly oscillating scalar field with potential V (ϕ )=k |ϕ |n nonminimally coupled to the Ricci scalar R via a term of the form (1 -8 π G0ξ ϕ2)R in the action. In the weak coupling limit, we calculate the effect of the nonminimal coupling on the time-averaged equation of state parameter γ =(p +ρ )/ρ . The change in ⟨γ ⟩ is always negative for n ≥2 and always positive for n <0.71 (which includes the case where the oscillating scalar field could serve as dark energy), while it can be either positive or negative for intermediate values of n . Constraints on the time variation of G force this change to be infinitesimally small at the present time whenever the scalar field dominates the expansion, but constraints in the early universe are not as stringent. The rapid oscillation induced in G also produces an additional contribution to the Friedman equation that behaves like an effective energy density with a stiff equation of state, but we show that, under reasonable assumptions, this effective energy density is always smaller than the density of the scalar field itself.

Initial conditions of inhomogeneous universe and the cosmological constant problem

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

Totani, Tomonori, E-mail: totani@astron.s.u-tokyo.ac.jp

Deriving the Einstein field equations (EFE) with matter fluid from the action principle is not straightforward, because mass conservation must be added as an additional constraint to make rest-frame mass density variable in reaction to metric variation. This can be avoided by introducing a constraint 0δ(√− g ) = to metric variations δ g {sup μν}, and then the cosmological constant Λ emerges as an integration constant. This is a removal of one of the four constraints on initial conditions forced by EFE at the birth of the universe, and it may imply that EFE are unnecessarily restrictive about initialmore » conditions. I then adopt a principle that the theory of gravity should be able to solve time evolution starting from arbitrary inhomogeneous initial conditions about spacetime and matter. The equations of gravitational fields satisfying this principle are obtained, by setting four auxiliary constraints on δ g {sup μν} to extract six degrees of freedom for gravity. The cost of achieving this is a loss of general covariance, but these equations constitute a consistent theory if they hold in the special coordinate systems that can be uniquely specified with respect to the initial space-like hypersurface when the universe was born. This theory predicts that gravity is described by EFE with non-zero Λ in a homogeneous patch of the universe created by inflation, but Λ changes continuously across different patches. Then both the smallness and coincidence problems of the cosmological constant are solved by the anthropic argument. This is just a result of inhomogeneous initial conditions, not requiring any change of the fundamental physical laws in different patches.« less

Brute force meets Bruno force in parameter optimisation: introduction of novel constraints for parameter accuracy improvement by symbolic computation.

PubMed

Nakatsui, M; Horimoto, K; Lemaire, F; Ürgüplü, A; Sedoglavic, A; Boulier, F

2011-09-01

Recent remarkable advances in computer performance have enabled us to estimate parameter values by the huge power of numerical computation, the so-called 'Brute force', resulting in the high-speed simultaneous estimation of a large number of parameter values. However, these advancements have not been fully utilised to improve the accuracy of parameter estimation. Here the authors review a novel method for parameter estimation using symbolic computation power, 'Bruno force', named after Bruno Buchberger, who found the Gröbner base. In the method, the objective functions combining the symbolic computation techniques are formulated. First, the authors utilise a symbolic computation technique, differential elimination, which symbolically reduces an equivalent system of differential equations to a system in a given model. Second, since its equivalent system is frequently composed of large equations, the system is further simplified by another symbolic computation. The performance of the authors' method for parameter accuracy improvement is illustrated by two representative models in biology, a simple cascade model and a negative feedback model in comparison with the previous numerical methods. Finally, the limits and extensions of the authors' method are discussed, in terms of the possible power of 'Bruno force' for the development of a new horizon in parameter estimation.

Impact of mechanism vibration characteristics by joint clearance and optimization design of its multi-objective robustness

NASA Astrophysics Data System (ADS)

Zeng, Baoping; Wang, Chao; Zhang, Yu; Gong, Yajun; Hu, Sanbao

2017-12-01

Joint clearances and friction characteristics significantly influence the mechanism vibration characteristics; for example: as for joint clearances, the shaft and bearing of its clearance joint collide to bring about the dynamic normal contact force and tangential coulomb friction force while the mechanism works; thus, the whole system may vibrate; moreover, the mechanism is under contact-impact with impact force constraint from free movement under action of the above dynamic forces; in addition, the mechanism topology structure also changes. The constraint relationship between joints may be established by a repeated complex nonlinear dynamic process (idle stroke - contact-impact - elastic compression - rebound - impact relief - idle stroke movement - contact-impact). Analysis of vibration characteristics of joint parts is still a challenging open task by far. The dynamic equations for any mechanism with clearance is often a set of strong coupling, high-dimensional and complex time-varying nonlinear differential equations which are solved very difficultly. Moreover, complicated chaotic motions very sensitive to initial values in impact and vibration due to clearance let high-precision simulation and prediction of their dynamic behaviors be more difficult; on the other hand, their subsequent wearing necessarily leads to some certain fluctuation of structure clearance parameters, which acts as one primary factor for vibration of the mechanical system. A dynamic model was established to the device for opening the deepwater robot cabin door with joint clearance by utilizing the finite element method and analysis was carried out to its vibration characteristics in this study. Moreover, its response model was carried out by utilizing the DOE method and then the robust optimization design was performed to sizes of the joint clearance and the friction coefficient change range so that the optimization design results may be regarded as reference data for selecting bearings and controlling manufacturing process parameters for the opening mechanism. Several optimization objectives such as x/y/z accelerations for various measuring points and dynamic reaction forces of mounting brackets, and a few constraints including manufacturing process were taken into account in the optimization models, which were solved by utilizing the multi-objective genetic algorithm (NSGA-II). The vibration characteristics of the optimized opening mechanism are superior to those of the original design. In addition, the numerical forecast results are in good agreement with the test results of the prototype.

Modeling, Control and Simulation of Three-Dimensional Robotic Systems with Applications to Biped Locomotion.

NASA Astrophysics Data System (ADS)

Zheng, Yuan-Fang

A three-dimensional, five link biped system is established. Newton-Euler state space formulation is employed to derive the equations of the system. The constraint forces involved in the equations can be eliminated by projection onto a smaller state space system for deriving advanced control laws. A model-referenced adaptive control scheme is developed to control the system. Digital computer simulations of point to point movement are carried out to show that the model-referenced adaptive control increases the dynamic range and speeds up the response of the system in comparison with linear and nonlinear feedback control. Further, the implementation of the controller is simpler. Impact effects of biped contact with the environment are modeled and studied. The instant velocity change at the moment of impact is derived as a function of the biped state and contact speed. The effects of impact on the state, as well as constraints are studied in biped landing on heels and toes simultaneously or on toes first. Rate and nonlinear position feedback are employed for stability of the biped after the impact. The complex structure of the foot is properly modeled. A spring and dashpot pair is suggested to represent the action of plantar fascia during the impact. This action prevents the arch of the foot from collapsing. A mathematical model of the skeletal muscle is discussed. A direct relationship between the stimulus rate and the active state is established. A piecewise linear relation between the length of the contractile element and the isometric force is considered. Hill's characteristic equation is maintained for determining the actual output force during different shortening velocities. A physical threshold model is proposed for recruitment which encompasses the size principle, its manifestations and exceptions to the size principle. Finally the role of spindle feedback in stability of the model is demonstrated by study of a pair of muscles.

Low-thrust trajectory optimization in a full ephemeris model

NASA Astrophysics Data System (ADS)

Cai, Xing-Shan; Chen, Yang; Li, Jun-Feng

2014-10-01

The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft's own electric propulsion only, and the gravity assist (GA) is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body's gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.

Maggi's equations of motion and the determination of constraint reactions

NASA Astrophysics Data System (ADS)

Papastavridis, John G.

1990-04-01

This paper presents a geometrical derivation of the constraint reaction-free equations of Maggi for mechanical systems subject to linear (first-order) nonholonomic and/or holonomic constraints. These results follow directly from the proper application of the concepts of virtual displacement and quasi-coordinates to the variational equation of motion, i.e., Lagrange's principle. The method also makes clear how to compute the constraint reactions (kinetostatics) without introducing Lagrangian multipliers.

Motions, efforts and actuations in constrained dynamic systems: a multi-link open-chain example

NASA Astrophysics Data System (ADS)

Duke Perreira, N.

1999-08-01

The effort-motion method, which describes the dynamics of open- and closed-chain topologies of rigid bodies interconnected with revolute and prismatic pairs, is interpreted geometrically. Systems are identified for which the simultaneous control of forces and velocities is desirable, and a representative open-chain system is selected for use in the ensuing analysis. Gauge invariant transformations are used to recast the commonly used kinetic and kinematic equations into a dimensional gauge invariant form. Constraint elimination techniques based on singular value decompositions then recast the invariant equations into orthogonal and reciprocal sets of motion and effort equations written in state variable form. The ideal actuation is found that simultaneously achieves the obtainable portions of the desired constraining efforts and motions. The performance is then evaluated of using the actuation closest to the ideal actuation.

The effects of Poynting-Robertson drag on solar sails

NASA Astrophysics Data System (ADS)

Abd El-Salam, F. A.

2018-06-01

In the present work, the concept of solar sailing and its developing spacecraft are presented. The effects of Poynting-Robertson drag on solar sails are considered. Some analytical control laws with some mentioned input constraints for optimizing solar sails dynamics in heliocentric orbit using Lagrange's planetary equations are obtained. Optimum force vector in a required direction is maximized by deriving optimal sail cone angle. New control laws that maximize thrust to obtain certain required maximization in some particular orbital element are obtained.

Calibration and Validation of the Sage Software Cost/Schedule Estimating System to United States Air Force Databases

DTIC Science & Technology

1997-09-01

factor values are identified. For SASET, revised cost estimating relationships are provided ( Apgar et al., 1991). A 1991 AFIT thesis by Gerald Ourada...description of the model is a paragraph directly quoted from the user’s manual . This is not to imply that a lack of a thorough analysis indicates...constraints imposed by the system. The effective technology rating is computed from the basic technology rating by the following equation ( Apgar et al., 1991

Solitonic properties for a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Qu, Qi-Xing; Zhen, Hui-Ling; Chai, Han-Peng

2018-07-01

In this paper, investigation is given to a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon. Based on the Lax pair, under certain variable-coefficient-dependent constraints, we present an infinite sequence of the conservation laws. Through the Riccati equations obtained from the Lax pair, a Wahlquist-Estabrook-type Bäcklund transformation (BT) is derived, based on which the nonlinear superposition formula as well as one- and two-soliton-like solutions are obtained. Via the truncated Painlevé expansion, we give a Painlevé BT, along with the one-soliton-like solutions. With the Painlevé BT, bilinear forms are constructed, and we get a bilinear BT as well as the corresponding one-soliton-like solutions. Bell-type bright and dark soliton-like waves and kink-type soliton-like waves are observed, respectively. Graphic analysis shows that (1) the velocities of the soliton-like waves are related to h(t), d(t), f(t) and R(t), while the soliton-like wave amplitudes just depend on f(t), and (2) with the nonzero f(t) and R(t), soliton-like waves propagate on the varying backgrounds, where h(t), d(t) and f(t) are the dispersive, dissipative and line-damping coefficients, respectively, R(t) is the external-force term, and t is the scaled time coordinate.

Hybrid position/force control of multi-arm cooperating robots

NASA Technical Reports Server (NTRS)

Hayati, Samad

1986-01-01

This paper extends the theory of hybrid position/force control to the case of multi-arm cooperating robots. Cooperation between n robot arms is achieved by controlling each arm such that the burden of actuation is shared between the arms in a nonconflicting way as they control the position of and force on a designated point on an object. The object, which may or may not be in contact with a rigid environment, is assumed to be held rigidly by n robot end-effectors. Natural and artificial position and force constraints are defined for a point on the object and two selection matrices are obtained to control the arms. The position control loops are designed based on each manipulator's Cartesian space dynamic equations. In the position control subspace, a feature is provided which allows the robot arms to exert additional forces/torques to achieve compression, tension, or torsion in the object without affecting the execution of the motion trajectories. In the force control subspace, a method is introduced to minimize the total force/torque magnitude square while realizing the net desired force/torque on the environment.

Learning to push and learning to move: the adaptive control of contact forces

PubMed Central

Casadio, Maura; Pressman, Assaf; Mussa-Ivaldi, Ferdinando A.

2015-01-01

To be successful at manipulating objects one needs to apply simultaneously well controlled movements and contact forces. We present a computational theory of how the brain may successfully generate a vast spectrum of interactive behaviors by combining two independent processes. One process is competent to control movements in free space and the other is competent to control contact forces against rigid constraints. Free space and rigid constraints are singularities at the boundaries of a continuum of mechanical impedance. Within this continuum, forces and motions occur in “compatible pairs” connected by the equations of Newtonian dynamics. The force applied to an object determines its motion. Conversely, inverse dynamics determine a unique force trajectory from a movement trajectory. In this perspective, we describe motor learning as a process leading to the discovery of compatible force/motion pairs. The learned compatible pairs constitute a local representation of the environment's mechanics. Experiments on force field adaptation have already provided us with evidence that the brain is able to predict and compensate the forces encountered when one is attempting to generate a motion. Here, we tested the theory in the dual case, i.e., when one attempts at applying a desired contact force against a simulated rigid surface. If the surface becomes unexpectedly compliant, the contact point moves as a function of the applied force and this causes the applied force to deviate from its desired value. We found that, through repeated attempts at generating the desired contact force, subjects discovered the unique compatible hand motion. When, after learning, the rigid contact was unexpectedly restored, subjects displayed after effects of learning, consistent with the concurrent operation of a motion control system and a force control system. Together, theory and experiment support a new and broader view of modularity in the coordinated control of forces and motions. PMID:26594163

Vainshtein mechanism after GW170817

NASA Astrophysics Data System (ADS)

Crisostomi, Marco; Koyama, Kazuya

2018-01-01

The almost simultaneous detection of gravitational waves and a short gamma-ray burst from a neutron star merger has put a tight constraint on the difference between the speed of gravity and light. In the four-dimensional scalar-tensor theory with second-order equations of motion, the Horndeski theory, this translates into a significant reduction of the viable parameter space of the theory. Recently, extensions of Horndeski theory, which are free from Ostrogradsky ghosts despite the presence of higher-order derivatives in the equations of motion, have been identified and classified exploiting the degeneracy criterium. In these new theories, the fifth force mediated by the scalar field must be suppressed in order to evade the stringent Solar System constraints. We study the Vainshtein mechanism in the most general degenerate higher-order scalar-tensor theory in which light and gravity propagate at the same speed. We find that the Vainshtein mechanism generally works outside a matter source but it is broken inside matter, similarly to beyond Horndeski theories. This leaves interesting possibilities to test these theories that are compatible with gravitational wave observations using astrophysical objects.

Radial vorticity constraint in core flow modeling

NASA Astrophysics Data System (ADS)

Asari, S.; Lesur, V.

2011-11-01

We present a new method for estimating core surface flows by relaxing the tangentially geostrophic (TG) constraint. Ageostrophic flows are allowed if they are consistent with the radial component of the vorticity equation under assumptions of the magnetostrophic force balance and an insulating mantle. We thus derive a tangentially magnetostrophic (TM) constraint for flows in the spherical harmonic domain and implement it in a least squares inversion of GRIMM-2, a recently proposed core field model, for temporally continuous core flow models (2000.0-2010.0). Comparing the flows calculated using the TG and TM constraints, we show that the number of degrees of freedom for the poloidal flows is notably increased by admitting ageostrophic flows compatible with the TM constraint. We find a significantly improved fit to the GRIMM-2 secular variation (SV) by including zonal poloidal flow in TM flow models. Correlations between the predicted and observed length-of-day variations are equally good under the TG and TM constraints. In addition, we estimate flow models by imposing the TM constraint together with other dynamical constraints: either purely toroidal (PT) flow or helical flow constraint. For the PT case we cannot find any flow which explains the observed SV, while for the helical case the SV can be fitted. The poor compatibility between the TM and PT constraints seems to arise from the absence of zonal poloidal flows. The PT flow assumption is likely to be negated when the radial magnetostrophic vorticity balance is taken into account, even if otherwise consistent with magnetic observations.

Methodologies to determine forces on bones and muscles of body segments during exercise, employing compact sensors suitable for use in crowded space vehicles

NASA Technical Reports Server (NTRS)

Figueroa, Fernando

1995-01-01

Work under this grant was carried out by the author and by a graduate research assistant. An instrumented bicycle ergometer was implemented focusing on the stated objective: to estimate the forces exerted by each muscle of the feet, calf, and thigh of an individual while bicycling. The sensors used were light and compact. These were probes to measure muscle EMG activity, miniature accelerometers, miniature load sensors, and small encoders to measure angular positions of the pedal. A methodology was developed and implemented to completely describe the kinematics of the limbs using data from the sensors. This work has been published as a Master's Thesis by the Graduate student supported by the grant. The instrumented ergometer along with the sensors and instrumentation were tested during a KC-135 Zero-Gravity flight in July, 1994. A complete description of the system and the tests performed have been published as a report submitted to NASA Johnson Space Center. The data collected during the KC-135 flight is currently being processed so that a kinematic description of the bicycling experiment will be soon determined. A methodology to estimate the muscle forces has been formulated based on previous work. The methodology involves the use of optimization concepts so that the individual muscle forces that represent variables in dynamic equations of motion may be estimated. Optimization of a criteria (goal) function such as minimization of energy will be used along with constraint equations defined by rigid body equations of motion. Use of optimization principles is necessary, because the equations of motion alone constitute an indeterminate system of equations with respect to the large amount of muscle forces which constitute the variables in these equations. The number of variables is reduced somewhat by using forces measured by the load cells installed on the pedal. These load cells measure pressure and shear forces on the foot. The author and his collaborators at NASA and at the University of Alabama, Tuscaloosa, are continuing the work of reducing the experimental data from the KC-135 flight, and the implementation of the optimization methods to estimate muscle forces. As soon as results from these efforts are available, they will be published in reputable journals. Results of this work will impact studies addressing bone density loss and development of countermeasures to minimize bone loss in zero gravity conditions. By analyzing muscle forces on Earth and in Space during exercise, scientists could eventually formulate new exercises and machines to help maintain bone density. On Earth, this work will impact studies concerning arthritis, and will provide the means to study possible exercise countermeasures to minimize arthritis problems.

On the theory of the relativistic motion of a charged particle in the field of intense electromagnetic radiation

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

Milant'ev, V. P., E-mail: vmilantiev@sci.pfu.edu.ru; Castillo, A. J., E-mail: vmilant@mail.ru

2013-04-15

Averaged relativistic equations of motion of a charged particle in the field of intense electromagnetic radiation have been obtained in the geometrical optics approximation using the Bogoliubov method. Constraints are determined under which these equations are valid. Oscillating additions to the smoothed dynamical variables of the particle have been found; they are reduced to known expressions in the case of the circularly and linearly polarized plane waves. It has been shown that the expressions for the averaged relativistic force in both cases contain new additional small terms weakening its action. The known difference between the expressions for the ponderomotive forcemore » in the cases of circularly and linearly polarized waves has been confirmed.« less

Strong-field gravitational-wave emission in Schwarzschild and Kerr geometries: some general considerations

NASA Astrophysics Data System (ADS)

Rodríguez, J. F.; Rueda, J. A.; Ruffini, R.

2018-01-01

We have used the perturbations of the exact solutions of the Einstein equations to estimate the relativistic wave emission of a test particle orbiting around a black hole. We show how the hamiltonian equations of motion of a test particle augmented with the radiation-reaction force can establish a priori constraints on the possible phenomena occurring in the merger of compact objects. The dynamical evolution consists of a helicoidal sequence of quasi-circular orbits, induced by the radiation-reaction and the background spacetime. Near the innermost stable circular orbit the evolution is followed by a smooth transition and finally plunges geodesically into the black hole horizon. This analysis gives physical insight of the merger of two equal masses objects.

Actuation for simultaneous motions and constraining efforts: an open chain example

NASA Astrophysics Data System (ADS)

Perreira, N. Duke

1997-06-01

A brief discussion on systems where simultaneous control of forces and velocities are desirable is given and an example linkage with revolute and prismatic joint is selected for further analysis. The Newton-Euler approach for dynamic system analysis is applied to the example to provide a basis of comparison. Gauge invariant transformations are used to convert the dynamic equations into invariant form suitable for use in a new dynamic system analysis method known as the motion-effort approach. This approach uses constraint elimination techniques based on singular value decompositions to recast the invariant form of dynamic system equations into orthogonal sets of motion and effort equations. Desired motions and constraining efforts are partitioned into ideally obtainable and unobtainable portions which are then used to determine the required actuation. The method is applied to the example system and an analytic estimate to its success is made.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

The free energy of a reaction coordinate at multiple constraints: a concise formulation

NASA Astrophysics Data System (ADS)

Schlitter, Jürgen; Klähn, Marco

The free energy as a function of the reaction coordinate (rc) is the key quantity for the computation of equilibrium and kinetic quantities. When it is considered as the potential of mean force, the problem is the calculation of the mean force for given values of the rc. We reinvestigate the PMCF (potential of mean constraint force) method which applies a constraint to the rc to compute the mean force as the mean negative constraint force and a metric tensor correction. The latter allows for the constraint imposed to the rc and possible artefacts due to multiple constraints of other variables which for practical reasons are often used in numerical simulations. Two main results are obtained that are of theoretical and practical interest. First, the correction term is given a very concise and simple shape which facilitates its interpretation and evaluation. Secondly, a theorem describes various rcs and possible combinations with constraints that can be used without introducing any correction to the constraint force. The results facilitate the computation of free energy by molecular dynamics simulations.

Order Reduction, Projectability and Constraints of Second-Order Field Theories and Higher-Order Mechanics

NASA Astrophysics Data System (ADS)

Gaset, Jordi; Román-Roy, Narciso

2016-12-01

The projectability of Poincaré-Cartan forms in a third-order jet bundle J3π onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint algorithm for the associated Euler-Lagrange equations in J3π. The results are applied to study the Hilbert Lagrangian for the Einstein equations (in vacuum) from a multisymplectic point of view. Thus we show how these equations are a consequence of the application of the constraint algorithm to the geometric field equations, meanwhile the other constraints are related with the fact that this second-order theory is equivalent to a first-order theory. Furthermore, the case of higher-order mechanics is also studied as a particular situation.

Constraints on neutron star radii based on chiral effective field theory interactions.

PubMed

Hebeler, K; Lattimer, J M; Pethick, C J; Schwenk, A

2010-10-15

We show that microscopic calculations based on chiral effective field theory interactions constrain the properties of neutron-rich matter below nuclear densities to a much higher degree than is reflected in commonly used equations of state. Combined with observed neutron star masses, our results lead to a radius R=9.7-13.9  km for a 1.4M⊙ star, where the theoretical range is due, in about equal amounts, to uncertainties in many-body forces and to the extrapolation to high densities.

A validated computational model for the design of surface textures in full-film lubricated sliding

NASA Astrophysics Data System (ADS)

Schuh, Jonathon; Lee, Yong Hoon; Allison, James; Ewoldt, Randy

2016-11-01

Our recent experimental work showed that asymmetry is needed for surface textures to decrease friction in full-film lubricated sliding (thrust bearings) with Newtonian fluids; textures reduce the shear load and produce a separating normal force. The sign of the separating normal force is not predicted by previous 1-D theories. Here we model the flow with the Reynolds equation in cylindrical coordinates, numerically implemented with a pseudo-spectral method. The model predictions match experiments, rationalize the sign of the normal force, and allow for design of surface texture geometry. To minimize sliding friction with angled cylindrical textures, an optimal angle of asymmetry β exists. The optimal angle depends on the film thickness but not the sliding velocity within the applicable range of the model. The model has also been used to optimize generalized surface texture topography while satisfying manufacturability constraints.

A variational approach to dynamics of flexible multibody systems

NASA Technical Reports Server (NTRS)

Wu, Shih-Chin; Haug, Edward J.; Kim, Sung-Soo

1989-01-01

This paper presents a variational formulation of constrained dynamics of flexible multibody systems, using a vector-variational calculus approach. Body reference frames are used to define global position and orientation of individual bodies in the system, located and oriented by position of its origin and Euler parameters, respectively. Small strain linear elastic deformation of individual components, relative to their body references frames, is defined by linear combinations of deformation modes that are induced by constraint reaction forces and normal modes of vibration. A library of kinematic couplings between flexible and/or rigid bodies is defined and analyzed. Variational equations of motion for multibody systems are obtained and reduced to mixed differential-algebraic equations of motion. A space structure that must deform during deployment is analyzed, to illustrate use of the methods developed.

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

NASA Astrophysics Data System (ADS)

Liska, Sebastian; Colonius, Tim

2017-02-01

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.

A study of snake-like locomotion through the analysis of a flexible robot model

PubMed Central

Cicconofri, Giancarlo; DeSimone, Antonio

2015-01-01

We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment. PMID:26807040

Equatorial superrotation in a thermally driven zonally symmetric circulation

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.

1981-01-01

Near the equator where the Coriolis force vanishes, the momentum balance for the axially symmetric circulation is established between horizontal and vertical diffusion, which, a priori, does not impose constraints on the direction or magnitude of the zonal winds. Solar radiation absorbed at low latitudes is a major force in driving large scale motions with air rising near the equator and falling at higher latitudes. In the upper leg of the meridional cell, angular momentum is redistributed so that the atmosphere tends to subrotate (or corotate) at low latitudes and superrotate at high latitudes. In the lower leg, however, the process is reversed and produces a tendency for the equatorial region to superrotate. The outcome depends on the energy budget which is closely coupled to the momentum budget through the thermal wind equation; a pressure (temperature) maximum is required to sustain equatorial superrotation. Such a condition arises in regions which are convectively unstable and the temperature lapse rate is superadiabatic. It should arise in the tropospheres of Jupiter and Saturn; planetary energy from the interior is carried to higher altitudes where radiation to space becomes important. Upward equatorial motions in the direct and indirect circulations (Ferrel-Thomson type) imposed by insolation can then trap dynamic energy for equatorial heating which can sustain the superrotation of the equatorial region.

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1987-01-01

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

An Optimization-based Atomistic-to-Continuum Coupling Method

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

Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell

2014-08-21

In this paper, we present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the latter as a constrained optimization problem with virtual Dirichlet controls on the interfaces between the atomistic and continuum subdomains. The optimization objective is to minimize the error between the atomistic and continuum solutions on the overlap between the two subdomains, while the atomistic and continuum force balance equations provide the constraints. Separation, rather then blending of the atomistic and continuum problems, and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. Finally,more » we present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body potential with next-nearest neighbor interactions.« less

The motion of interconnected flexible bodies

NASA Technical Reports Server (NTRS)

Hopkins, A. S.

1975-01-01

The equations of motion for an arbitrarily interconnected collection of substructures are derived. The substructures are elastic bodies which may be idealized as finite element assemblies and are subject to small deformations relative to a nominal state. Interconnections between the elastic substructures permit large relative translations and rotations between substructures, governed by Pfaffian constraints describing the connections. Screw connections (permitting rotation about and translation along a single axis) eliminate constraint forces and incorporate modal coupling. The problem of flexible spacecraft simulation is discussed. Hurty's component mode approach is extended by permitting interconnected elastic substructures large motions relative to each other and relative to inertial space. The hybrid coordinate methods are generalized by permitting all substructures to be flexible (rather than only the terminal members of a topological tree of substructures). The basic relationships of continuum mechanics are developed.

Modeling and vibration control of the flapping-wing robotic aircraft with output constraint

NASA Astrophysics Data System (ADS)

He, Wei; Mu, Xinxing; Chen, Yunan; He, Xiuyu; Yu, Yao

2018-06-01

In this paper, we propose the boundary control for undesired vibrations suppression with output constraint of the flapping-wing robotic aircraft (FWRA). We also present the dynamics of the flexible wing of FWRA with governing equations and boundary conditions, which are partial differential equations (PDEs) and ordinary differential equations (ODEs), respectively. An energy-based barrier Lyapunov function is introduced to analyze the system stability and prevent violation of output constraint. With the effect of the proposed boundary controller, distributed states of the system remain in the constrained spaces. Then the IBLF-based boundary controls are proposed to assess the stability of the FWRA in the presence of output constraint.

Optimal design of high damping force engine mount featuring MR valve structure with both annular and radial flow paths

NASA Astrophysics Data System (ADS)

Nguyen, Q. H.; Choi, S. B.; Lee, Y. S.; Han, M. S.

2013-11-01

This paper focuses on the optimal design of a compact and high damping force engine mount featuring magnetorheological fluid (MRF). In the mount, a MR valve structure with both annular and radial flows is employed to generate a high damping force. First, the configuration and working principle of the proposed MR mount is introduced. The MRF flows in the mount are then analyzed and the governing equations of the MR mount are derived based on the Bingham plastic behavior of the MRF. An optimal design of the MR mount is then performed to find the optimal structure of the MR valve to generate a maximum damping force with certain design constraints. In addition, the gap size of MRF ducts is empirically chosen considering the ‘lockup’ problem of the mount at high frequency. Performance of the optimized MR mount is then evaluated based on finite element analysis and discussions on performance results of the optimized MR mount are given. The effectiveness of the proposed MR engine mount is demonstrated via computer simulation by presenting damping force and power consumption.

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

PubMed

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

PubMed Central

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605

The momentum constraints on the shallow meridional circulation associated with the marine ITCZ

NASA Astrophysics Data System (ADS)

Dixit, Vishal; Srinivasan, J.

2017-12-01

Recent studies have shown that the shallow meridional circulation (SMC) coexists with the deep circulation in the marine ITCZ. The SMC has been assumed to be forced by strong meridional gradients of Sea Surface Temperature (SST) which affect the atmosphere under hydrostatic balance. In this paper, we present a new viewpoint that the shallow meridional circulation is a part of circulation that forms when the marine ITCZ is located away from the equator. To support this view, we have used reanalysis data over east Pacific ocean to show that the shallow meridional circulation is absent when the ITCZ is located near the equator while it is strong to the south of the ITCZ when the ITCZ is located away from the equator. To further support this view, we have conducted idealized aquaplanet experiments by shifting SST maximum polewards to simulate the observed contrast in the meridional circulation associated with near equatorial and off-equatorial ITCZ. The detailed momentum budget of the flow above the boundary layer shows that, to the south of an off-equatorial ITCZ, the dominant balance between the Coriolis force and the advection of relative vorticity by the mean flow leads to cancellation of the planetary rotational effects. As a result, the net rotational effects experienced by the diverging flow above the boundary layer are negligible and a shallow meridional flow along the pressure gradients is generated. This dominant balance does not occur in the aquaplanet GCM when the ITCZ forms near the equator.

Directional constraint of endpoint force emerges from hindlimb anatomy.

PubMed

Bunderson, Nathan E; McKay, J Lucas; Ting, Lena H; Burkholder, Thomas J

2010-06-15

Postural control requires the coordination of force production at the limb endpoints to apply an appropriate force to the body. Subjected to horizontal plane perturbations, quadruped limbs stereotypically produce force constrained along a line that passes near the center of mass. This phenomenon, referred to as the force constraint strategy, may reflect mechanical constraints on the limb or body, a specific neural control strategy or an interaction among neural controls and mechanical constraints. We used a neuromuscular model of the cat hindlimb to test the hypothesis that the anatomical constraints restrict the mechanical action of individual muscles during stance and constrain the response to perturbations to a line independent of perturbation direction. In a linearized neuromuscular model of the cat hindlimb, muscle lengthening directions were highly conserved across 10,000 different muscle activation patterns, each of which produced an identical, stance-like endpoint force. These lengthening directions were closely aligned with the sagittal plane and reveal an anatomical structure for directionally constrained force responses. Each of the 10,000 activation patterns was predicted to produce stable stance based on Lyapunov stability analysis. In forward simulations of the nonlinear, seven degree of freedom model under the action of 200 random muscle activation patterns, displacement of the endpoint from its equilibrium position produced restoring forces, which were also biased toward the sagittal plane. The single exception was an activation pattern based on minimum muscle stress optimization, which produced destabilizing force responses in some perturbation directions. The sagittal force constraint increased during simulations as the system shifted from an inertial response during the acceleration phase to a viscoelastic response as peak velocity was obtained. These results qualitatively match similar experimental observations and suggest that the force constraint phenomenon may result from the anatomical arrangement of the limb.

Directional constraint of endpoint force emerges from hindlimb anatomy

PubMed Central

Bunderson, Nathan E.; McKay, J. Lucas; Ting, Lena H.; Burkholder, Thomas J.

2010-01-01

Postural control requires the coordination of force production at the limb endpoints to apply an appropriate force to the body. Subjected to horizontal plane perturbations, quadruped limbs stereotypically produce force constrained along a line that passes near the center of mass. This phenomenon, referred to as the force constraint strategy, may reflect mechanical constraints on the limb or body, a specific neural control strategy or an interaction among neural controls and mechanical constraints. We used a neuromuscular model of the cat hindlimb to test the hypothesis that the anatomical constraints restrict the mechanical action of individual muscles during stance and constrain the response to perturbations to a line independent of perturbation direction. In a linearized neuromuscular model of the cat hindlimb, muscle lengthening directions were highly conserved across 10,000 different muscle activation patterns, each of which produced an identical, stance-like endpoint force. These lengthening directions were closely aligned with the sagittal plane and reveal an anatomical structure for directionally constrained force responses. Each of the 10,000 activation patterns was predicted to produce stable stance based on Lyapunov stability analysis. In forward simulations of the nonlinear, seven degree of freedom model under the action of 200 random muscle activation patterns, displacement of the endpoint from its equilibrium position produced restoring forces, which were also biased toward the sagittal plane. The single exception was an activation pattern based on minimum muscle stress optimization, which produced destabilizing force responses in some perturbation directions. The sagittal force constraint increased during simulations as the system shifted from an inertial response during the acceleration phase to a viscoelastic response as peak velocity was obtained. These results qualitatively match similar experimental observations and suggest that the force constraint phenomenon may result from the anatomical arrangement of the limb. PMID:20511528

Finite-difference time-domain synthesis of infrasound propagation through an absorbing atmosphere.

PubMed

de Groot-Hedlin, C

2008-09-01

Equations applicable to finite-difference time-domain (FDTD) computation of infrasound propagation through an absorbing atmosphere are derived and examined in this paper. It is shown that over altitudes up to 160 km, and at frequencies relevant to global infrasound propagation, i.e., 0.02-5 Hz, the acoustic absorption in dB/m varies approximately as the square of the propagation frequency plus a small constant term. A second-order differential equation is presented for an atmosphere modeled as a compressible Newtonian fluid with low shear viscosity, acted on by a small external damping force. It is shown that the solution to this equation represents pressure fluctuations with the attenuation indicated above. Increased dispersion is predicted at altitudes over 100 km at infrasound frequencies. The governing propagation equation is separated into two partial differential equations that are first order in time for FDTD implementation. A numerical analysis of errors inherent to this FDTD method shows that the attenuation term imposes additional stability constraints on the FDTD algorithm. Comparison of FDTD results for models with and without attenuation shows that the predicted transmission losses for the attenuating media agree with those computed from synthesized waveforms.

A simple orbit-attitude coupled modelling method for large solar power satellites

NASA Astrophysics Data System (ADS)

Li, Qingjun; Wang, Bo; Deng, Zichen; Ouyang, Huajiang; Wei, Yi

2018-04-01

A simple modelling method is proposed to study the orbit-attitude coupled dynamics of large solar power satellites based on natural coordinate formulation. The generalized coordinates are composed of Cartesian coordinates of two points and Cartesian components of two unitary vectors instead of Euler angles and angular velocities, which is the reason for its simplicity. Firstly, in order to develop natural coordinate formulation to take gravitational force and gravity gradient torque of a rigid body into account, Taylor series expansion is adopted to approximate the gravitational potential energy. The equations of motion are constructed through constrained Hamilton's equations. Then, an energy- and constraint-conserving algorithm is presented to solve the differential-algebraic equations. Finally, the proposed method is applied to simulate the orbit-attitude coupled dynamics and control of a large solar power satellite considering gravity gradient torque and solar radiation pressure. This method is also applicable to dynamic modelling of other rigid multibody aerospace systems.

A high-fidelity method to analyze perturbation evolution in turbulent flows

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

Unnikrishnan, S., E-mail: sasidharannair.1@osu.edu; Gaitonde, Datta V., E-mail: gaitonde.3@osu.edu

2016-04-01

Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier–Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state,more » its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted “baseline” and “twin”) of simultaneous synchronized Large-Eddy Simulations (LES). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier–Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, “native” forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous terms or turbulence closures. The method is illustrated by application to a well-validated Mach 1.3 jet. Specifically, the effects of turbulence on the jet lipline and core collapse regions on the near-acoustic field are isolated. The properties of the method, including linearity and effect of initial transients, are discussed. The results provide insight into how turbulence from different parts of the jet contribute to the observed dominance of low and high frequency content at shallow and sideline angles, respectively.« less

A high-fidelity method to analyze perturbation evolution in turbulent flows

NASA Astrophysics Data System (ADS)

Unnikrishnan, S.; Gaitonde, Datta V.

2016-04-01

Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier-Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state, its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted "baseline" and "twin") of simultaneous synchronized Large-Eddy Simulations (LES). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier-Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, "native" forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous terms or turbulence closures. The method is illustrated by application to a well-validated Mach 1.3 jet. Specifically, the effects of turbulence on the jet lipline and core collapse regions on the near-acoustic field are isolated. The properties of the method, including linearity and effect of initial transients, are discussed. The results provide insight into how turbulence from different parts of the jet contribute to the observed dominance of low and high frequency content at shallow and sideline angles, respectively.

Analysis of forced convective modified Burgers liquid flow considering Cattaneo-Christov double diffusion

NASA Astrophysics Data System (ADS)

Waqas, M.; Hayat, T.; Shehzad, S. A.; Alsaedi, A.

2018-03-01

A mathematical model is formulated to characterize the non-Fourier and Fick's double diffusive models of heat and mass in moving flow of modified Burger's liquid. Temperature-dependent conductivity of liquid is taken into account. The concept of stratification is utilized to govern the equations of energy and mass species. The idea of boundary layer theory is employed to obtain the mathematical model of considered physical problem. The obtained partial differential system is converted into ordinary ones with the help of relevant variables. The homotopic concept lead to the convergent solutions of governing expressions. Convergence is attained and acceptable values are certified by expressing the so called ℏ -curves and numerical benchmark. Several graphs are made for different values of physical constraints to explore the mechanism of heat and mass transportation. We explored that the liquid temperature and concentration are retard for the larger thermal/concentration relaxation time constraint.

Realization of non-holonomic constraints and singular perturbation theory for plane dumbbells

NASA Astrophysics Data System (ADS)

Koshkin, Sergiy; Jovanovic, Vojin

2017-10-01

We study the dynamics of pairs of connected masses in the plane, when nonholonomic (knife-edge) constraints are realized by forces of viscous friction, in particular its relation to constrained dynamics, and its approximation by the method of matching asymptotics of singular perturbation theory when the mass to friction ratio is taken as the small parameter. It turns out that long term behaviors of the frictional and constrained systems may differ dramatically no matter how small the perturbation is, and when this happens is not determined by any transparent feature of the equations of motion. The choice of effective time scales for matching asymptotics is also subtle and non-obvious, and secular terms appearing in them can not be dealt with by the classical methods. Our analysis is based on comparison to analytic solutions, and we present a reduction procedure for plane dumbbells that leads to them in some cases.

Optimal control problems with mixed control-phase variable equality and inequality constraints

NASA Technical Reports Server (NTRS)

Makowski, K.; Neustad, L. W.

1974-01-01

In this paper, necessary conditions are obtained for optimal control problems containing equality constraints defined in terms of functions of the control and phase variables. The control system is assumed to be characterized by an ordinary differential equation, and more conventional constraints, including phase inequality constraints, are also assumed to be present. Because the first-mentioned equality constraint must be satisfied for all t (the independent variable of the differential equation) belonging to an arbitrary (prescribed) measurable set, this problem gives rise to infinite-dimensional equality constraints. To obtain the necessary conditions, which are in the form of a maximum principle, an implicit-function-type theorem in Banach spaces is derived.

Mitotic cells generate protrusive extracellular forces to divide in three-dimensional microenvironments

NASA Astrophysics Data System (ADS)

Nam, Sungmin; Chaudhuri, Ovijit

2018-06-01

During mitosis, or cell division, mammalian cells undergo extensive morphological changes, including elongation along the mitotic axis, which is perpendicular to the plane that bisects the two divided cells. Although much is known about the intracellular dynamics of mitosis, it is unclear how cells are able to divide in tissues, where the changes required for mitosis are mechanically constrained by surrounding cells and extracellular matrix. Here, by confining cells three dimensionally in hydrogels, we show that dividing cells generate substantial protrusive forces that deform their surroundings along the mitotic axis, clearing space for mitotic elongation. When forces are insufficient to create space for mitotic elongation, mitosis fails. We identify one source of protrusive force as the elongation of the interpolar spindle, an assembly of microtubules aligned with the mitotic axis. Another source of protrusive force is shown to be contraction of the cytokinetic ring, the polymeric structure that cleaves a dividing cell at its equator, which drives expansion along the mitotic axis. These findings reveal key functions for the interpolar spindle and cytokinetic ring in protrusive extracellular force generation, and explain how dividing cells overcome mechanical constraints in confining microenvironments, including some types of tumour.

Optimal actuator location within a morphing wing scissor mechanism configuration

NASA Astrophysics Data System (ADS)

Joo, James J.; Sanders, Brian; Johnson, Terrence; Frecker, Mary I.

2006-03-01

In this paper, the optimal location of a distributed network of actuators within a scissor wing mechanism is investigated. The analysis begins by developing a mechanical understanding of a single cell representation of the mechanism. This cell contains four linkages connected by pin joints, a single actuator, two springs to represent the bidirectional behavior of a flexible skin, and an external load. Equilibrium equations are developed using static analysis and the principle of virtual work equations. An objective function is developed to maximize the efficiency of the unit cell model. It is defined as useful work over input work. There are two constraints imposed on this problem. The first is placed on force transferred from the external source to the actuator. It should be less than the blocked actuator force. The other is to require the ratio of output displacement over input displacement, i.e., geometrical advantage (GA), of the cell to be larger than a prescribed value. Sequential quadratic programming is used to solve the optimization problem. This process suggests a systematic approach to identify an optimum location of an actuator and to avoid the selection of location by trial and error. Preliminary results show that optimum locations of an actuator can be selected out of feasible regions according to the requirements of the problem such as a higher GA, a higher efficiency, or a smaller transferred force from external force. Results include analysis of single and multiple cell wing structures and some experimental comparisons.

L{sup {infinity}} Variational Problems with Running Costs and Constraints

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

Aronsson, G., E-mail: gunnar.aronsson@liu.se; Barron, E. N., E-mail: enbarron@math.luc.edu

2012-02-15

Various approaches are used to derive the Aronsson-Euler equations for L{sup {infinity}} calculus of variations problems with constraints. The problems considered involve holonomic, nonholonomic, isoperimetric, and isosupremic constraints on the minimizer. In addition, we derive the Aronsson-Euler equation for the basic L{sup {infinity}} problem with a running cost and then consider properties of an absolute minimizer. Many open problems are introduced for further study.

Solution of the Skyrme-Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VIII) HFODD (v2.73y): A new version of the program

DOE PAGES

Schunck, N.; Dobaczewski, J.; Satuła, W.; ...

2017-03-27

Here, we describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree–Fock or Skyrme Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton–neutron mixing in the particle–hole channel for Skyrme functionals, (ii) the Gogny force in both particle–hole and particle–particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy ofmore » each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.« less

Solution of the Skyrme-Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VIII) HFODD (v2.73y): A new version of the program

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

Schunck, N.; Dobaczewski, J.; Satuła, W.

Here, we describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree–Fock or Skyrme Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton–neutron mixing in the particle–hole channel for Skyrme functionals, (ii) the Gogny force in both particle–hole and particle–particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy ofmore » each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.« less

Constraint Embedding Technique for Multibody System Dynamics

NASA Technical Reports Server (NTRS)

Woo, Simon S.; Cheng, Michael K.

2011-01-01

Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with closure-constraints into an equivalent tree-topology system, and thus allows one to take advantage of the host of techniques available to the latter class of systems. This technology is highly suitable for the class of multibody systems where the closure-constraints are local, i.e., where they are confined to small groupings of bodies within the system. Important examples of such local closure-constraints are constraints associated with four-bar linkages, geared motors, differential suspensions, etc. One can eliminate these closure-constraints and convert the system into a tree-topology system by embedding the constraints directly into the system dynamics and effectively replacing the body groupings with virtual aggregate bodies. Once eliminated, one can apply the well-known results and algorithms for tree-topology systems to solve the dynamics of such closed-chain system.

Rapid sampling of stochastic displacements in Brownian dynamics simulations with stresslet constraints.

PubMed

Fiore, Andrew M; Swan, James W

2018-01-28

Brownian Dynamics simulations are an important tool for modeling the dynamics of soft matter. However, accurate and rapid computations of the hydrodynamic interactions between suspended, microscopic components in a soft material are a significant computational challenge. Here, we present a new method for Brownian dynamics simulations of suspended colloidal scale particles such as colloids, polymers, surfactants, and proteins subject to a particular and important class of hydrodynamic constraints. The total computational cost of the algorithm is practically linear with the number of particles modeled and can be further optimized when the characteristic mass fractal dimension of the suspended particles is known. Specifically, we consider the so-called "stresslet" constraint for which suspended particles resist local deformation. This acts to produce a symmetric force dipole in the fluid and imparts rigidity to the particles. The presented method is an extension of the recently reported positively split formulation for Ewald summation of the Rotne-Prager-Yamakawa mobility tensor to higher order terms in the hydrodynamic scattering series accounting for force dipoles [A. M. Fiore et al., J. Chem. Phys. 146(12), 124116 (2017)]. The hydrodynamic mobility tensor, which is proportional to the covariance of particle Brownian displacements, is constructed as an Ewald sum in a novel way which guarantees that the real-space and wave-space contributions to the sum are independently symmetric and positive-definite for all possible particle configurations. This property of the Ewald sum is leveraged to rapidly sample the Brownian displacements from a superposition of statistically independent processes with the wave-space and real-space contributions as respective covariances. The cost of computing the Brownian displacements in this way is comparable to the cost of computing the deterministic displacements. The addition of a stresslet constraint to the over-damped particle equations of motion leads to a stochastic differential algebraic equation (SDAE) of index 1, which is integrated forward in time using a mid-point integration scheme that implicitly produces stochastic displacements consistent with the fluctuation-dissipation theorem for the constrained system. Calculations for hard sphere dispersions are illustrated and used to explore the performance of the algorithm. An open source, high-performance implementation on graphics processing units capable of dynamic simulations of millions of particles and integrated with the software package HOOMD-blue is used for benchmarking and made freely available in the supplementary material.

Time dependent response of low velocity impact induced composite conical shells under multiple delamination

NASA Astrophysics Data System (ADS)

Dey, Sudip; Karmakar, Amit

2014-02-01

This paper presents the time dependent response of multiple delaminated angle-ply composite pretwisted conical shells subjected to low velocity normal impact. The finite element formulation is based on Mindlin's theory incorporating rotary inertia and effects of transverse shear deformation. An eight-noded isoparametric plate bending element is employed to satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. A multipoint constraint algorithm is incorporated which leads to asymmetric stiffness matrices. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the contact force, and the time dependent equations are solved by Newmark's time integration algorithm. Parametric studies are conducted with respect to triggering parameters like laminate configuration, location of delamination, angle of twist, velocity of impactor, and impactor's displacement for centrally impacted shells.

Coupled pendula chains under parametric PT-symmetric driving force

NASA Astrophysics Data System (ADS)

Destyl, E.; Nuiro, S. P.; Pelinovsky, D. E.; Poullet, P.

2017-12-01

We consider a chain of coupled pendula pairs, where each pendulum is connected to the nearest neighbors in the longitudinal and transverse directions. The common strings in each pair are modulated periodically by an external force. In the limit of small coupling and near the 1 : 2 parametric resonance, we derive a novel system of coupled PT-symmetric discrete nonlinear Schrödinger equations, which has Hamiltonian symmetry but has no phase invariance. By using the conserved energy, we find the parameter range for the linear and nonlinear stability of the zero equilibrium. Numerical experiments illustrate how destabilization of the zero equilibrium takes place when the stability constraints are not satisfied. The central pendulum excites nearest pendula and this process continues until a dynamical equilibrium is reached where each pendulum in the chain oscillates at a finite amplitude.

How the 2SLS/IV estimator can handle equality constraints in structural equation models: a system-of-equations approach.

PubMed

Nestler, Steffen

2014-05-01

Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non-iterative, equation-by-equation estimator that uses instrumental variables. Although this two-stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models. © 2013 The British Psychological Society.

Open groups of constraints. Integrating arbitrary involutions

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

1998-11-01

A new type of quantum master equation is presented which is expressed in terms of a recently introduced quantum antibracket. The equation involves only two operators: an extended nilpotent BFV-BRST charge and an extended ghost charge. It is proposed to determine the generalized quantum Maurer-Cartan equations for arbitrary open groups. These groups are the integration of constraints in arbitrary involutions. The only condition for this is that the constraint operators may be embedded in an odd nilpotent operator, the BFV-BRST charge. The proposal is verified at the quasigroup level. The integration formulas are also used to construct a generating operator for quantum antibrackets of operators in arbitrary involutions.

Characteristics of manipulator for industrial robot with three rotational pairs having parallel axes

NASA Astrophysics Data System (ADS)

Poteyev, M. I.

1986-01-01

The dynamics of a manipulator with three rotatinal kinematic pairs having parallel axes are analyzed, for application in an industrial robot. The system of Lagrange equations of the second kind, describing the motion of such a mechanism in terms of kinetic energy in generalized coordinates, is reduced to equations of motion in terms of Newton's laws. These are useful not only for either determining the moments of force couples which will produce a prescribed motion or, conversely determining the motion which given force couples will produce but also for solving optimization problems under constraints in both cases and for estimating dynamic errors. As a specific example, a manipulator with all three axes of vertical rotation is considered. The performance of this manipulator, namely the parameters of its motion as functions of time, is compared with that of a manipulator having one rotational and two translational kinematic pairs. Computer aided simulation of their motion on the basis of ideal models, with all three links represented by identical homogeneous bars, has yielded velocity time diagrams which indicate that the manipulator with three rotational pairs is 4.5 times faster.

Boundedness of the mixed velocity-temperature derivative skewness in homogeneous isotropic turbulence

NASA Astrophysics Data System (ADS)

Tang, S. L.; Antonia, R. A.; Djenidi, L.; Danaila, L.; Zhou, Y.

2016-09-01

The transport equation for the mean scalar dissipation rate ɛ ¯ θ is derived by applying the limit at small separations to the generalized form of Yaglom's equation in two types of flows, those dominated mainly by a decay of energy in the streamwise direction and those which are forced, through a continuous injection of energy at large scales. In grid turbulence, the imbalance between the production of ɛ ¯ θ due to stretching of the temperature field and the destruction of ɛ ¯ θ by the thermal diffusivity is governed by the streamwise advection of ɛ ¯ θ by the mean velocity. This imbalance is intrinsically different from that in stationary forced periodic box turbulence (or SFPBT), which is virtually negligible. In essence, the different types of imbalance represent different constraints imposed by the large-scale motion on the relation between the so-called mixed velocity-temperature derivative skewness ST and the scalar enstrophy destruction coefficient Gθ in different flows, thus resulting in non-universal approaches of ST towards a constant value as Reλ increases. The data for ST collected in grid turbulence and in SFPBT indicate that the magnitude of ST is bounded, this limit being close to 0.5.

Solitons for a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Xie, Xi-Yang; Chai, Han-Peng

2016-12-01

Investigation is given to a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon. Applying the double-logarithmic and rational transformations, respectively, under certain variable-coefficient constraints, we get two different types of bilinear forms: (a) Based on the first type, the bilinear Bäcklund transformation (BT) is derived, the N-soliton solutions in the Wronskian form are constructed, and the (N - 1)- and N-soliton solutions are proved to satisfy the bilinear BT; (b) Based on the second type, via the Hirota method, the one- and two-soliton solutions are obtained. Those two types of solutions are different. Graphic analysis on the two types shows that the soliton velocity depends on d(t), h(t), f(t) and R(t), the soliton amplitude is merely related to f(t), and the background depends on R(t) and f(t), where d(t), h(t), q(t) and f(t) are the dissipative, dispersive, nonuniform and line-damping coefficients, respectively, and R(t) is the external-force term. We present some types of interactions between the two solitons, including the head-on and overtaking interactions, interactions between the velocity- and amplitude-unvarying two solitons, between the velocity-varying while amplitude-unvarying two solitons and between the velocity- and amplitude-varying two solitons, as well as the interactions occurring on the constant and varying backgrounds.

Effect of anharmonicity on the phonon density of states and specific heat of a monoatomic, one-dimensional crystal lattice

NASA Astrophysics Data System (ADS)

Mukherjee, Krishnendu; Hossain, S. Minhaz

2008-12-01

We analyze the lattice equation of motion involving terms up to third order in lattice displacement. The phenomenological arguments suggest that the force constant D1 of the quadratic term must always be positive and the force constant B1 of the cubic term may take either positive or negative value. The criterion for stability of the lattice provides constraint on the relative magnitudes of the three force constants. We solve the equation of motion using root mean-square spatial fluctuation approximation and obtain the seminonperturbative dispersion relation both for positive and negative B1 . The nature of phonon density of states curves for positive B1 show some close resemblance with the experimental observations. At very low temperature, the specific heat of this system to leading order in large positive B1 varies as square root of temperature and it obeys Debye’s T law in one dimension for small negative B1 . At very high temperature, the specific heat may fall below or above its classical value depending on the relative magnitudes of B1 and D1 for B1>0 and it always falls above its classical value for B1<0 . The lattice model with positive B1 emerges as a good candidate for description of a monoatomic crystal.

Geometry and symmetry in non-equilibrium thermodynamic systems

NASA Astrophysics Data System (ADS)

Sonnino, Giorgio

2017-06-01

The ultimate aim of this series of works is to establish the closure equations, valid for thermodynamic systems out from the Onsager region, and to describe the geometry and symmetry in thermodynamic systems far from equilibrium. Geometry of a non-equilibrium thermodynamic system is constructed by taking into account the second law of thermodynamics and by imposing the validity of the Glansdorff-Prigogine Universal Criterion of Evolution. These two constraints allow introducing the metrics and the affine connection of the Space of the Thermodynamic Forces, respectively. The Lie group associated to the nonlinear Thermodynamic Coordinate Transformations (TCT) leaving invariant both the entropy production σ and the Glansdorff-Prigogine dissipative quantity P, is also described. The invariance under TCT leads to the formulation of the Thermodynamic Covariance Principle (TCP): The nonlinear closure equations, i.e. the flux-force relations, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces (i.e. under TCT). The symmetry properties of a physical system are intimately related to the conservation laws characterizing the thermodynamic system. Noether's theorem gives a precise description of this relation. The macroscopic theory for closure relations, based on this geometrical description and subject to the TCP, is referred to as the Thermodynamic Field Theory (TFT). This theory ensures the validity of the fundamental theorems for systems far from equilibrium.

A Novel Face-on-Face Contact Method for Nonlinear Solid Mechanics

NASA Astrophysics Data System (ADS)

Wopschall, Steven Robert

The implicit solution to contact problems in nonlinear solid mechanics poses many difficulties. Traditional node-to-segment methods may suffer from locking and experience contact force chatter in the presence of sliding. More recent developments include mortar based methods, which resolve local contact interactions over face-pairs and feature a kinematic constraint in integral form that smoothes contact behavior, especially in the presence of sliding. These methods have been shown to perform well in the presence of geometric nonlinearities and are demonstratively more robust than node-to-segment methods. These methods are typically biased, however, interpolating contact tractions and gap equations on a designated non-mortar face, which leads to an asymmetry in the formulation. Another challenge is constraint enforcement. The general selection of the active set of constraints is brought with difficulty, often leading to non-physical solutions and easily resulting in missed face-pair interactions. Details on reliable constraint enforcement methods are lacking in the greater contact literature. This work presents an unbiased contact formulation utilizing a median-plane methodology. Up to linear polynomials are used for the discrete pressure representation and integral gap constraints are enforced using a novel subcycling procedure. This procedure reliably determines the active set of contact constraints leading to physical and kinematically admissible solutions void of heuristics and user action. The contact method presented herein successfully solves difficult quasi-static contact problems in the implicit computational setting. These problems feature finite deformations, material nonlinearity, and complex interface geometries, all of which are challenging characteristics for contact implementations and constraint enforcement algorithms. The subcycling procedure is a key feature of this method, handling active constraint selection for complex interfaces and mesh geometries.

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Karpel, Mordechay

1989-01-01

Various control analysis, design, and simulation techniques for aeroelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamics forces have to be approximated as rational functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of denominator roots in the rational approximation. Results are shown of applying various approximation enhancements (including optimization, frequency dependent weighting of the tabular data, and constraint selection) with the minimum-state formulation to the active flexible wing wind-tunnel model. The results demonstrate that good models can be developed which have an order of magnitude fewer augmenting aerodynamic equations more than traditional approaches. This reduction facilitates the design of lower order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena.

High effective inverse dynamics modelling for dual-arm robot

NASA Astrophysics Data System (ADS)

Shen, Haoyu; Liu, Yanli; Wu, Hongtao

2018-05-01

To deal with the problem of inverse dynamics modelling for dual arm robot, a recursive inverse dynamics modelling method based on decoupled natural orthogonal complement is presented. In this model, the concepts and methods of Decoupled Natural Orthogonal Complement matrices are used to eliminate the constraint forces in the Newton-Euler kinematic equations, and the screws is used to express the kinematic and dynamics variables. On this basis, the paper has developed a special simulation program with symbol software of Mathematica and conducted a simulation research on the a dual-arm robot. Simulation results show that the proposed method based on decoupled natural orthogonal complement can save an enormous amount of CPU time that was spent in computing compared with the recursive Newton-Euler kinematic equations and the results is correct and reasonable, which can verify the reliability and efficiency of the method.

Load balancing and closed chain multiple arm control

NASA Technical Reports Server (NTRS)

Kreutz, Kenneth; Lokshin, Anatole

1988-01-01

The authors give the general dynamical equations for several rigid link manipulators rigidly grasping a commonly held rigid object. It is shown that the number of arm-configuration degrees of freedom lost due to imposing the closed-loop kinematic constraints is the same as the number of degrees of freedom gained for controlling the internal forces of the closed-chain system. This number is equal to the dimension of the kernel of the Jacobian operator which transforms contact forces to the net forces acting on the held object, and it is shown that this kernel can be identified with the subspace of controllable internal forces of the closed-chain system. Control of these forces makes it possible to regulate the grasping forces imparted to the held object or to control the load taken by each arm. It is shown that the internal forces can be influenced without affecting the control of the configuration degrees of freedom. Control laws of the feedback linearization type are shown to be useful for controlling the location and attitude of a frame fixed with respect to the held object, while simultaneously controlling the internal forces of the closed-chain system. Force feedback can be used to linearize and control the system even when the held object has unknown mass properties. If saturation effects are ignored, an unconstrained quadratic optimization can be performed to distribute the load optimally among the joint actuators.

Affine group formulation of the Standard Model coupled to gravity

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

Chou, Ching-Yi, E-mail: l2897107@mail.ncku.edu.tw; Ita, Eyo, E-mail: ita@usna.edu; Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw

In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder’s affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological constant Λ, as an affine Lie algebra. We use the hermitian action of fermions coupled to gravitation and Yang–Mills theory to find the density weight one fermionic super-Hamiltonian constraint. This term, combined with the Yang–Mills and Higgs energy densities, are composed with York’s integrated time functional. The result, when combined with the imaginary part of themore » Chern–Simons functional Q, forms the affine commutation relation with the volume element V(x). Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant. -- Highlights: •Wheeler–DeWitt equation (WDW) quantized as affine algebra, realizing Klauder’s program. •WDW formulated for interaction of matter and all forces, including gravity, as affine algebra. •WDW features Hermitian generators in spite of fermionic content: Standard Model addressed. •Constructed a family of physical states for the full, coupled theory via affine coherent states. •Fundamental uncertainty relation, predicated on non-vanishing cosmological constant.« less

Constraint elimination in dynamical systems

NASA Technical Reports Server (NTRS)

Singh, R. P.; Likins, P. W.

1989-01-01

Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.

Simultaneous prediction of muscle and contact forces in the knee during gait.

PubMed

Lin, Yi-Chung; Walter, Jonathan P; Banks, Scott A; Pandy, Marcus G; Fregly, Benjamin J

2010-03-22

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process. Copyright (c) 2009 Elsevier Ltd. All rights reserved.

Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task

NASA Astrophysics Data System (ADS)

Nazemizadeh, M.; Rahimi, H. N.; Amini Khoiy, K.

2012-03-01

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange's principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect solution of the optimal control method is employed, and conditions of the optimality derived as a set of coupled nonlinear differential equations. The optimality equations are solved numerically, and various simulations are performed for a nonholonomic mobile robot to illustrate effectiveness of the proposed method.

Canonical structures for dispersive waves in shallow water

NASA Astrophysics Data System (ADS)

Neyzi, Fahrünisa; Nutku, Yavuz

1987-07-01

The canonical Hamiltonian structure of the equations of fluid dynamics obtained in the Boussinesq approximation are considered. New variational formulations of these equations are proposed and it is found that, as in the case of the KdV equation and the equations governing long waves in shallow water, they are degenerate Lagrangian systems. Therefore, in order to cast these equations into canonical form it is again necessary to use Dirac's theory of constraints. It is found that there are primary and secondary constraints which are second class and it is possible to construct the Hamiltonian in terms of canonical variables. Among the examples of Boussinesq equations that are discussed are the equations of Whitham-Broer-Kaup which Kupershmidt has recently expressed in symmetric form and shown to admit tri-Hamiltonian structure.

The algebraic-hyperbolic approach to the linearized gravitational constraints on a Minkowski background

NASA Astrophysics Data System (ADS)

Winicour, Jeffrey

2017-08-01

An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein’s equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed.

Hermeneutical Field Theory and the Structural Character of Understanding.

NASA Astrophysics Data System (ADS)

Whitehouse, William Leonard

Through a series of exploratory case studies focusing on hermeneutics, phenomenology, relativity, field theory, quantum mechanics, chronobiology, chaos theory, holographic theory and various aspects of mathematics, a set of hermeneutical constraints and degrees of freedom are generated. There are a set of eight field equations given in the thesis which give qualitative symbolic expression to the aforementioned spectrum of constraints and degrees of freedom that constitute the structural character of understanding. However, as is sometimes the case with their quantitative mathematical counterparts, the hermeneutical field equations are capable of giving a variety of descriptions or solutions for one and the same set of conditions. The task, therefore, is to try to sort out those solutions which have reflective properties with respect to the structural character of reality from those which do not have such properties. The thesis addresses this task by introducing the idea of hermeneutical field theory. In this theory the notion of a semiotic operator or semiotic quantum plays a central role. More specifically, this quantum is considered to be the carrier of hermeneutical force. It arises as a field property at the complex, horizontal membrane-manifold linking human consciousness with different levels of scale of reality. When taken collectively, the aforementioned set of equations gives expression to the structural character of hermeneutical field theory. Therefore, when one begins to run concrete variables through the theory underlying these equations, one encounters various kinds of hermeneutical constraints and degrees of freedom. These constraints and degrees of freedom characterize the dialectical engagement of consciousness and reality as one seeks to acquire understanding concerning the above mentioned variables and the context which gives rise to them. Hermeneutical field theory is really the study of the factors that affect the state of the six internal 'spin' components of the semiotic quantum (i.e., identifying reference, reflexive consciousness, characterization, the interrogative imperative, inferential mapping, and congruence functions) in any given instance of dialectical interaction between consciousness and reality. Consequently, on the one hand, hermeneutical field theory involves an investigation of the potential sources of curvature or distortion which may be introduced into the exchange or transduction process occurring during the dialectical engagement between consciousness and reality. On the other hand, hermeneutical field theory is a study of the factors which need to be taken into consideration to establish hermeneutical point-structures, neighborhoods or latticeworks which can serve as analogs for different aspects of reality toward which attention is being directed. (Abstract shortened by UMI.).

Impact of a variational objective analysis scheme on a regional area numerical model: The Italian Air Force Weather Service experience

NASA Astrophysics Data System (ADS)

Bonavita, M.; Torrisi, L.

2005-03-01

A new data assimilation system has been designed and implemented at the National Center for Aeronautic Meteorology and Climatology of the Italian Air Force (CNMCA) in order to improve its operational numerical weather prediction capabilities and provide more accurate guidance to operational forecasters. The system, which is undergoing testing before operational use, is based on an “observation space” version of the 3D-VAR method for the objective analysis component, and on the High Resolution Regional Model (HRM) of the Deutscher Wetterdienst (DWD) for the prognostic component. Notable features of the system include a completely parallel (MPI+OMP) implementation of the solution of analysis equations by a preconditioned conjugate gradient descent method; correlation functions in spherical geometry with thermal wind constraint between mass and wind field; derivation of the objective analysis parameters from a statistical analysis of the innovation increments.

Necessary constraints for an equation of state to be physically acceptable

NASA Astrophysics Data System (ADS)

Sheelendra, K.; Vijay, A.

2018-04-01

We have pointed out the constraints required for an equation of state (EOS) to be physically acceptable and universally applicable for the entire range of compressions for a material at high pressures. We have discussed the boundary conditions valid at zero pressure and infinite pressure. The concept of infinite pressure behavior has been discussed. It has been emphasized that the Stacey reciprocal K-primed EOS satisfies all the necessary criterion for the validity of EOS. On the other hand, equations of state reported previously do not satisfy the condition of physical acceptability of an equation of state.

Reduced Dynamics of the Non-holonomic Whipple Bicycle

NASA Astrophysics Data System (ADS)

Boyer, Frédéric; Porez, Mathieu; Mauny, Johan

2018-06-01

Though the bicycle is a familiar object of everyday life, modeling its full nonlinear three-dimensional dynamics in a closed symbolic form is a difficult issue for classical mechanics. In this article, we address this issue without resorting to the usual simplifications on the bicycle kinematics nor its dynamics. To derive this model, we use a general reduction-based approach in the principal fiber bundle of configurations of the three-dimensional bicycle. This includes a geometrically exact model of the contacts between the wheels and the ground, the explicit calculation of the kernel of constraints, along with the dynamics of the system free of any external forces, and its projection onto the kernel of admissible velocities. The approach takes benefits of the intrinsic formulation of geometric mechanics. Along the path toward the final equations, we show that the exact model of the bicycle dynamics requires to cope with a set of non-symmetric constraints with respect to the structural group of its configuration fiber bundle. The final reduced dynamics are simulated on several examples representative of the bicycle. As expected the constraints imposed by the ground contacts, as well as the energy conservation, are satisfied, while the dynamics can be numerically integrated in real time.

Dikin-type algorithms for dextrous grasping force optimization

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

Buss, M.; Faybusovich, L.; Moore, J.B.

1998-08-01

One of the central issues in dextrous robotic hand grasping is to balance external forces acting on the object and at the same time achieve grasp stability and minimum grasping effort. A companion paper shows that the nonlinear friction-force limit constraints on grasping forces are equivalent to the positive definiteness of a certain matrix subject to linear constraints. Further, compensation of the external object force is also a linear constraint on this matrix. Consequently, the task of grasping force optimization can be formulated as a problem with semidefinite constraints. In this paper, two versions of strictly convex cost functions, onemore » of them self-concordant, are considered. These are twice-continuously differentiable functions that tend to infinity at the boundary of possible definiteness. For the general class of such cost functions, Dikin-type algorithms are presented. It is shown that the proposed algorithms guarantee convergence to the unique solution of the semidefinite programming problem associated with dextrous grasping force optimization. Numerical examples demonstrate the simplicity of implementation, the good numerical properties, and the optimality of the approach.« less

Dynamics and Control of Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Part I

NASA Astrophysics Data System (ADS)

Amengonu, Yawo H.; Kakad, Yogendra P.

2014-07-01

Quasivelocity techniques such as Maggi's and Boltzmann-Hamel's equations eliminate Lagrange multipliers from the beginning as opposed to the Euler-Lagrange method where one has to solve for the n configuration variables and the multipliers as functions of time when there are m nonholonomic constraints. Maggi's equation produces n second-order differential equations of which (n-m) are derived using (n-m) independent quasivelocities and the time derivative of the m kinematic constraints which add the remaining m second order differential equations. This technique is applied to derive the dynamics of a differential mobile robot and a controller which takes into account these dynamics is developed.

MHD Turbulence, div B = 0 and Lattice Boltzmann Simulations

NASA Astrophysics Data System (ADS)

Phillips, Nate; Keating, Brian; Vahala, George; Vahala, Linda

2006-10-01

The question of div B = 0 in MHD simulations is a crucial issue. Here we consider lattice Boltzmann simulations for MHD (LB-MHD). One introduces a scalar distribution function for the velocity field and a vector distribution function for the magnetic field. This asymmetry is due to the different symmetries in the tensors arising in the time evolution of these fields. The simple algorithm of streaming and local collisional relaxation is ideally parallelized and vectorized -- leading to the best sustained performance/PE of any code run on the Earth Simulator. By reformulating the BGK collision term, a simple implicit algorithm can be immediately transformed into an explicit algorithm that permits simulations at quite low viscosity and resistivity. However the div B is not an imposed constraint. Currently we are examining a new formulations of LB-MHD that impose the div B constraint -- either through an entropic like formulation or by introducing forcing terms into the momentum equations and permitting simpler forms of relaxation distributions.

Ab initio predictions of the symmetry energy and recent constraints

NASA Astrophysics Data System (ADS)

Sammarruca, Francesca

2017-01-01

The symmetry energy plays a crucial role in the structure and the dynamics of neutron-rich systems, including the formation of neutron skins, the location of neutron drip lines, as well as intriguing correlations with the structure of compact stars. With experimental efforts in progress or being planned to shed light on the less known aspects of the nuclear chart, microscopic predictions based on ab initio approaches are very important. In recent years, chiral effective field theory has become popular because of its firm connection with quantum chromodynamics and its systematic approach to the development of nuclear forces. Predictions of the symmetry energy obtained from modern chiral interactions will be discussed in the light of recent empirical constraints extracted from heavy ion collisions at 400 MeV per nucleon at GSI. Applications of our equations of state to neutron-rich systems will also be discussed, with particular emphasis on neutron skins, which are sensitive to the density dependence of the symmetry energy.

The Use of Laser Altimetry in the Orbit and Attitude Determination of Mars Global Surveyor

NASA Technical Reports Server (NTRS)

Rowlands, D. D.; Pavlis, D. E.; Lemoine, F. G.; Neumann, G. A.; Luthcke, S. B.

1999-01-01

Altimetry from the Mars Observer Laser Altimeter (MOLA) which is carried on board Mars Global Surveyor (MGS) has been analyzed for the period of the MOS mission known as Science Phasing Orbit 1 (SPO-1). We have used these altimeter ranges to improve orbit and attitude knowledge for MGS. This has been accomplished by writing crossover constraint equations that have been derived from short passes of MOLA data. These constraint equations differ from traditional Crossover constraints and exploit the small foot print associated with laser altimetry.

Rapid sampling of stochastic displacements in Brownian dynamics simulations with stresslet constraints

NASA Astrophysics Data System (ADS)

Fiore, Andrew M.; Swan, James W.

2018-01-01

Brownian Dynamics simulations are an important tool for modeling the dynamics of soft matter. However, accurate and rapid computations of the hydrodynamic interactions between suspended, microscopic components in a soft material are a significant computational challenge. Here, we present a new method for Brownian dynamics simulations of suspended colloidal scale particles such as colloids, polymers, surfactants, and proteins subject to a particular and important class of hydrodynamic constraints. The total computational cost of the algorithm is practically linear with the number of particles modeled and can be further optimized when the characteristic mass fractal dimension of the suspended particles is known. Specifically, we consider the so-called "stresslet" constraint for which suspended particles resist local deformation. This acts to produce a symmetric force dipole in the fluid and imparts rigidity to the particles. The presented method is an extension of the recently reported positively split formulation for Ewald summation of the Rotne-Prager-Yamakawa mobility tensor to higher order terms in the hydrodynamic scattering series accounting for force dipoles [A. M. Fiore et al., J. Chem. Phys. 146(12), 124116 (2017)]. The hydrodynamic mobility tensor, which is proportional to the covariance of particle Brownian displacements, is constructed as an Ewald sum in a novel way which guarantees that the real-space and wave-space contributions to the sum are independently symmetric and positive-definite for all possible particle configurations. This property of the Ewald sum is leveraged to rapidly sample the Brownian displacements from a superposition of statistically independent processes with the wave-space and real-space contributions as respective covariances. The cost of computing the Brownian displacements in this way is comparable to the cost of computing the deterministic displacements. The addition of a stresslet constraint to the over-damped particle equations of motion leads to a stochastic differential algebraic equation (SDAE) of index 1, which is integrated forward in time using a mid-point integration scheme that implicitly produces stochastic displacements consistent with the fluctuation-dissipation theorem for the constrained system. Calculations for hard sphere dispersions are illustrated and used to explore the performance of the algorithm. An open source, high-performance implementation on graphics processing units capable of dynamic simulations of millions of particles and integrated with the software package HOOMD-blue is used for benchmarking and made freely available in the supplementary material (ftp://ftp.aip.org/epaps/journ_chem_phys/E-JCPSA6-148-012805)

'Constraint consistency' at all orders in cosmological perturbation theory

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

Nandi, Debottam; Shankaranarayanan, S., E-mail: debottam@iisertvm.ac.in, E-mail: shanki@iisertvm.ac.in

2015-08-01

We study the equivalence of two—order-by-order Einstein's equation and Reduced action—approaches to cosmological perturbation theory at all orders for different models of inflation. We point out a crucial consistency check which we refer to as 'Constraint consistency' condition that needs to be satisfied in order for the two approaches to lead to identical single variable equation of motion. The method we propose here is quick and efficient to check the consistency for any model including modified gravity models. Our analysis points out an important feature which is crucial for inflationary model building i.e., all 'constraint' inconsistent models have higher ordermore » Ostrogradsky's instabilities but the reverse is not true. In other words, one can have models with constraint Lapse function and Shift vector, though it may have Ostrogradsky's instabilities. We also obtain single variable equation for non-canonical scalar field in the limit of power-law inflation for the second-order perturbed variables.« less

The KP Approximation Under a Weak Coriolis Forcing

NASA Astrophysics Data System (ADS)

Melinand, Benjamin

2018-02-01

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

Moment measurements in dynamic and quasi-static spine segment testing using eccentric compression are susceptible to artifacts based on loading configuration.

PubMed

Van Toen, Carolyn; Carter, Jarrod W; Oxland, Thomas R; Cripton, Peter A

2014-12-01

The tolerance of the spine to bending moments, used for evaluation of injury prevention devices, is often determined through eccentric axial compression experiments using segments of the cadaver spine. Preliminary experiments in our laboratory demonstrated that eccentric axial compression resulted in "unexpected" (artifact) moments. The aim of this study was to evaluate the static and dynamic effects of test configuration on bending moments during eccentric axial compression typical in cadaver spine segment testing. Specific objectives were to create dynamic equilibrium equations for the loads measured inferior to the specimen, experimentally verify these equations, and compare moment responses from various test configurations using synthetic (rubber) and human cadaver specimens. The equilibrium equations were verified by performing quasi-static (5 mm/s) and dynamic experiments (0.4 m/s) on a rubber specimen and comparing calculated shear forces and bending moments to those measured using a six-axis load cell. Moment responses were compared for hinge joint, linear slider and hinge joint, and roller joint configurations tested at quasi-static and dynamic rates. Calculated shear force and bending moment curves had similar shapes to those measured. Calculated values in the first local minima differed from those measured by 3% and 15%, respectively, in the dynamic test, and these occurred within 1.5 ms of those measured. In the rubber specimen experiments, for the hinge joint (translation constrained), quasi-static and dynamic posterior eccentric compression resulted in flexion (unexpected) moments. For the slider and hinge joints and the roller joints (translation unconstrained), extension ("expected") moments were measured quasi-statically and initial flexion (unexpected) moments were measured dynamically. In the cadaver experiments with roller joints, anterior and posterior eccentricities resulted in extension moments, which were unexpected and expected, for those configurations, respectively. The unexpected moments were due to the inertia of the superior mounting structures. This study has shown that eccentric axial compression produces unexpected moments due to translation constraints at all loading rates and due to the inertia of the superior mounting structures in dynamic experiments. It may be incorrect to assume that bending moments are equal to the product of compression force and eccentricity, particularly where the test configuration involves translational constraints and where the experiments are dynamic. In order to reduce inertial moment artifacts, the mass, and moment of inertia of any loading jig structures that rotate with the specimen should be minimized. Also, the distance between these structures and the load cell should be reduced.

The Boeing plastic analysis capability for engines

NASA Technical Reports Server (NTRS)

Vos, R. G.

1976-01-01

The current BOPACE program is described as a nonlinear stress analysis program, which is based on a family of isoparametric finite elements. The theoretical, user, programmer, preprocessing aspects are discussed, and example problems are included. New features in the current program version include substructuring, an out-of-core Gauss wavefront equation solver, multipoint constraints, combined material and geometric nonlinearities, automatic calculation of inertia effects, provision for distributed as well as concentrated mechanical loads, follower forces, singular crack-tip elements, the SAIL automatic generation capability, and expanded user control over input quantity definition, output selection, and program execution. BOPACE is written in FORTRAN 4 and is currently available for both the IBM 360/370 and the UNIVAC 1108 machines.

Phenomenologically viable Lorentz-violating quantum gravity.

PubMed

Sotiriou, Thomas P; Visser, Matt; Weinfurtner, Silke

2009-06-26

Horava's "Lifschitz point gravity" has many desirable features, but in its original incarnation one is forced to accept a nonzero cosmological constant of the wrong sign to be compatible with observation. We develop an extension of Horava's model that abandons "detailed balance" and regains parity invariance, and in 3+1 dimensions exhibit all five marginal (renormalizable) and four relevant (super-renormalizable) operators, as determined by power counting. We also consider the classical limit of this theory, evaluate the Hamiltonian and supermomentum constraints, and extract the classical equations of motion in a form similar to the Arnowitt-Deser-Misner formulation of general relativity. This puts the model in a framework amenable to developing detailed precision tests.

The Forced Hard Spring Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2006-01-01

Through numerical investigations, various examples of the Duffing type forced spring equation with epsilon positive, are studied. Since [epsilon] is positive, all solutions to the associated homogeneous equation are periodic and the same is true with the forcing applied. The damped equation exhibits steady state trajectories with the interesting…

Statistical Neurodynamics.

NASA Astrophysics Data System (ADS)

Paine, Gregory Harold

1982-03-01

The primary objective of the thesis is to explore the dynamical properties of small nerve networks by means of the methods of statistical mechanics. To this end, a general formalism is developed and applied to elementary groupings of model neurons which are driven by either constant (steady state) or nonconstant (nonsteady state) forces. Neuronal models described by a system of coupled, nonlinear, first-order, ordinary differential equations are considered. A linearized form of the neuronal equations is studied in detail. A Lagrange function corresponding to the linear neural network is constructed which, through a Legendre transformation, provides a constant of motion. By invoking the Maximum-Entropy Principle with the single integral of motion as a constraint, a probability distribution function for the network in a steady state can be obtained. The formalism is implemented for some simple networks driven by a constant force; accordingly, the analysis focuses on a study of fluctuations about the steady state. In particular, a network composed of N noninteracting neurons, termed Free Thinkers, is considered in detail, with a view to interpretation and numerical estimation of the Lagrange multiplier corresponding to the constant of motion. As an archetypical example of a net of interacting neurons, the classical neural oscillator, consisting of two mutually inhibitory neurons, is investigated. It is further shown that in the case of a network driven by a nonconstant force, the Maximum-Entropy Principle can be applied to determine a probability distribution functional describing the network in a nonsteady state. The above examples are reconsidered with nonconstant driving forces which produce small deviations from the steady state. Numerical studies are performed on simplified models of two physical systems: the starfish central nervous system and the mammalian olfactory bulb. Discussions are given as to how statistical neurodynamics can be used to gain a better understanding of the behavior of these systems.

Well-posedness of the Einstein-Euler system in asymptotically flat spacetimes: The constraint equations

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

This paper deals with the construction of initial data for the coupled Einstein-Euler system. We consider the condition where the energy density might vanish or tend to zero at infinity, and where the pressure is a fractional power of the energy density. In order to achieve our goals we use a type of weighted Sobolev space of fractional order. The common Lichnerowicz-York scaling method (Choquet-Bruhat and York, 1980 [9]; Cantor, 1979 [7]) for solving the constraint equations cannot be applied here directly. The basic problem is that the matter sources are scaled conformally and the fluid variables have to be recovered from the conformally transformed matter sources. This problem has been addressed, although in a different context, by Dain and Nagy (2002) [11]. We show that if the matter variables are restricted to a certain region, then the Einstein constraint equations have a unique solution in the weighted Sobolev spaces of fractional order. The regularity depends upon the fractional power of the equation of state.

Radiation reaction on a classical charged particle: a modified form of the equation of motion.

PubMed

Alcaine, Guillermo García; Llanes-Estrada, Felipe J

2013-09-01

We present and numerically solve a modified form of the equation of motion for a charged particle under the influence of an external force, taking into account the radiation reaction. This covariant equation is integro-differential, as Dirac-Röhrlich's, but has several technical improvements. First, the equation has the form of Newton's second law, with acceleration isolated on the left hand side and the force depending only on positions and velocities: Thus, the equation is linear in the highest derivative. Second, the total four-force is by construction perpendicular to the four-velocity. Third, if the external force vanishes for all future times, the total force and the acceleration automatically vanish at the present time. We show the advantages of this equation by solving it numerically for several examples of external force.

Radiation reaction on a classical charged particle: A modified form of the equation of motion

NASA Astrophysics Data System (ADS)

Alcaine, Guillermo García; Llanes-Estrada, Felipe J.

2013-09-01

We present and numerically solve a modified form of the equation of motion for a charged particle under the influence of an external force, taking into account the radiation reaction. This covariant equation is integro-differential, as Dirac-Röhrlich's, but has several technical improvements. First, the equation has the form of Newton's second law, with acceleration isolated on the left hand side and the force depending only on positions and velocities: Thus, the equation is linear in the highest derivative. Second, the total four-force is by construction perpendicular to the four-velocity. Third, if the external force vanishes for all future times, the total force and the acceleration automatically vanish at the present time. We show the advantages of this equation by solving it numerically for several examples of external force.

Equation of state for neutron stars. Some recent developments

NASA Astrophysics Data System (ADS)

Haensel, P.; Fortin, M.

2017-12-01

Calculations using the chiral effective field theory (ChEFT) indicate that the four-body force contribution to the equation of state (EOS) of pure neutron matter (PNM) at the nuclear density n 0 is negligibly small. However, the overall uncertainty in the EOS of PNM at n 0 remains ∼ 20%. Relativistic mean field (RMF) calculations with in-medium scaling, and including hyperons and Δ resonances, can be made consistent with recent nuclear and astrophysical constraints. Dirac-Brueckner-Hartree-Fock calculations with some medium dependence of the nuclear interaction yield neutron star (NS) models with hyperonic cores consistent with 2 M⊙ stars and agreeing with the saturation parameters of nuclear matter. Many unified EOS for the NS crust and core were calculated, and are reviewed here. The effect of the finite size of baryons on the EOS, its treatment via the excluded-volume approximation, and its relevance for the hypothetical hybrid-star twins at ∼ 2 M⊙ are dicussed.

Nonlinear core deflection in injection molding

NASA Astrophysics Data System (ADS)

Poungthong, P.; Giacomin, A. J.; Saengow, C.; Kolitawong, C.; Liao, H.-C.; Tseng, S.-C.

2018-05-01

Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this liquid exerts a lateral force of the slender core causing the core to bend, and this bending is governed by a nonlinear fifth order ordinary differential equation for the deflection that is not directly in the position along the core. Here we subject this differential equation to 6 sets of boundary conditions, corresponding to 6 commercial core constraints. For each such set of boundary conditions, we develop an explicit approximate analytical solution, including both a linear term and a nonlinear term. By comparison with finite difference solutions, we find our new analytical solutions to be accurate. We then use these solutions to derive explicit analytical approximations for maximum deflections and for the core position of these maximum deflections. Our experiments on the base-gated free-tip boundary condition agree closely with our new explicit approximate analytical solution.

Tune-stabilized, non-scaling, fixed-field, alternating gradient accelerator

DOEpatents

Johnstone, Carol J [Warrenville, IL

2011-02-01

A FFAG is a particle accelerator having turning magnets with a linear field gradient for confinement and a large edge angle to compensate for acceleration. FODO cells contain focus magnets and defocus magnets that are specified by a number of parameters. A set of seven equations, called the FFAG equations relate the parameters to one another. A set of constraints, call the FFAG constraints, constrain the FFAG equations. Selecting a few parameters, such as injection momentum, extraction momentum, and drift distance reduces the number of unknown parameters to seven. Seven equations with seven unknowns can be solved to yield the values for all the parameters and to thereby fully specify a FFAG.

Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

NASA Astrophysics Data System (ADS)

Ikegami, Kenji; Kimura, Tadahiko; Mochizuki, Riuji

1993-04-01

We study the treatment of the constraints in the stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking into account the Ito calculus. Then we obtain an improved Langevi equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to an O( N) non-linear α model and it is shown that singular terms appearing in the improved Langevin equation cancel out the σ n(O) divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of idependent variables, is actually equivalent to the one in the general-coordinate transformation covariant and vielbein-rotation invariant formalish.

Constraint reasoning in deep biomedical models.

PubMed

Cruz, Jorge; Barahona, Pedro

2005-05-01

Deep biomedical models are often expressed by means of differential equations. Despite their expressive power, they are difficult to reason about and make decisions, given their non-linearity and the important effects that the uncertainty on data may cause. The objective of this work is to propose a constraint reasoning framework to support safe decisions based on deep biomedical models. The methods used in our approach include the generic constraint propagation techniques for reducing the bounds of uncertainty of the numerical variables complemented with new constraint reasoning techniques that we developed to handle differential equations. The results of our approach are illustrated in biomedical models for the diagnosis of diabetes, tuning of drug design and epidemiology where it was a valuable decision-supporting tool notwithstanding the uncertainty on data. The main conclusion that follows from the results is that, in biomedical decision support, constraint reasoning may be a worthwhile alternative to traditional simulation methods, especially when safe decisions are required.

Infinite horizon problems on stratifiable state-constraints sets

NASA Astrophysics Data System (ADS)

Hermosilla, C.; Zidani, H.

2015-02-01

This paper deals with a state-constrained control problem. It is well known that, unless some compatibility condition between constraints and dynamics holds, the Value Function has not enough regularity, or can fail to be the unique constrained viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. Here, we consider the case of a set of constraints having a stratified structure. Under this circumstance, the interior of this set may be empty or disconnected, and the admissible trajectories may have the only option to stay on the boundary without possible approximation in the interior of the constraints. In such situations, the classical pointing qualification hypothesis is not relevant. The discontinuous Value Function is then characterized by means of a system of HJB equations on each stratum that composes the state-constraints. This result is obtained under a local controllability assumption which is required only on the strata where some chattering phenomena could occur.

A Technique for Analysing Constrained Rigid-Body Systems, and Its Application to the Constraint Force Algorithm

NASA Technical Reports Server (NTRS)

Fijany, A.; Featherstone, R.

1999-01-01

This paper presents a new formulation of the Constraint Force Algorithm that corrects a major limitation in the original, and sheds new light on the relationship between it and other dynamics algoritms.

Diffuse interface models of locally inextensible vesicles in a viscous fluid

PubMed Central

Aland, Sebastian; Egerer, Sabine; Lowengrub, John; Voigt, Axel

2014-01-01

We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid with inertial forces. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. We introduce a new equation for the local Lagrange multiplier whose solution essentially provides a harmonic extension of the multiplier off the interface while maintaining the local inextensibility constraint near the interface. We also develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. Asymptotic analysis is presented that shows that our new system converges to a relaxed version of the inextensible sharp interface model. This is also verified numerically. To solve the equations, we use an adaptive finite element method with implicit coupling between the Navier-Stokes and the diffuse interface inextensibility equations. Numerical simulations of a single vesicle in a shear flow at different Reynolds numbers demonstrate that errors in enforcing local inextensibility may accumulate and lead to large differences in the dynamics in the tumbling regime and smaller differences in the inclination angle of vesicles in the tank-treading regime. The local relaxation algorithm is shown to prevent the accumulation of stretching and compression errors very effectively. Simulations of two vesicles in an extensional flow show that local inextensibility plays an important role when vesicles are in close proximity by inhibiting fluid drainage in the near contact region. PMID:25246712

Geometrically constrained kinematic global navigation satellite systems positioning: Implementation and performance

NASA Astrophysics Data System (ADS)

Asgari, Jamal; Mohammadloo, Tannaz H.; Amiri-Simkooei, Ali Reza

2015-09-01

GNSS kinematic techniques are capable of providing precise coordinates in extremely short observation time-span. These methods usually determine the coordinates of an unknown station with respect to a reference one. To enhance the precision, accuracy, reliability and integrity of the estimated unknown parameters, GNSS kinematic equations are to be augmented by possible constraints. Such constraints could be derived from the geometric relation of the receiver positions in motion. This contribution presents the formulation of the constrained kinematic global navigation satellite systems positioning. Constraints effectively restrict the definition domain of the unknown parameters from the three-dimensional space to a subspace defined by the equation of motion. To test the concept of the constrained kinematic positioning method, the equation of a circle is employed as a constraint. A device capable of moving on a circle was made and the observations from 11 positions on the circle were analyzed. Relative positioning was conducted by considering the center of the circle as the reference station. The equation of the receiver's motion was rewritten in the ECEF coordinates system. A special attention is drawn onto how a constraint is applied to kinematic positioning. Implementing the constraint in the positioning process provides much more precise results compared to the unconstrained case. This has been verified based on the results obtained from the covariance matrix of the estimated parameters and the empirical results using kinematic positioning samples as well. The theoretical standard deviations of the horizontal components are reduced by a factor ranging from 1.24 to 2.64. The improvement on the empirical standard deviation of the horizontal components ranges from 1.08 to 2.2.

Detached eddy simulation for turbulent fluid-structure interaction of moving bodies using the constraint-based immersed boundary method

NASA Astrophysics Data System (ADS)

Nangia, Nishant; Bhalla, Amneet P. S.; Griffith, Boyce E.; Patankar, Neelesh A.

2016-11-01

Flows over bodies of industrial importance often contain both an attached boundary layer region near the structure and a region of massively separated flow near its trailing edge. When simulating these flows with turbulence modeling, the Reynolds-averaged Navier-Stokes (RANS) approach is more efficient in the former, whereas large-eddy simulation (LES) is more accurate in the latter. Detached-eddy simulation (DES), based on the Spalart-Allmaras model, is a hybrid method that switches from RANS mode of solution in attached boundary layers to LES in detached flow regions. Simulations of turbulent flows over moving structures on a body-fitted mesh incur an enormous remeshing cost every time step. The constraint-based immersed boundary (cIB) method eliminates this operation by placing the structure on a Cartesian mesh and enforcing a rigidity constraint as an additional forcing in the Navier-Stokes momentum equation. We outline the formulation and development of a parallel DES-cIB method using adaptive mesh refinement. We show preliminary validation results for flows past stationary bodies with both attached and separated boundary layers along with results for turbulent flows past moving bodies. This work is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1324585.

A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations

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

Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu

2016-07-15

Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished bymore » allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.« less

Computational tools for calculating alternative muscle force patterns during motion: a comparison of possible solutions.

PubMed

Martelli, Saulo; Calvetti, Daniela; Somersalo, Erkki; Viceconti, Marco; Taddei, Fulvia

2013-08-09

Comparing the available electromyography (EMG) and the related uncertainties with the space of muscle forces potentially driving the same motion can provide insights into understanding human motion in healthy and pathological neuromotor conditions. However, it is not clear how effective the available computational tools are in completely sample the possible muscle forces. In this study, we compared the effectiveness of Metabolica and the Null-Space algorithm at generating a comprehensive spectrum of possible muscle forces for a representative motion frame. The hip force peak during a selected walking trial was identified using a lower-limb musculoskeletal model. The joint moments, the muscle lever arms, and the muscle force constraints extracted from the model constituted the indeterminate equilibrium equation at the joints. Two spectra, each containing 200,000 muscle force samples, were calculated using Metabolica and the Null-Space algorithm. The full hip force range was calculated using optimization and compared with the hip force ranges derived from the Metabolica and the Null-Space spectra. The Metabolica spectrum spanned a much larger force range than the NS spectrum, reaching 811N difference for the gluteus maximus intermediate bundle. The Metabolica hip force range exhibited a 0.3-0.4 BW error on the upper and lower boundaries of the full hip force range (3.4-11.3 BW), whereas the full range was imposed in the NS spectrum. The results suggest that Metabolica is well suited for exhaustively sample the spectrum of possible muscle recruitment strategy. Future studies will investigate the muscle force range in healthy and pathological neuromotor conditions. Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

Efficient dynamic modeling of manipulators containing closed kinematic loops

NASA Astrophysics Data System (ADS)

Ferretti, Gianni; Rocco, Paolo

An approach to efficiently solve the forward dynamics problem for manipulators containing closed chains is proposed. The two main distinctive features of this approach are: the dynamics of the equivalent open loop tree structures (any closed loop can be in general modeled by imposing some additional kinematic constraints to a suitable tree structure) is computed through an efficient Newton Euler formulation; the constraint equations relative to the most commonly adopted closed chains in industrial manipulators are explicitly solved, thus, overcoming the redundancy of Lagrange's multipliers method while avoiding the inefficiency due to a numerical solution of the implicit constraint equations. The constraint equations considered for an explicit solution are those imposed by articulated gear mechanisms and planar closed chains (pantograph type structures). Articulated gear mechanisms are actually used in all industrial robots to transmit motion from actuators to links, while planar closed chains are usefully employed to increase the stiffness of the manipulators and their load capacity, as well to reduce the kinematic coupling of joint axes. The accuracy and the efficiency of the proposed approach are shown through a simulation test.

A crack opening stress equation for fatigue crack growth

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.

1984-01-01

A general crack opening stress equation is presented which may be used to correlate crack growth rate data for various materials and thicknesses, under constant amplitude loading, once the proper constraint factor has been determined. The constraint factor, alpha, is a constraint on tensile yielding; the material yields when the stress is equal to the product of alpha and sigma. Delta-K (LEFM) is plotted against rate for 2024-T3 aluminum alloy specimens 2.3 mm thick at various stress ratios. Delta-K sub eff was plotted against rate for the same data with alpha = 1.8; the rates correlate well within a factor of two.

Validity Study of a Jump Mat Compared to the Reference Standard Force Plate.

PubMed

Rogan, Slavko; Radlinger, Lorenz; Imhasly, Caroline; Kneubuehler, Andrea; Hilfiker, Roger

2015-12-01

In the field of vertical jump diagnostics, force plates (FP) are the reference standard. Recently, despite a lack of evidence, jump mats have been used increasingly. Important factors in favor of jumping mats are their low cost and portability. This validity study compared the Haynl-Elektronik jump mat (HE jump mat) with the reference standard force plate. Ten healthy volunteers participated and each participant completed three series of five drop jumps (DJ). The parameters ground contact time (GCT) and vertical jump height (VJH) from the HE jump mat and the FP were used to evaluate the concurrent validity. The following statistical calculations were performed: Pearson's correlation (r), Bland-Altman plots (standard and for adjusted trend), and regression equations. The Bland-Altman plots suggest that the HE jump mat measures shorter contact times and higher jump heights than the FP. The trend-adjusted Bland-Altman plot shows higher mean differences and wider wing-spreads of confidence limits during longer GCT. During the VJH the mean differences and the wing-spreads of the confidence limits throughout the range present as relatively constant. The following regression equations were created, as close as possible to the true value: GCT = 5.920385 + 1.072293 × [value HE jump mat] and VJH = -1.73777 + 1.011156 × [value HE jump mat]. The HE jump mat can be recommended in relation to the validity of constraints. In this study, only a part of the quality criteria were examined. For the final recommendation it is advised to examine the HE jump mat on the other quality criteria (test-retest reliability, sensitivity change).

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1988-01-01

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

The formulation of dynamical contact problems with friction in the case of systems of rigid bodies and general discrete mechanical systems—Painlevé and Kane paradoxes revisited

NASA Astrophysics Data System (ADS)

Charles, Alexandre; Ballard, Patrick

2016-08-01

The dynamics of mechanical systems with a finite number of degrees of freedom (discrete mechanical systems) is governed by the Lagrange equation which is a second-order differential equation on a Riemannian manifold (the configuration manifold). The handling of perfect (frictionless) unilateral constraints in this framework (that of Lagrange's analytical dynamics) was undertaken by Schatzman and Moreau at the beginning of the 1980s. A mathematically sound and consistent evolution problem was obtained, paving the road for many subsequent theoretical investigations. In this general evolution problem, the only reaction force which is involved is a generalized reaction force, consistently with the virtual power philosophy of Lagrange. Surprisingly, such a general formulation was never derived in the case of frictional unilateral multibody dynamics. Instead, the paradigm of the Coulomb law applying to reaction forces in the real world is generally invoked. So far, this paradigm has only enabled to obtain a consistent evolution problem in only some very few specific examples and to suggest numerical algorithms to produce computational examples (numerical modeling). In particular, it is not clear what is the evolution problem underlying the computational examples. Moreover, some of the few specific cases in which this paradigm enables to write down a precise evolution problem are known to show paradoxes: the Painlevé paradox (indeterminacy) and the Kane paradox (increase in kinetic energy due to friction). In this paper, we follow Lagrange's philosophy and formulate the frictional unilateral multibody dynamics in terms of the generalized reaction force and not in terms of the real-world reaction force. A general evolution problem that governs the dynamics is obtained for the first time. We prove that all the solutions are dissipative; that is, this new formulation is free of Kane paradox. We also prove that some indeterminacy of the Painlevé paradox is fixed in this formulation.

Prosthetic Leg Control in the Nullspace of Human Interaction.

PubMed

Gregg, Robert D; Martin, Anne E

2016-07-01

Recent work has extended the control method of virtual constraints, originally developed for autonomous walking robots, to powered prosthetic legs for lower-limb amputees. Virtual constraints define desired joint patterns as functions of a mechanical phasing variable, which are typically enforced by torque control laws that linearize the output dynamics associated with the virtual constraints. However, the output dynamics of a powered prosthetic leg generally depend on the human interaction forces, which must be measured and canceled by the feedback linearizing control law. This feedback requires expensive multi-axis load cells, and actively canceling the interaction forces may minimize the human's influence over the prosthesis. To address these limitations, this paper proposes a method for projecting virtual constraints into the nullspace of the human interaction terms in the output dynamics. The projected virtual constraints naturally render the output dynamics invariant with respect to the human interaction forces, which instead enter into the internal dynamics of the partially linearized prosthetic system. This method is illustrated with simulations of a transfemoral amputee model walking with a powered knee-ankle prosthesis that is controlled via virtual constraints with and without the proposed projection.

Effects of the oceans on polar motion: Extended investigations

NASA Technical Reports Server (NTRS)

Dickman, Steven R.

1987-01-01

Matrix formulation of the tide equations (pole tide in nonglobal oceans); matrix formulation of the associated boundary conditions (constraints on the tide velocity at coastlines); and FORTRAN encoding of the tide equations excluding boundary conditions were completed. The need for supercomputer facilities was evident. Large versions of the programs were successfully run on the CYBER, submitting the jobs from SUNY through the BITNET network. The code was also restructured to include boundary constraints.

Nonlinear robust controller design for multi-robot systems with unknown payloads

NASA Technical Reports Server (NTRS)

Song, Y. D.; Anderson, J. N.; Homaifar, A.; Lai, H. Y.

1992-01-01

This work is concerned with the control problem of a multi-robot system handling a payload with unknown mass properties. Force constraints at the grasp points are considered. Robust control schemes are proposed that cope with the model uncertainty and achieve asymptotic path tracking. To deal with the force constraints, a strategy for optimally sharing the task is suggested. This strategy basically consists of two steps. The first detects the robots that need help and the second arranges that help. It is shown that the overall system is not only robust to uncertain payload parameters, but also satisfies the force constraints.

Simulating squeeze flows in multiaxial laminates using an improved TIF model

NASA Astrophysics Data System (ADS)

Ibañez, R.; Abisset-Chavanne, Emmanuelle; Chinesta, Francisco

2017-10-01

Thermoplastic composites are widely considered in structural parts. In this paper attention is paid to squeeze flow of continuous fiber laminates. In the case of unidirectional prepregs, the ply constitutive equation is modeled as a transversally isotropic fluid, that must satisfy both the fiber inextensibility as well as the fluid incompressibility. When laminate is squeezed the flow kinematics exhibits a complex dependency along the laminate thickness requiring a detailed velocity description through the thickness. In a former work the solution making use of an in-plane-out-of-plane separated representation within the PGD - Poper Generalized Decomposition - framework was successfully accomplished when both kinematic constraints (inextensibility and in-compressibility) were introduced using a penalty formulation for circumventing the LBB constraints. However, such a formulation makes difficult the calculation on fiber tractions and compression forces, the last required in rheological characterizations. In this paper the former penalty formulation is substituted by a mixed formulation that makes use of two Lagrange multipliers, while addressing the LBB stability conditions within the separated representation framework, questions never until now addressed.

Non-CMC solutions to the Einstein constraint equations on asymptotically Euclidean manifolds with apparent horizon boundaries

NASA Astrophysics Data System (ADS)

Holst, Michael; Meier, Caleb

2015-01-01

In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary Σ. Building on recent results for both the asymptotically Euclidean and compact with boundary settings, we show the existence of far-from-CMC and near-CMC solutions to the conformal formulation of the Einstein constraints when nonlinear Robin boundary conditions are imposed on Σ, similar to those analyzed previously by Dain (2004 Class. Quantum Grav. 21 555-73), by Maxwell (2004, 2005 Commun. Math. Phys. 253 561-83), and by Holst and Tsogtgerel (2013 Class. Quantum Grav. 30 205011) as a model of black holes in various CMC settings, and by Holst et al (2013 Non-CMC solutions to the einstein constraint equations with apparent horizon boundaries arXiv:1310.2302v1) in the setting of far-from-CMC solutions on compact manifolds with boundary. These ‘marginally trapped surface’ Robin conditions ensure that the expansion scalars along null geodesics perpendicular to the boundary region Σ are non-positive, which is considered the correct mathematical model for black holes in the context of the Einstein constraint equations. Assuming a suitable form of weak cosmic censorship, the results presented in this article guarantee the existence of initial data that will evolve into a space-time containing an arbitrary number of black holes. A particularly important feature of our results are the minimal restrictions we place on the mean curvature, giving both near- and far-from-CMC results that are new.

Constraint Optimization Literature Review

DTIC Science & Technology

2015-11-01

COPs. 15. SUBJECT TERMS high-performance computing, mobile ad hoc network, optimization, constraint, satisfaction 16. SECURITY CLASSIFICATION OF: 17...Optimization Problems 1 2.1 Constraint Satisfaction Problems 1 2.2 Constraint Optimization Problems 3 3. Constraint Optimization Algorithms 9 3.1...Constraint Satisfaction Algorithms 9 3.1.1 Brute-Force search 9 3.1.2 Constraint Propagation 10 3.1.3 Depth-First Search 13 3.1.4 Local Search 18

An enhanced nonlinear damping approach accounting for system constraints in active mass dampers

NASA Astrophysics Data System (ADS)

Venanzi, Ilaria; Ierimonti, Laura; Ubertini, Filippo

2015-11-01

Active mass dampers are a viable solution for mitigating wind-induced vibrations in high-rise buildings and improve occupants' comfort. Such devices suffer particularly when they reach force saturation of the actuators and maximum extension of their stroke, which may occur in case of severe loading conditions (e.g. wind gust and earthquake). Exceeding actuators' physical limits can impair the control performance of the system or even lead to devices damage, with consequent need for repair or substitution of part of the control system. Controllers for active mass dampers should account for their technological limits. Prior work of the authors was devoted to stroke issues and led to the definition of a nonlinear damping approach, very easy to implement in practice. It consisted of a modified skyhook algorithm complemented with a nonlinear braking force to reverse the direction of the mass before reaching the stroke limit. This paper presents an enhanced version of this approach, also accounting for force saturation of the actuator and keeping the simplicity of implementation. This is achieved by modulating the control force by a nonlinear smooth function depending on the ratio between actuator's force and saturation limit. Results of a numerical investigation show that the proposed approach provides similar results to the method of the State Dependent Riccati Equation, a well-established technique for designing optimal controllers for constrained systems, yet very difficult to apply in practice.

Multiexponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models

NASA Astrophysics Data System (ADS)

de Alfaro, V.; Filippov, A. T.

2010-01-01

We study general properties of a class of two-dimensional dilaton gravity (DG) theories with potentials containing several exponential terms. We isolate and thoroughly study a subclass of such theories in which the equations of motion reduce to Toda and Liouville equations. We show that the equation parameters must satisfy a certain constraint, which we find and solve for the most general multiexponential model. It follows from the constraint that integrable Toda equations in DG theories generally cannot appear without accompanying Liouville equations. The most difficult problem in the two-dimensional Toda-Liouville (TL) DG is to solve the energy and momentum constraints. We discuss this problem using the simplest examples and identify the main obstacles to solving it analytically. We then consider a subclass of integrable two-dimensional theories where scalar matter fields satisfy the Toda equations and the two-dimensional metric is trivial. We consider the simplest case in some detail. In this example, we show how to obtain the general solution. We also show how to simply derive wavelike solutions of general TL systems. In the DG theory, these solutions describe nonlinear waves coupled to gravity and also static states and cosmologies. For static states and cosmologies, we propose and study a more general one-dimensional TL model typically emerging in one-dimensional reductions of higher-dimensional gravity and supergravity theories. We especially attend to making the analytic structure of the solutions of the Toda equations as simple and transparent as possible.

Shaping tissues by balancing active forces and geometric constraints

NASA Astrophysics Data System (ADS)

Foolen, Jasper; Yamashita, Tadahiro; Kollmannsberger, Philip

2016-02-01

The self-organization of cells into complex tissues during growth and regeneration is a combination of physical-mechanical events and biochemical signal processing. Cells actively generate forces at all stages in this process, and according to the laws of mechanics, these forces result in stress fields defined by the geometric boundary conditions of the cell and tissue. The unique ability of cells to translate such force patterns into biochemical information and vice versa sets biological tissues apart from any other material. In this topical review, we summarize the current knowledge and open questions of how forces and geometry act together on scales from the single cell to tissues and organisms, and how their interaction determines biological shape and structure. Starting with a planar surface as the simplest type of geometric constraint, we review literature on how forces during cell spreading and adhesion together with geometric constraints impact cell shape, stress patterns, and the resulting biological response. We then move on to include cell-cell interactions and the role of forces in monolayers and in collective cell migration, and introduce curvature at the transition from flat cell sheets to three-dimensional (3D) tissues. Fibrous 3D environments, as cells experience them in the body, introduce new mechanical boundary conditions and change cell behaviour compared to flat surfaces. Starting from early work on force transmission and collagen remodelling, we discuss recent discoveries on the interaction with geometric constraints and the resulting structure formation and network organization in 3D. Recent literature on two physiological scenarios—embryonic development and bone—is reviewed to demonstrate the role of the force-geometry balance in living organisms. Furthermore, the role of mechanics in pathological scenarios such as cancer is discussed. We conclude by highlighting common physical principles guiding cell mechanics, tissue patterning and matrix organization under geometric constraints across multiple length and time scales.

Semiclassical Wheeler-DeWitt equation: Solutions for long-wavelength fields

NASA Astrophysics Data System (ADS)

Salopek, D. S.; Stewart, J. M.; Parry, J.

1993-07-01

In the long-wavelength approximation, a general set of semiclassical wave functionals is given for gravity and matter interacting in 3+1 dimensions. In the long-wavelength theory, one neglects second-order spatial gradients in the energy constraint. These solutions satisfy the Hamilton-Jacobi equation, the momentum constraint, and the equation of continuity. It is essential to introduce inhomogeneities to discuss the role of time. The time hypersurface is chosen to be a homogeneous field in the wave functional. It is shown how to introduce tracer particles through a dust field χ into the dynamical system. The formalism can be used to describe stochastic inflation.

Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints

NASA Astrophysics Data System (ADS)

Burić, Nikola

2010-12-01

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent, i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory.

A universal constraint-based formulation for freely moving immersed bodies in fluids

NASA Astrophysics Data System (ADS)

Patankar, Neelesh A.

2012-11-01

Numerical simulation of moving immersed bodies in fluids is now practiced routinely. A variety of variants of these approaches have been published, most of which rely on using a background mesh for the fluid equations and tracking the body using Lagrangian points. In this talk, generalized constraint-based governing equations will be presented that provide a unified framework for various immersed body techniques. The key idea that is common to these methods is to assume that the entire fluid-body domain is a ``fluid'' and then to constrain the body domain to move in accordance with its governing equations. The immersed body can be rigid or deforming. The governing equations are developed so that they are independent of the nature of temporal or spatial discretization schemes. Specific choices of time stepping and spatial discretization then lead to techniques developed in prior literature ranging from freely moving rigid to elastic self-propelling bodies. To simulate Brownian systems, thermal fluctuations can be included in the fluid equations via additional random stress terms. Solving the fluctuating hydrodynamic equations coupled with the immersed body results in the Brownian motion of that body. The constraint-based formulation leads to fractional time stepping algorithms a la Chorin-type schemes that are suitable for fast computations of rigid or self-propelling bodies whose deformation kinematics are known. Support from NSF is gratefully acknowledged.

Solution of underdetermined systems of equations with gridded a priori constraints.

PubMed

Stiros, Stathis C; Saltogianni, Vasso

2014-01-01

The TOPINV, Topological Inversion algorithm (or TGS, Topological Grid Search) initially developed for the inversion of highly non-linear redundant systems of equations, can solve a wide range of underdetermined systems of non-linear equations. This approach is a generalization of a previous conclusion that this algorithm can be used for the solution of certain integer ambiguity problems in Geodesy. The overall approach is based on additional (a priori) information for the unknown variables. In the past, such information was used either to linearize equations around approximate solutions, or to expand systems of observation equations solved on the basis of generalized inverses. In the proposed algorithm, the a priori additional information is used in a third way, as topological constraints to the unknown n variables, leading to an R(n) grid containing an approximation of the real solution. The TOPINV algorithm does not focus on point-solutions, but exploits the structural and topological constraints in each system of underdetermined equations in order to identify an optimal closed space in the R(n) containing the real solution. The centre of gravity of the grid points defining this space corresponds to global, minimum-norm solutions. The rationale and validity of the overall approach are demonstrated on the basis of examples and case studies, including fault modelling, in comparison with SVD solutions and true (reference) values, in an accuracy-oriented approach.

Simplified Relativistic Force Transformation Equation.

ERIC Educational Resources Information Center

Stewart, Benjamin U.

1979-01-01

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic forces on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and relate it to Coulomb's law.…

DISCOS- DYNAMIC INTERACTION SIMULATION OF CONTROLS AND STRUCTURES (DEC VAX VERSION)

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1994-01-01

The Dynamic Interaction Simulation of Controls and Structure (DISCOS) program was developed for the dynamic simulation and stability analysis of passive and actively controlled spacecraft. In the use of DISCOS, the physical system undergoing analysis may be generally described as a cluster of contiguous flexible structures (bodies) that comprise a mechanical system, such as a spacecraft. The entire system (spacecraft) or portions thereof may be either spinning or nonspinning. Member bodies of the system may undergo large relative excursions, such as those of appendage deployment or rotor/ stator motion. The general system of bodies is, by its inherent nature, a feedback system in which inertial forces (such as those due to centrifugal and Coriolis acceleration) and the restoring and damping forces are motion-dependent. The system may possess a control system in which certain position and rate errors are actively controlled through the use of reaction control jets, servomotors, or momentum wheels. Bodies of the system may be interconnected by linear or nonlinear springs and dampers, by a gimbal and slider block mechanism, or by any combination of these. The DISCOS program can be used to obtain nonlinear and linearized time response of the system, interaction constant forces in the system, total system resonance properties, and frequency domain response and stability information for the system. DISCOS is probably the most powerful computational tool to date for the computer simulation of actively controlled coupled multi-flexible-body systems. The program is not easy to understand and effectively apply, but is not intended for simple problems. The DISCOS user is expected to have extensive working knowledge of rigid-body and flexible-body dynamics, finite-element techniques, numerical methods, and frequency-domain analysis. Various applications of DISCOS include simulation of the Shuttle payload deployment/retrieval mechanism, solar panel array deployment, antenna deployment, analysis of multispin satellites, and analysis of large, highly flexible satellites, including the design of attitude-control systems. The overall approach of DISCOS is unique in that any member body of the system may be flexible, and the system is not restricted to a topological tree configuration. The equations of motion are developed using the most general form of Lagrange's equations, including auxiliary nonholonomic rehenomic conditions of constraint. Lagrange multipliers are used as interaction forces/ torques to maintain prescribed constraints. Nonlinear flexible/rigid dynamic coupling effects are accounted for in unabridged fashion for individual bodies and for the total system. Elastic deformation can be represented by normal vibration modes or by any adequate series of Rayleigh functions, including 'quasi-static' displacement functions. To 'solve' Lagrange's equations of motion, the explicit form of the kinetic and potential energy functions, the dissipation function, and the form of the transformation relating ordinary Cartesian position coordinates to the generalized coordinates must be defined. The potential energy and dissipation functions for a structure are determined with standard finite-element techniques by the NASTRAN program. In order to use the computed functions, the Lagrange's equations and the system kinematic constraint equations are expressed in matrix format. These differential matrix equations are solved numerically by the DISCOS program. Provisions are included for environmental loading of the structure (spacecraft), including solar pressure, gravity gradient, and aerodynamic drag. Input to DISCOS includes topological and geometrical descriptions of the structure under analysis, initial conditions, control system descriptions, and NASTRAN-derived structural matrices. Specialized routines are supplied that read the input data and redimension the DISCOS programs to minimize core requirements. Output includes an extensive list of calculated parameters for each body of the structure, system state vector and its time derivatives, euler angles and position coordinates and their time derivatives, control system variables and their time derivatives, and various system parameters at a given simulation time. For linearized system analysis, output includes the various transfer matrices, eigenvectors, and calculated eigenvalues. The DISCOS program is available by license for a period of ten (10) years to approved licensees. The licensed program product delivered includes the source code and supporting documentation. Additional documentation may be purchased separately at any time. The IBM version of DISCOS is written in FORTRAN IV for batch execution and has been implemented on an IBM 360 series computer under OS with a central memory requirement of approximately 1,100K of 8 bit bytes. The DEC VAX version of DISCOS is written in FORTRAN for batch execution and has been implemented on a DEC VAX series computer under VMS. For plotted output a SC4020 plotting system is required. DISCOS was developed on the IBM in 1978 and was adapted (with enhancements) to the DEC VAX in 1982.

DISCOS- DYNAMIC INTERACTION SIMULATION OF CONTROLS AND STRUCTURES (IBM VERSION)

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1994-01-01

The Dynamic Interaction Simulation of Controls and Structure (DISCOS) program was developed for the dynamic simulation and stability analysis of passive and actively controlled spacecraft. In the use of DISCOS, the physical system undergoing analysis may be generally described as a cluster of contiguous flexible structures (bodies) that comprise a mechanical system, such as a spacecraft. The entire system (spacecraft) or portions thereof may be either spinning or nonspinning. Member bodies of the system may undergo large relative excursions, such as those of appendage deployment or rotor/ stator motion. The general system of bodies is, by its inherent nature, a feedback system in which inertial forces (such as those due to centrifugal and Coriolis acceleration) and the restoring and damping forces are motion-dependent. The system may possess a control system in which certain position and rate errors are actively controlled through the use of reaction control jets, servomotors, or momentum wheels. Bodies of the system may be interconnected by linear or nonlinear springs and dampers, by a gimbal and slider block mechanism, or by any combination of these. The DISCOS program can be used to obtain nonlinear and linearized time response of the system, interaction constant forces in the system, total system resonance properties, and frequency domain response and stability information for the system. DISCOS is probably the most powerful computational tool to date for the computer simulation of actively controlled coupled multi-flexible-body systems. The program is not easy to understand and effectively apply, but is not intended for simple problems. The DISCOS user is expected to have extensive working knowledge of rigid-body and flexible-body dynamics, finite-element techniques, numerical methods, and frequency-domain analysis. Various applications of DISCOS include simulation of the Shuttle payload deployment/retrieval mechanism, solar panel array deployment, antenna deployment, analysis of multispin satellites, and analysis of large, highly flexible satellites, including the design of attitude-control systems. The overall approach of DISCOS is unique in that any member body of the system may be flexible, and the system is not restricted to a topological tree configuration. The equations of motion are developed using the most general form of Lagrange's equations, including auxiliary nonholonomic rehenomic conditions of constraint. Lagrange multipliers are used as interaction forces/ torques to maintain prescribed constraints. Nonlinear flexible/rigid dynamic coupling effects are accounted for in unabridged fashion for individual bodies and for the total system. Elastic deformation can be represented by normal vibration modes or by any adequate series of Rayleigh functions, including 'quasi-static' displacement functions. To 'solve' Lagrange's equations of motion, the explicit form of the kinetic and potential energy functions, the dissipation function, and the form of the transformation relating ordinary Cartesian position coordinates to the generalized coordinates must be defined. The potential energy and dissipation functions for a structure are determined with standard finite-element techniques by the NASTRAN program. In order to use the computed functions, the Lagrange's equations and the system kinematic constraint equations are expressed in matrix format. These differential matrix equations are solved numerically by the DISCOS program. Provisions are included for environmental loading of the structure (spacecraft), including solar pressure, gravity gradient, and aerodynamic drag. Input to DISCOS includes topological and geometrical descriptions of the structure under analysis, initial conditions, control system descriptions, and NASTRAN-derived structural matrices. Specialized routines are supplied that read the input data and redimension the DISCOS programs to minimize core requirements. Output includes an extensive list of calculated parameters for each body of the structure, system state vector and its time derivatives, euler angles and position coordinates and their time derivatives, control system variables and their time derivatives, and various system parameters at a given simulation time. For linearized system analysis, output includes the various transfer matrices, eigenvectors, and calculated eigenvalues. The DISCOS program is available by license for a period of ten (10) years to approved licensees. The licensed program product delivered includes the source code and supporting documentation. Additional documentation may be purchased separately at any time. The IBM version of DISCOS is written in FORTRAN IV for batch execution and has been implemented on an IBM 360 series computer under OS with a central memory requirement of approximately 1,100K of 8 bit bytes. The DEC VAX version of DISCOS is written in FORTRAN for batch execution and has been implemented on a DEC VAX series computer under VMS. For plotted output a SC4020 plotting system is required. DISCOS was developed on the IBM in 1978 and was adapted (with enhancements) to the DEC VAX in 1982.

Covariant Hamiltonian tetrad approach to numerical relativity

NASA Astrophysics Data System (ADS)

Hamilton, Andrew J. S.

2017-12-01

A Hamiltonian approach to the equations of general relativity is proposed using the powerful mathematical language of multivector-valued differential forms. In the approach, the gravitational coordinates are the 12 spatial components of the line interval (the vierbein) including their antisymmetric parts, and their 12 conjugate momenta. A feature of the proposed formalism is that it allows Lorentz gauge freedoms to be imposed on the Lorentz connections rather than on the vierbein, which may facilitate numerical integration in some challenging problems. The 40 Hamilton's equations comprise 12 +12 =24 equations of motion, ten constraint equations (first class constraints, which must be arranged on the initial hypersurface of constant time, but which are guaranteed thereafter by conservation laws), and six identities (second class constraints). The six identities define a trace-free spatial tensor that is the gravitational analog of the magnetic field of electromagnetism. If the gravitational magnetic field is promoted to an independent field satisfying its own equation of motion, then the system becomes the Wahlquist-Estabrook-Buchman-Bardeen (WEBB) system, which is known to be strongly hyperbolic. Some other approaches, including Arnowitt-Deser-Misner, Baumgarte-Shapiro-Shibata-Nakamura, WEBB, and loop quantum gravity, are translated into the language of multivector-valued forms, bringing out their underlying mathematical structure.

A New Empirical Constraint on the Prevalence of Technological Species in the Universe

NASA Astrophysics Data System (ADS)

Frank, A.; Sullivan, W. T., III

2016-05-01

In this article, we address the cosmic frequency of technological species. Recent advances in exoplanet studies provide strong constraints on all astrophysical terms in the Drake equation. Using these and modifying the form and intent of the Drake equation, we set a firm lower bound on the probability that one or more technological species have evolved anywhere and at any time in the history of the observable Universe. We find that as long as the probability that a habitable zone planet develops a technological species is larger than ˜10-24, humanity is not the only time technological intelligence has evolved. This constraint has important scientific and philosophical consequences.

Einstein Equations Under Polarized U (1) Symmetry in an Elliptic Gauge

NASA Astrophysics Data System (ADS)

Huneau, Cécile; Luk, Jonathan

2018-06-01

We prove local existence of solutions to the Einstein-null dust system under polarized U (1) symmetry in an elliptic gauge. Using in particular the previous work of the first author on the constraint equations, we show that one can identify freely prescribable data, solve the constraints equations, and construct a unique local in time solution in an elliptic gauge. Our main motivation for this work, in addition to merely constructing solutions in an elliptic gauge, is to provide a setup for our companion paper in which we study high frequency backreaction for the Einstein equations. In that work, the elliptic gauge we consider here plays a crucial role to handle high frequency terms in the equations. The main technical difficulty in the present paper, in view of the application in our companion paper, is that we need to build a framework consistent with the solution being high frequency, and therefore having large higher order norms. This difficulty is handled by exploiting a reductive structure in the system of equations.

Geochemical mole-balance modeling with uncertain data

USGS Publications Warehouse

Parkhurst, David L.

1997-01-01

Geochemical mole-balance models are sets of chemical reactions that quantitatively account for changes in the chemical and isotopic composition of water along a flow path. A revised mole-balance formulation that includes an uncertainty term for each chemical and isotopic datum is derived. The revised formulation is comprised of mole-balance equations for each element or element redox state, alkalinity, electrons, solvent water, and each isotope; a charge-balance equation and an equation that relates the uncertainty terms for pH, alkalinity, and total dissolved inorganic carbon for each aqueous solution; inequality constraints on the size of the uncertainty terms; and inequality constraints on the sign of the mole transfer of reactants. The equations and inequality constraints are solved by a modification of the simplex algorithm combined with an exhaustive search for unique combinations of aqueous solutions and reactants for which the equations and inequality constraints can be solved and the uncertainty terms minimized. Additional algorithms find only the simplest mole-balance models and determine the ranges of mixing fractions for each solution and mole transfers for each reactant that are consistent with specified limits on the uncertainty terms. The revised formulation produces simpler and more robust mole-balance models and allows the significance of mixing fractions and mole transfers to be evaluated. In an example from the central Oklahoma aquifer, inclusion of up to 5% uncertainty in the chemical data can reduce the number of reactants in mole-balance models from seven or more to as few as three, these being cation exchange, dolomite dissolution, and silica precipitation. In another example from the Madison aquifer, inclusion of the charge-balance constraint requires significant increases in the mole transfers of calcite, dolomite, and organic matter, which reduce the estimated maximum carbon 14 age of the sample by about 10,000 years, from 22,700 years to 12,600 years.

Full particle simulations of quasi-perpendicular shocks

NASA Astrophysics Data System (ADS)

Lembège, B.

This tutorial-style review is dedicated to the different strategies and constraints used for analysing the dynamics of a collisionless shocks with full particle simulations. Main results obtained with such simulations can be found in published materials (recent references are provided in this text); these will be only quoted herein in order to illustrate a few aspects of these simulations. Thanks to the large improvement of super computers, full particle simulations reveal to be quite helpful for analyzing in details the dynamics of collisionless shocks. The main characteristics of such codes can be shortly reminded as follows: one resolves the full set of Poisson and Maxwell's equations without any approximation. Two approaches are commonly used for resolving this equation's set, more precisely the space derivatives: (i) the finite difference approach and (ii) the use of FFT's (Fast Fourier Transform). Two advantages of approach (ii) are that FFT's are highly optimized in supercomputers libraries, and these allow to separate all fields components into two groups: the longitudinal electrostatic component El (solution of Poisson equation) and the transverse electromagnetic components Et and Bt solutions of the Maxwell's equations (so called "fields pusher"). Such a separation is quite helpful in the post processing stage necessary for the data analysis, as will be explained in the presentation. both ions and electrons populations are treated as individual finite-size particles and suffer the effects of all fields via the Lorentz force, so called "particle pusher", which is applied to each particle. Because of the large number of particles commonly used, the particle pusher represents the most expensive part of the calculations on which most efforts of optimisation needs to be performed (in terms of "vectorisation" or of "parallelism"). Relativistic effects may be included in this force via the use of particle momemtum. Each particle has three velocity components (vx, vy, vz), but may have 1, 2 or 3 space coordinates (x, y, z) according to the dimension of the code of concern.

Dynamics modelling and Hybrid Suppression Control of space robots performing cooperative object manipulation

NASA Astrophysics Data System (ADS)

Zarafshan, P.; Moosavian, S. Ali A.

2013-10-01

Dynamics modelling and control of multi-body space robotic systems composed of rigid and flexible elements is elaborated here. Control of such systems is highly complicated due to severe under-actuated condition caused by flexible elements, and an inherent uneven nonlinear dynamics. Therefore, developing a compact dynamics model with the requirement of limited computations is extremely useful for controller design, also to develop simulation studies in support of design improvement, and finally for practical implementations. In this paper, the Rigid-Flexible Interactive dynamics Modelling (RFIM) approach is introduced as a combination of Lagrange and Newton-Euler methods, in which the motion equations of rigid and flexible members are separately developed in an explicit closed form. These equations are then assembled and solved simultaneously at each time step by considering the mutual interaction and constraint forces. The proposed approach yields a compact model rather than common accumulation approach that leads to a massive set of equations in which the dynamics of flexible elements is united with the dynamics equations of rigid members. To reveal such merits of this new approach, a Hybrid Suppression Control (HSC) for a cooperative object manipulation task will be proposed, and applied to usual space systems. A Wheeled Mobile Robotic (WMR) system with flexible appendages as a typical space rover is considered which contains a rigid main body equipped with two manipulating arms and two flexible solar panels, and next a Space Free Flying Robotic system (SFFR) with flexible members is studied. Modelling verification of these complicated systems is vigorously performed using ANSYS and ADAMS programs, while the limited computations of RFIM approach provides an efficient tool for the proposed controller design. Furthermore, it will be shown that the vibrations of the flexible solar panels results in disturbing forces on the base which may produce undesirable errors and perturb the object manipulation task. So, it is shown that these effects can be significantly eliminated by the proposed Hybrid Suppression Control algorithm.

Hamiltonian structure of Dubrovin's equation of associativity in 2-d topological field theory

NASA Astrophysics Data System (ADS)

Galvão, C. A. P.; Nutku, Y.

1996-12-01

A third order Monge-Ampère type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac's theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra.

Finite element solution of optimal control problems with state-control inequality constraints

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1992-01-01

It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.

A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

NASA Astrophysics Data System (ADS)

Li, Jinquan; Feng, Shuang; Mi, Honghai

In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.

Calculation of force and power during bench throws using a Smith machine: the importance of considering the effect of counterweights.

PubMed

Kobayashi, Y; Narazaki, K; Akagi, R; Nakagaki, K; Kawamori, N; Ohta, K

2013-09-01

For achieving accurate and safe measurements of the force and power exerted on a load during resistance exercise, the Smith machine has been used instead of free weights. However, because some Smith machines possess counterweights, the equation for the calculation of force and power in this system should be different from the one used for free weights. The purpose of this investigation was to calculate force and power using an equation derived from a dynamic equation for a Smith machine with counterweights and to determine the differences in force and power calculated using 2 different equations. One equation was established ignoring the effect of the counterweights (Method 1). The other equation was derived from a dynamic equation for a barbell and counterweight system (Method 2). 9 female collegiate judo athletes performed bench throws using a Smith machine with a counterweight at 6 different loading conditions. Barbell displacement was recorded using a linear position transducer. The force and power were subsequently calculated by Methods 1 and 2. The results showed that the mean and peak power and force in Method 1 were significantly lower relative to those of Method 2 under all loading conditions. These results indicate that the mean and peak power and force during bench throwing using a Smith machine with counterweights would be underestimated when the calculations used to determine these parameters do not account for the effect of counterweights. © Georg Thieme Verlag KG Stuttgart · New York.

Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints

NASA Astrophysics Data System (ADS)

Krasovskii, A. A.; Lebedev, P. D.; Tarasyev, A. M.

2017-05-01

We consider a neoclassical (economic) growth model. A nonlinear Ramsey equation, modeling capital dynamics, in the case of Cobb-Douglas production function is reduced to the linear differential equation via a Bernoulli substitution. This considerably facilitates the search for a solution to the optimal growth problem with logarithmic preferences. The study deals with solving the corresponding infinite horizon optimal control problem. We consider a vector field of the Hamiltonian system in the Pontryagin maximum principle, taking into account control constraints. We prove the existence of two alternative steady states, depending on the constraints. A proposed algorithm for constructing growth trajectories combines methods of open-loop control and closed-loop regulatory control. For some levels of constraints and initial conditions, a closed-form solution is obtained. We also demonstrate the impact of technological change on the economic equilibrium dynamics. Results are supported by computer calculations.

State-constrained booster trajectory solutions via finite elements and shooting

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.; Seywald, Hans

1993-01-01

This paper presents an extension of a FEM formulation based on variational principles. A general formulation for handling internal boundary conditions and discontinuities in the state equations is presented, and the general formulation is modified for optimal control problems subject to state-variable inequality constraints. Solutions which only touch the state constraint and solutions which have a boundary arc of finite length are considered. Suitable shape and test functions are chosen for a FEM discretization. All element quadrature (equivalent to one-point Gaussian quadrature over each element) may be done in closed form. The final form of the algebraic equations is then derived. A simple state-constrained problem is solved. Then, for a practical application of the use of the FEM formulation, a launch vehicle subject to a dynamic pressure constraint (a first-order state inequality constraint) is solved. The results presented for the launch-vehicle trajectory have some interesting features, including a touch-point solution.

Numerical Investigation of Two-Phase Flows With Charged Droplets in Electrostatic Field

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1996-01-01

A numerical method to solve two-phase turbulent flows with charged droplets in an electrostatic field is presented. The ensemble-averaged Navier-Stokes equations and the electrostatic potential equation are solved using a finite volume method. The transitional turbulence field is described using multiple-time-scale turbulence equations. The equations of motion of droplets are solved using a Lagrangian particle tracking scheme, and the inter-phase momentum exchange is described by the Particle-In-Cell scheme. The electrostatic force caused by an applied electrical potential is calculated using the electrostatic field obtained by solving a Laplacian equation and the force exerted by charged droplets is calculated using the Coulombic force equation. The method is applied to solve electro-hydrodynamic sprays. The calculated droplet velocity distributions for droplet dispersions occurring in a stagnant surrounding are in good agreement with the measured data. For droplet dispersions occurring in a two-phase flow, the droplet trajectories are influenced by aerodynamic forces, the Coulombic force, and the applied electrostatic potential field.

Spatial averaging of a dissipative particle dynamics model for active suspensions

NASA Astrophysics Data System (ADS)

Panchenko, Alexander; Hinz, Denis F.; Fried, Eliot

2018-03-01

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving-Kirkwood-Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.

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.

Technique to eliminate computational instability in multibody simulations employing the Lagrange multiplier

NASA Technical Reports Server (NTRS)

Watts, G.

1992-01-01

A programming technique to eliminate computational instability in multibody simulations that use the Lagrange multiplier is presented. The computational instability occurs when the attached bodies drift apart and violate the constraints. The programming technique uses the constraint equation, instead of integration, to determine the coordinates that are not independent. Although the equations of motion are unchanged, a complete derivation of the incorporation of the Lagrange multiplier into the equation of motion for two bodies is presented. A listing of a digital computer program which uses the programming technique to eliminate computational instability is also presented. The computer program simulates a solid rocket booster and parachute connected by a frictionless swivel.

SC-GRAPPA: Self-constraint noniterative GRAPPA reconstruction with closed-form solution.

PubMed

Ding, Yu; Xue, Hui; Ahmad, Rizwan; Ting, Samuel T; Simonetti, Orlando P

2012-12-01

Parallel MRI (pMRI) reconstruction techniques are commonly used to reduce scan time by undersampling the k-space data. GRAPPA, a k-space based pMRI technique, is widely used clinically because of its robustness. In GRAPPA, the missing k-space data are estimated by solving a set of linear equations; however, this set of equations does not take advantage of the correlations within the missing k-space data. All k-space data in a neighborhood acquired from a phased-array coil are correlated. The correlation can be estimated easily as a self-constraint condition, and formulated as an extra set of linear equations to improve the performance of GRAPPA. The authors propose a modified k-space based pMRI technique called self-constraint GRAPPA (SC-GRAPPA) which combines the linear equations of GRAPPA with these extra equations to solve for the missing k-space data. Since SC-GRAPPA utilizes a least-squares solution of the linear equations, it has a closed-form solution that does not require an iterative solver. The SC-GRAPPA equation was derived by incorporating GRAPPA as a prior estimate. SC-GRAPPA was tested in a uniform phantom and two normal volunteers. MR real-time cardiac cine images with acceleration rate 5 and 6 were reconstructed using GRAPPA and SC-GRAPPA. SC-GRAPPA showed a significantly lower artifact level, and a greater than 10% overall signal-to-noise ratio (SNR) gain over GRAPPA, with more significant SNR gain observed in low-SNR regions of the images. SC-GRAPPA offers improved pMRI reconstruction, and is expected to benefit clinical imaging applications in the future.

Equilibrium theory for braided elastic filaments

NASA Astrophysics Data System (ADS)

van der Heijden, Gert

Motivated by supercoiling of DNA and other filamentous structures, we formulate a theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. Unlike in previous work no assumption is made on the shape of the contact curve. Rather, this shape is found as part of the solution. The theory is developed in terms of a moving frame of directors attached to one of the strands with one of the directors pointing to the position of the other strand. The constant-distance constraint is automatically satisfied by the introduction of what we call braid strains. The price we pay is that the potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Simple analytical cases are discussed first and used as starting solutions in parameter continuation studies to compute classes of both open and closed (linked or knotted) braid solutions.

Theory of equilibria of elastic braids with applications to DNA supercoiling

NASA Astrophysics Data System (ADS)

van der Heijden, Gert; Starostin, Eugene

2014-03-01

Motivated by supercoiling of DNA and other filamentous structures, we formulate a new theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. Unlike in previous work no assumption is made on the shape of the contact curve. Rather, this shape is solved for. The theory is developed in terms of a moving frame of directors attached to one of the strands with one of the directors pointing to the position of the other strand. The constant-distance constraint is automatically satisfied by the introduction of what we call braid strains. The price we pay is that the potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Both open braid and closed braid solutions (links and knots) are computed and current applications to DNA supercoiling are discussed. Research supported by EPSRC and HFSP.

The Specific Analysis of Structural Equation Models

ERIC Educational Resources Information Center

McDonald, Roderick P.

2004-01-01

Conventional structural equation modeling fits a covariance structure implied by the equations of the model. This treatment of the model often gives misleading results because overall goodness of fit tests do not focus on the specific constraints implied by the model. An alternative treatment arising from Pearl's directed acyclic graph theory…

Solutions of the KPI equation with smooth initial data

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A.

1994-06-01

The solution $u(t,x,y)$ of the Kadomtsev--Petviashvili I (KPI) equation with given initial data $u(0,x,y)$ belonging to the Schwartz space is considered. No additional special constraints, usually considered in literature, as $\\int\\!dx\\,u(0,x,y)=0$ are required to be satisfied by the initial data. The problem is completely solved in the framework of the spectral transform theory and it is shown that $u(t,x,y)$ satisfies a special evolution version of the KPI equation and that, in general, $\\partial_t u(t,x,y)$ has different left and right limits at the initial time $t=0$. The conditions of the type $\\int\\!dx\\,u(t,x,y)=0$, $\\int\\!dx\\,xu_y(t,x,y)=0$ and so on (first, second, etc. `constraints') are dynamically generated by the evolution equation for $t\

Corrigendum: New Form of Kane's Equations of Motion for Constrained Systems

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Bajodah, Abdulrahman H.; Hodges, Dewey H.; Chen, Ye-Hwa

2007-01-01

A correction to the previously published article "New Form of Kane's Equations of Motion for Constrained Systems" is presented. Misuse of the transformation matrix between time rates of change of the generalized coordinates and generalized speeds (sometimes called motion variables) resulted in a false conclusion concerning the symmetry of the generalized inertia matrix. The generalized inertia matrix (sometimes referred to as the mass matrix) is in fact symmetric and usually positive definite when one forms nonminimal Kane's equations for holonomic or simple nonholonomic systems, systems subject to nonlinear nonholonomic constraints, and holonomic or simple nonholonomic systems subject to impulsive constraints according to Refs. 1, 2, and 3, respectively. The mass matrix is of course symmetric when one forms minimal equations for holonomic or simple nonholonomic systems using Kane s method as set forth in Ref. 4.

EQUATION OF STATE FOR NUCLEONIC AND HYPERONIC NEUTRON STARS WITH MASS AND RADIUS CONSTRAINTS

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

Tolos, Laura; Centelles, Mario; Ramos, Angels

We obtain a new equation of state for the nucleonic and hyperonic inner core of neutron stars that fulfils the 2 M {sub ⊙} observations as well as the recent determinations of stellar radii below 13 km. The nucleonic equation of state is obtained from a new parameterization of the FSU2 relativistic mean-field functional that satisfies these latest astrophysical constraints and, at the same time, reproduces the properties of nuclear matter and finite nuclei while fulfilling the restrictions on high-density matter deduced from heavy-ion collisions. On the one hand, the equation of state of neutron star matter is softened aroundmore » saturation density, which increases the compactness of canonical neutron stars leading to stellar radii below 13 km. On the other hand, the equation of state is stiff enough at higher densities to fulfil the 2 M {sub ⊙} limit. By a slight modification of the parameterization, we also find that the constraints of 2 M {sub ⊙} neutron stars with radii around 13 km are satisfied when hyperons are considered. The inclusion of the high magnetic fields present in magnetars further stiffens the equation of state. Hyperonic magnetars with magnetic fields in the surface of ∼10{sup 15} G and with values of ∼10{sup 18} G in the interior can reach maximum masses of 2 M {sub ⊙} with radii in the 12–13 km range.« less

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chiou, Jin-Chern

1990-01-01

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state

NASA Astrophysics Data System (ADS)

Alsing, Justin; Silva, Hector O.; Berti, Emanuele

2018-04-01

We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multi-modality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be 2.0M⊙ < mmax < 2.2M⊙ (68%), 2.0M⊙ < mmax < 2.6M⊙ (90%), and evidence for a cut-off is robust against the choice of model for the mass distribution and to removing the most extreme (highest mass) neutron stars from the dataset. If this sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts constraints on the equation of state. For a set of realistic equations of state that support >2M⊙ neutron stars, our inference of mmax is able to distinguish between models at odds ratios of up to 12: 1, whilst under a flexible piecewise polytropic equation of state model our maximum mass measurement improves constraints on the pressure at 3 - 7 × the nuclear saturation density by ˜30 - 50% compared to simply requiring mmax > 2M⊙. We obtain a lower bound on the maximum sound speed attained inside the neutron star of c_s^max > 0.63c (99.8%), ruling out c_s^max < c/√{3} at high significance. Our constraints on the maximum neutron star mass strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.

Analysis of the Constraint Joint Loading in the Thumb During Pipetting.

PubMed

Wu, John Z; Sinsel, Erik W; Zhao, Kristin D; An, Kai-Nan; Buczek, Frank L

2015-08-01

Dynamic loading on articular joints is essential for the evaluation of the risk of the articulation degeneration associated with occupational activities. In the current study, we analyzed the dynamic constraint loading for the thumb during pipetting. The constraint loading is considered as the loading that has to be carried by the connective tissues of the joints (i.e., the cartilage layer and the ligaments) to maintain the kinematic constraints of the system. The joint loadings are solved using a classic free-body approach, using the external loading and muscle forces, which were obtained in an inverse dynamic approach combined with an optimization procedure in anybody. The constraint forces in the thumb joint obtained in the current study are compared with those obtained in the pinch and grasp tests in a previous study (Cooney and Chao, 1977, "Biomechanical Analysis of Static Forces in the Thumb During Hand Function," J. Bone Joint Surg. Am., 59(1), pp. 27-36). The maximal compression force during pipetting is approximately 83% and 60% greater than those obtained in the tip pinch and key pinch, respectively, while substantially smaller than that obtained during grasping. The maximal lateral shear force is approximately six times, 32 times, and 90% greater than those obtained in the tip pinch, key pinch, and grasp, respectively. The maximal dorsal shear force during pipetting is approximately 3.2 and 1.4 times greater than those obtained in the tip pinch and key pinch, respectively, while substantially smaller than that obtained during grasping. Our analysis indicated that the thumb joints are subjected to repetitive, intensive loading during pipetting, compared to other daily activities.

Levels of Simplification. The Use of Assumptions, Restrictions, and Constraints in Engineering Analysis.

ERIC Educational Resources Information Center

Whitaker, Stephen

1988-01-01

Describes the use of assumptions, restrictions, and constraints in solving difficult analytical problems in engineering. Uses the Navier-Stokes equations as examples to demonstrate use, derivations, advantages, and disadvantages of the technique. (RT)

A New Empirical Constraint on the Prevalence of Technological Species in the Universe.

PubMed

Frank, A; Sullivan, W T

2016-05-01

In this article, we address the cosmic frequency of technological species. Recent advances in exoplanet studies provide strong constraints on all astrophysical terms in the Drake equation. Using these and modifying the form and intent of the Drake equation, we set a firm lower bound on the probability that one or more technological species have evolved anywhere and at any time in the history of the observable Universe. We find that as long as the probability that a habitable zone planet develops a technological species is larger than ∼10(-24), humanity is not the only time technological intelligence has evolved. This constraint has important scientific and philosophical consequences. Life-Intelligence-Extraterrestrial life. Astrobiology 2016, 359-362.

Updated observational constraints on quintessence dark energy models

NASA Astrophysics Data System (ADS)

Durrive, Jean-Baptiste; Ooba, Junpei; Ichiki, Kiyotomo; Sugiyama, Naoshi

2018-02-01

The recent GW170817 measurement favors the simplest dark energy models, such as a single scalar field. Quintessence models can be classified in two classes, freezing and thawing, depending on whether the equation of state decreases towards -1 or departs from it. In this paper, we put observational constraints on the parameters governing the equations of state of tracking freezing, scaling freezing, and thawing models using updated data, from the Planck 2015 release, joint light-curve analysis, and baryonic acoustic oscillations. Because of the current tensions on the value of the Hubble parameter H0, unlike previous authors, we let this parameter vary, which modifies significantly the results. Finally, we also derive constraints on neutrino masses in each of these scenarios.

Monocular Visual Odometry Based on Trifocal Tensor Constraint

NASA Astrophysics Data System (ADS)

Chen, Y. J.; Yang, G. L.; Jiang, Y. X.; Liu, X. Y.

2018-02-01

For the problem of real-time precise localization in the urban street, a monocular visual odometry based on Extend Kalman fusion of optical-flow tracking and trifocal tensor constraint is proposed. To diminish the influence of moving object, such as pedestrian, we estimate the motion of the camera by extracting the features on the ground, which improves the robustness of the system. The observation equation based on trifocal tensor constraint is derived, which can form the Kalman filter alone with the state transition equation. An Extend Kalman filter is employed to cope with the nonlinear system. Experimental results demonstrate that, compares with Yu’s 2-step EKF method, the algorithm is more accurate which meets the needs of real-time accurate localization in cities.

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

Krasnobaeva, L. A., E-mail: kla1983@mail.ru; Siberian State Medical University Moscowski Trakt 2, Tomsk, 634050; Shapovalov, A. V.

Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on dynamics local conformational perturbations (kink) propagating along the DNA molecule is investigated. Such waves have an important role in the regulation of important biological processes in living systems at the molecular level. As a dynamic model of DNA was used a modified sine-Gordon equation, simulating the rotational oscillations of bases in one of the chains DNA. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the frameworkmore » of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker– Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine–Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker–Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum.« less

Interval oscillation criteria for second-order forced impulsive delay differential equations with damping term.

PubMed

Thandapani, Ethiraju; Kannan, Manju; Pinelas, Sandra

2016-01-01

In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result.

Redundancy of constraints in the classical and quantum theories of gravitation.

NASA Technical Reports Server (NTRS)

Moncrief, V.

1972-01-01

It is shown that in Dirac's version of the quantum theory of gravitation, the Hamiltonian constraints are greatly redundant. If the Hamiltonian constraint condition is satisfied at one point on the underlying, closed three-dimensional manifold, then it is automatically satisfied at every point, provided only that the momentum constraints are everywhere satisfied. This permits one to replace the usual infinity of Hamiltonian constraints by a single condition which may be taken in the form of an integral over the manifold. Analogous theorems are given for the classical Einstein Hamilton-Jacobi equations.

Geomagnetic main field modeling using magnetohydrodynamic constraints

NASA Technical Reports Server (NTRS)

Estes, R. H.

1985-01-01

The influence of physical constraints are investigated which may be approximately satisfied by the Earth's liquid core on models of the geomagnetic main field and its secular variation. A previous report describes the methodology used to incorporate nonlinear equations of constraint into the main field model. The application of that methodology to the GSFC 12/83 field model to test the frozen-flux hypothesis and the usefulness of incorporating magnetohydrodynamic constraints for obtaining improved geomagnetic field models is described.

Momentum constraints as integrability conditions for the Hamiltonian constraint in general relativity.

NASA Technical Reports Server (NTRS)

Moncrief, V.; Teitelboim, C.

1972-01-01

It is shown that if the Hamiltonian constraint of general relativity is imposed as a restriction on the Hamilton principal functional in the classical theory, or on the state functional in the quantum theory, then the momentum constraints are automatically satisfied. This result holds both for closed and open spaces and it means that the full content of the theory is summarized by a single functional equation of the Tomonaga-Schwinger type.

Transient response for interaction of two dynamic bodies

NASA Technical Reports Server (NTRS)

Prabhakar, A.; Palermo, L. G.

1987-01-01

During the launch sequence of any space vehicle complicated boundary interactions occur between the vehicle and the launch stand. At the start of the sequence large forces exist between the two; contact is then broken in a short but finite time which depends on the release mechanism. The resulting vehicle response produces loads which are very high and often form the design case. It is known that the treatment of the launch pad as a second dynamic body is significant for an accurate prediction of launch response. A technique was developed for obtaining loads generated by the launch transient with the effect of pad dynamics included. The method solves uncoupled vehicle and pad equations of motion. The use of uncoupled models allows the simulation of vehicle launch in a single computer run. Modal formulation allows a closed-form solution to be written, eliminating any need for a numerical integration algorithm. When the vehicle is on the pad the uncoupled pad and vehicle equations have to be modified to account for the constraints they impose on each other. This necessitates the use of an iterative procedure to converge to a solution, using Lagrange multipliers to apply the required constraints. As the vehicle lifts off the pad the coupling between the vehicle and the pad is eliminated point by point until the vehicle flies free. Results obtained by this method were shown to be in good agreement with observed loads and other analysis methods. The resulting computer program is general, and was used without modification to solve a variety of contact problems.

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble.

PubMed

Gross, Markus; Gambassi, Andrea; Dietrich, S

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ε=4-d, where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ε and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

Statistical field theory with constraints: Application to critical Casimir forces in the canonical ensemble

NASA Astrophysics Data System (ADS)

Gross, Markus; Gambassi, Andrea; Dietrich, S.

2017-08-01

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ɛ =4 -d , where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ɛ and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.

Quasi-generalized variables

NASA Technical Reports Server (NTRS)

Baumgarten, J.; Ostermeyer, G. P.

1986-01-01

The numerical solution of a system of differential and algebraic equations is difficult, due to the appearance of numerical instabilities. A method is presented here which permits numerical solutions of such a system to be obtained which satisfy the algebraic constraint equations exactly without reducing the order of the differential equations. The method is demonstrated using examples from mechanics.

Analysis of magnetic fields using variational principles and CELAS2 elements

NASA Technical Reports Server (NTRS)

Frye, J. W.; Kasper, R. G.

1977-01-01

Prospective techniques for analyzing magnetic fields using NASTRAN are reviewed. A variational principle utilizing a vector potential function is presented which has as its Euler equations, the required field equations and boundary conditions for static magnetic fields including current sources. The need for an addition to this variational principle of a constraint condition is discussed. Some results using the Lagrange multiplier method to apply the constraint and CELAS2 elements to simulate the matrices are given. Practical considerations of using large numbers of CELAS2 elements are discussed.

Flutter and Forced Response Analyses of Cascades using a Two-Dimensional Linearized Euler Solver

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Srivastava, R.; Mehmed, O.

1999-01-01

Flutter and forced response analyses for a cascade of blades in subsonic and transonic flow is presented. The structural model for each blade is a typical section with bending and torsion degrees of freedom. The unsteady aerodynamic forces due to bending and torsion motions. and due to a vortical gust disturbance are obtained by solving unsteady linearized Euler equations. The unsteady linearized equations are obtained by linearizing the unsteady nonlinear equations about the steady flow. The predicted unsteady aerodynamic forces include the effect of steady aerodynamic loading due to airfoil shape, thickness and angle of attack. The aeroelastic equations are solved in the frequency domain by coupling the un- steady aerodynamic forces to the aeroelastic solver MISER. The present unsteady aerodynamic solver showed good correlation with published results for both flutter and forced response predictions. Further improvements are required to use the unsteady aerodynamic solver in a design cycle.

Numerical simulations of Kadomtsev-Petviashvili soliton interactions

NASA Astrophysics Data System (ADS)

Infeld, E.; Senatorski, A.; Skorupski, A. A.

1995-04-01

The Kadomtsev-Petviashvili equation generalizes that of Korteweg and de Vries to two space dimensions and arises in various weakly dispersive media. Two very different species of soliton solutions are known for one variant, KPI. The first species to be discovered are line solitons, the second are two dimensional lumps. This paper describes numerical simulations, consistent with all constraints of the equation, in which very distorted line solitons break up into smaller line solitons and arrays of lumps. The arrays can interact with one another. In some cases, aspects of the results of the simulations can be understood in the light of specially constructed exact solutions. Simulations in which initial conditions fail to satisfy the constraints of the equation are also described.

Gauge covariance of the fermion Schwinger–Dyson equation in QED

DOE PAGES

Jia, Shaoyang; Pennington, Michael R.

2017-03-27

Any practical application of the Schwinger–Dyson equations to the study of n-point Green's functions in a strong coupling field theory requires truncations. In the case of QED, the gauge covariance, governed by the Landau–Khalatnikov–Fradkin transformations (LKFT), provides a unique constraint on such truncation. Here, by using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the LKFT are linear operations on the spectral densities. We formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gaugemore » covariance of any viable truncation of the Schwinger–Dyson equation for the fermion 2-point function.« less

Free geometric adjustment of the SECOR Equatorial Network (Solution SECOR-27)

NASA Technical Reports Server (NTRS)

Mueller, I. I.; Kumar, M.; Soler, T.

1973-01-01

The basic purpose of this experiment is to compute reduced normal equations from the observational data of the SECOR Equatorial Network obtained from DMA/Topographic Center, D/Geodesy, Geosciences Div. Washington, D.C. These reduced normal equations are to be combined with reduced normal equations of other satellite networks of the National Geodetic Satellite Program to provide station coordinates from a single least square adjustment. An individual SECOR solution was also obtained and is presented in this report, using direction constraints computed from BC-4 optical data from stations collocated with SECOR stations. Due to the critical configuration present in the range observations, weighted height constraints were also applied in order to break the near coplanarity of the observing stations.

Dark energy equation of state parameter and its evolution at low redshift

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

Tripathi, Ashutosh; Sangwan, Archana; Jassal, H.K., E-mail: ashutosh_tripathi@fudan.edu.cn, E-mail: archanakumari@iisermohali.ac.in, E-mail: hkjassal@iisermohali.ac.in

In this paper, we constrain dark energy models using a compendium of observations at low redshifts. We consider the dark energy as a barotropic fluid, with the equation of state a constant as well the case where dark energy equation of state is a function of time. The observations considered here are Supernova Type Ia data, Baryon Acoustic Oscillation data and Hubble parameter measurements. We compare constraints obtained from these data and also do a combined analysis. The combined observational constraints put strong limits on variation of dark energy density with redshift. For varying dark energy models, the range ofmore » parameters preferred by the supernova type Ia data is in tension with the other low redshift distance measurements.« less

Grip Force Control Is Dependent on Task Constraints in Children with and without Developmental Coordination Disorder

ERIC Educational Resources Information Center

Law, Sui-Heung; Lo, Sing Kai; Chow, Susanna; Cheing, Gladys L.Y.

2011-01-01

Excessive grip force (GF) is often found in children with developmental coordination disorder (DCD). However, their GF control may vary when task constraints are imposed upon their motor performance. This study aimed to investigate how their GF control changes in response to task demands, and to examine their tactile sensitivity. Twenty-one…

Study of salt transport processes in Delaware Bay

USGS Publications Warehouse

Walters, Roy

1992-01-01

The study described here is a subset of a broader climate-related study, and is focused primarily on salinity intrusion into Delaware Bay and River. Given changes in freshwater discharge into the Delaware River as determined from the larger study, and given probable sea level rise estimates, the purpose here is to calculate the distribution of salinity within Delaware Bay and River. The approach adopted for this study is composed of two parts: an analysis of existing physical data in order to derive a basic understanding of the salt dynamics, and numerical simulation of future conditions based on this analysis. There are two important constraints in the model used: it must resolve the spatial scales important to the salt dynamics, and it must be sufficiently efficient to allow extensive sensitivity studies. This has led to the development of a 3D model that uses harmonic decomposition in time and irregular finite elements in space. All nonlinear terms are retained in the governing equations, including quadratic bottom stress, advection, and wave transport (continuity nonlinearity). These equations are coupled to the advection-diffusion equation for salt so that density gradient forcing is included in the momentum equations. Although this study is still in progress, the model has reproduced sea level variations and the 3D structure of tidal and residual currents very well. In addition, the study has addressed the effects of a 1-meter rise in mean sea level on hydrodynamics of the study area. Current work is focused on salt dynamics.

Constraints on muon-specific dark forces

NASA Astrophysics Data System (ADS)

Karshenboim, Savely G.; McKeen, David; Pospelov, Maxim

2014-10-01

The recent measurement of the Lamb shift in muonic hydrogen allows for the most precise extraction of the charge radius of the proton which is currently in conflict with other determinations based on e-p scattering and hydrogen spectroscopy. This discrepancy could be the result of some new muon-specific force with O(1-100) MeV force carrier—in this paper we concentrate on vector mediators. Such an explanation faces challenges from the constraints imposed by the g-2 of the muon and electron as well as precision spectroscopy of muonic atoms. In this work we complement the family of constraints by calculating the contribution of hypothetical forces to the muonium hyperfine structure. We also compute the two-loop contribution to the electron parity-violating amplitude due to a muon loop, which is sensitive to the muon axial-vector coupling. Overall, we find that the combination of low-energy constraints favors the mass of the mediator to be below 10 MeV and that a certain degree of tuning is required between vector and axial-vector couplings of new vector particles to muons in order to satisfy constraints from muon g-2. However, we also observe that in the absence of a consistent standard model embedding high-energy weak-charged processes accompanied by the emission of new vector particles are strongly enhanced by (E/mV)2, with E a characteristic energy scale and mV the mass of the mediator. In particular, leptonic W decays impose the strongest constraints on such models completely disfavoring the remainder of the parameter space.

Boundary control of elliptic solutions to enforce local constraints

NASA Astrophysics Data System (ADS)

Bal, G.; Courdurier, M.

We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded from below by a positive constant in the vicinity of a finite number of prescribed points; (ii) the determinant of gradients of n solutions is bounded from below in the vicinity of a finite number of prescribed points. Such constructions find applications in recent hybrid medical imaging modalities. The methodology is based on starting from a controlled setting in which the constraints are satisfied and continuously modifying the coefficients in the second-order elliptic equation. The boundary condition is evolved by solving an ordinary differential equation (ODE) defined via appropriate optimality conditions. Unique continuations and standard regularity results for elliptic equations are used to show that the ODE admits a solution for sufficiently long times.

Force distribution in a semiflexible loop.

PubMed

Waters, James T; Kim, Harold D

2016-04-01

Loops undergoing thermal fluctuations are prevalent in nature. Ringlike or cross-linked polymers, cyclic macromolecules, and protein-mediated DNA loops all belong to this category. Stability of these molecules are generally described in terms of free energy, an average quantity, but it may also be impacted by local fluctuating forces acting within these systems. The full distribution of these forces can thus give us insights into mechanochemistry beyond the predictive capability of thermodynamics. In this paper, we study the force exerted by an inextensible semiflexible polymer constrained in a looped state. By using a simulation method termed "phase-space sampling," we generate the equilibrium distribution of chain conformations in both position and momentum space. We compute the constraint forces between the two ends of the loop in this chain ensemble using Lagrangian mechanics, and show that the mean of these forces is equal to the thermodynamic force. By analyzing kinetic and potential contributions to the forces, we find that the mean force acts in the direction of increasing extension not because of bending stress, but in spite of it. Furthermore, we obtain a distribution of constraint forces as a function of chain length, extension, and stiffness. Notably, increasing contour length decreases the average force, but the additional freedom allows fluctuations in the constraint force to increase. The force distribution is asymmetric and falls off less sharply than a Gaussian distribution. Our work exemplifies a system where large-amplitude fluctuations occur in a way unforeseen by a purely thermodynamic framework, and offers computational tools useful for efficient, unbiased simulation of a constrained system.

Force distribution in a semiflexible loop

PubMed Central

Waters, James T.; Kim, Harold D.

2017-01-01

Loops undergoing thermal fluctuations are prevalent in nature. Ringlike or cross-linked polymers, cyclic macromolecules, and protein-mediated DNA loops all belong to this category. Stability of these molecules are generally described in terms of free energy, an average quantity, but it may also be impacted by local fluctuating forces acting within these systems. The full distribution of these forces can thus give us insights into mechanochemistry beyond the predictive capability of thermodynamics. In this paper, we study the force exerted by an inextensible semiflexible polymer constrained in a looped state. By using a simulation method termed “phase-space sampling,” we generate the equilibrium distribution of chain conformations in both position and momentum space. We compute the constraint forces between the two ends of the loop in this chain ensemble using Lagrangian mechanics, and show that the mean of these forces is equal to the thermodynamic force. By analyzing kinetic and potential contributions to the forces, we find that the mean force acts in the direction of increasing extension not because of bending stress, but in spite of it. Furthermore, we obtain a distribution of constraint forces as a function of chain length, extension, and stiffness. Notably, increasing contour length decreases the average force, but the additional freedom allows fluctuations in the constraint force to increase. The force distribution is asymmetric and falls off less sharply than a Gaussian distribution. Our work exemplifies a system where large-amplitude fluctuations occur in a way unforeseen by a purely thermodynamic framework, and offers computational tools useful for efficient, unbiased simulation of a constrained system. PMID:27176436

Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.

PubMed

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chen, Jie; Yin, Linmao; Chew, Jia Wei

2017-04-01

Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.

Constraints for the Trifocal Tensor

NASA Astrophysics Data System (ADS)

Alzati, Alberto; Tortora, Alfonso

In this chapter we give an account of two different methods to find constraints for the trifocal tensor Т, used in geometric computer vision. We also show how to single out a set of only eight equations that are generically complete, i.e. for a generic choice of Т, they suffice to decide whether Т is indeed trifocal. Note that eight is minimum possible number of constraints.

General relativity in two dimensions: A Hamilton-Jacobi analysis

NASA Astrophysics Data System (ADS)

Bertin, M. C.; Pimentel, B. M.; Pompeia, P. J.

2010-11-01

We analyzed the constraint structure of the Einstein-Hilbert first-order action in two dimensions using the Hamilton-Jacobi approach. We were able to find a set of involutive, as well as a set of non-involutive constraints. Using generalized brackets we showed how to assure integrability of the theory, to eliminate the set of non-involutive constraints and how to build the field equations.

Geometrical force constraint method for vessel and x-ray angiogram simulation.

PubMed

Song, Shuang; Yang, Jian; Fan, Jingfan; Cong, Weijian; Ai, Danni; Zhao, Yitian; Wang, Yongtian

2016-01-01

This study proposes a novel geometrical force constraint method for 3-D vasculature modeling and angiographic image simulation. For this method, space filling force, gravitational force, and topological preserving force are proposed and combined for the optimization of the topology of the vascular structure. The surface covering force and surface adhesion force are constructed to drive the growth of the vasculature on any surface. According to the combination effects of the topological and surface adhering forces, a realistic vasculature can be effectively simulated on any surface. The image projection of the generated 3-D vascular structures is simulated according to the perspective projection and energy attenuation principles of X-rays. Finally, the simulated projection vasculature is fused with a predefined angiographic mask image to generate a realistic angiogram. The proposed method is evaluated on a CT image and three generally utilized surfaces. The results fully demonstrate the effectiveness and robustness of the proposed method.

The equation of motion for a radiating charged particle without self-interaction term

NASA Astrophysics Data System (ADS)

Herrera, L.

1990-03-01

The motion of a radiating charged particle is studied from the point of view of relativistic classical mechanics. Thus, the resulting equation of motion emerges from equating the total rate of change of momentum to the external force, without the introduction of a “self-force” term. Doing so, one is forced to abandon either one, or both, of the following restrictions: (a) the external force is non-dissipative, (b) the proper mass of the particle is constant. By abandoning (a) we obtain the Mo and Papas equation of motion, whereas allowing variations in the proper mass one is led, uniquely, to the Bonnor equation. A new equation of motion is proposed by abandoning both (a) and (b).

Hamiltonian formulation of Palatini f(R) theories a la Brans-Dicke theory

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

Olmo, Gonzalo J.; Sanchis-Alepuz, Helios; Institut fuer Physik, Karl-Franzens-Universitaet Graz

2011-05-15

We study the Hamiltonian formulation of f(R) theories of gravity both in metric and in Palatini formalism using their classical equivalence with Brans-Dicke theories with a nontrivial potential. The Palatini case, which corresponds to the {omega}=-3/2 Brans-Dicke theory, requires special attention because of new constraints associated with the scalar field, which is nondynamical. We derive, compare, and discuss the constraints and evolution equations for the {omega}=-3/2 and {omega}{ne}-3/2 cases. Based on the properties of the constraint and evolution equations, we find that, contrary to certain claims in the literature, the Cauchy problem for the {omega}=-3/2 case is well formulated andmore » there is no reason to believe that it is not well posed in general.« less

Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Eleshaky, Mohamed E.

1991-01-01

A new and efficient method is presented for aerodynamic design optimization, which is based on a computational fluid dynamics (CFD)-sensitivity analysis algorithm. The method is applied to design a scramjet-afterbody configuration for an optimized axial thrust. The Euler equations are solved for the inviscid analysis of the flow, which in turn provides the objective function and the constraints. The CFD analysis is then coupled with the optimization procedure that uses a constrained minimization method. The sensitivity coefficients, i.e. gradients of the objective function and the constraints, needed for the optimization are obtained using a quasi-analytical method rather than the traditional brute force method of finite difference approximations. During the one-dimensional search of the optimization procedure, an approximate flow analysis (predicted flow) based on a first-order Taylor series expansion is used to reduce the computational cost. Finally, the sensitivity of the optimum objective function to various design parameters, which are kept constant during the optimization, is computed to predict new optimum solutions. The flow analysis of the demonstrative example are compared with the experimental data. It is shown that the method is more efficient than the traditional methods.

Health status and labour force participation: evidence from Australia.

PubMed

Cai, Lixin; Kalb, Guyonne

2006-03-01

This paper examines the effect of health on labour force participation using the Household, Income and Labour Dynamics in Australia (HILDA) Survey. The potential endogeneity of health, especially self-assessed health, in the labour force participation equation is addressed by estimating the health equation and the labour force participation equation simultaneously. Taking into account the correlation between the error terms in the two equations, the estimation is conducted separately for males aged 15-49, males aged 50-64, females aged 15-49 and females aged 50-60. The results indicate that better health increases the probability of labour force participation for all four groups. However, the effect is larger for the older groups and for women. As for the feedback effect, it is found that labour force participation has a significant positive impact on older females' health, and a significant negative effect on younger males' health. For younger females and older males, the impact of labour force participation on health is not significant. The null-hypothesis of exogeneity of health to labour force participation is rejected for all groups. Copyright 2005 John Wiley & Sons, Ltd.

How Cells Can Control Their Size by Pumping Ions.

PubMed

Kay, Alan R

2017-01-01

The ability of all cells to set and regulate their size is a fundamental aspect of cellular physiology. It has been known for sometime but not widely so, that size stability in animal cells is dependent upon the operation of the sodium pump, through the so-called pump-leak mechanism (Tosteson and Hoffman, 1960). Impermeant molecules in cells establish an unstable osmotic condition, the Donnan effect, which is counteracted by the operation of the sodium pump, creating an asymmetry in the distribution of Na + and K + staving off water inundation. In this paper, which is in part a tutorial, I show how to model quantitatively the ion and water fluxes in a cell that determine the cell volume and membrane potential. The movement of water and ions is constrained by both osmotic and charge balance, and is driven by ion and voltage gradients and active ion transport. Transforming these constraints and forces into a set of coupled differential equations allows us to model how the ion distributions, volume and voltage change with time. I introduce an analytical solution to these equations that clarifies the influence of ion conductances, pump rates and water permeability in this multidimensional system. I show that the number of impermeant ions ( x ) and their average charge have a powerful influence on the distribution of ions and voltage in a cell. Moreover, I demonstrate that in a cell where the operation of active ion transport eliminates an osmotic gradient, the size of the cell is directly proportional to x . In addition, I use graphics to reveal how the physico-chemical constraints and chemical forces interact with one another in apportioning ions inside the cell. The form of model used here is applicable to all membrane systems, including mitochondria and bacteria, and I show how pumps other than the sodium pump can be used to stabilize cells. Cell biologists may think of electrophysiology as the exclusive domain of neuroscience, however the electrical effects of ion fluxes need to become an intimate part of cell biology if we are to understand a fundamental process like cell size regulation.

Control of constraint forces and trajectories in a rich sensory and actuation environment.

PubMed

Hemami, Hooshang; Dariush, Behzad

2010-12-01

A simple control strategy is proposed and applied to a class of non-linear systems that have abundant sensory and actuation channels as in living systems. The main objective is the independent control of constrained trajectories of motion, and control of the corresponding constraint forces. The peripheral controller is a proportional, derivative and integral (PID) controller. A central controller produces, via pattern generators, reference signals that are the desired constrained position and velocity trajectories, and the desired constraint forces. The basic tenet of the this hybrid control strategy is the use of two mechanisms: 1. linear state and force feedback, and 2. non-linear constraint velocity feedback - sliding mode feedback. The first mechanism can be envisioned as a high gain feedback systems. The high gain attribute imitates the agonist-antagonist co-activation in natural systems. The strategy is applied to the control of the force and trajectory of a two-segment thigh-leg planar biped leg with a mass-less foot cranking a pedal that is analogous to a bicycle pedal. Five computational experiments are presented to show the effectiveness of the strategy and the performance of the controller. The findings of this paper are applicable to the design of orthoses and prostheses to supplement functional electrical stimulation for support purposes in the spinally injured cases. Copyright © 2010 Elsevier Inc. All rights reserved.

Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

PubMed

Schuss, Z; Nadler, B; Eisenberg, R S

2001-09-01

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time averages over long times of the motion of a quasiparticle that diffuses with the same diffusion coefficient as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.

Massive graviton on arbitrary background: derivation, syzygies, applications

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

Bernard, Laura; Deffayet, Cédric; IHES, Institut des Hautes Études Scientifiques,Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette

2015-06-23

We give the detailed derivation of the fully covariant form of the quadratic action and the derived linear equations of motion for a massive graviton in an arbitrary background metric (which were presented in arXiv:1410.8302 [hep-th]). Our starting point is the de Rham-Gabadadze-Tolley (dRGT) family of ghost free massive gravities and using a simple model of this family, we are able to express this action and these equations of motion in terms of a single metric in which the graviton propagates, hence removing in particular the need for a “reference metric' which is present in the non perturbative formulation. Wemore » show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes the Boulware-Deser ghost. This last constraint involves powers and combinations of the curvature of the background metric. The 5 constraints are obtained for a background metric which is unconstrained, i.e. which does not have to obey the background field equations. We then apply these results to the case of Einstein space-times, where we show that the 5 constraints become trivial, and Friedmann-Lemaître-Robertson-Walker space-times, for which we correct in particular some results that appeared elsewhere. To reach our results, we derive several non trivial identities, syzygies, involving the graviton fields, its derivatives and the background metric curvature. These identities have their own interest. We also discover that there exist backgrounds for which the dRGT equations cannot be unambiguously linearized.« less

Massive graviton on arbitrary background: derivation, syzygies, applications

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

Bernard, Laura; Deffayet, Cédric; Strauss, Mikael von, E-mail: bernard@iap.fr, E-mail: deffayet@iap.fr, E-mail: strauss@iap.fr

2015-06-01

We give the detailed derivation of the fully covariant form of the quadratic action and the derived linear equations of motion for a massive graviton in an arbitrary background metric (which were presented in arXiv:1410.8302 [hep-th]). Our starting point is the de Rham-Gabadadze-Tolley (dRGT) family of ghost free massive gravities and using a simple model of this family, we are able to express this action and these equations of motion in terms of a single metric in which the graviton propagates, hence removing in particular the need for a ''reference metric' which is present in the non perturbative formulation. Wemore » show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes the Boulware-Deser ghost. This last constraint involves powers and combinations of the curvature of the background metric. The 5 constraints are obtained for a background metric which is unconstrained, i.e. which does not have to obey the background field equations. We then apply these results to the case of Einstein space-times, where we show that the 5 constraints become trivial, and Friedmann-Lemaître-Robertson-Walker space-times, for which we correct in particular some results that appeared elsewhere. To reach our results, we derive several non trivial identities, syzygies, involving the graviton fields, its derivatives and the background metric curvature. These identities have their own interest. We also discover that there exist backgrounds for which the dRGT equations cannot be unambiguously linearized.« less

Continuous Optimization on Constraint Manifolds

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

This paper demonstrates continuous optimization on the differentiable manifold formed by continuous constraint functions. The first order tensor geodesic differential equation is solved on the manifold in both numerical and closed analytic form for simple nonlinear programs. Advantages and disadvantages with respect to conventional optimization techniques are discussed.

Free-Surface Flow and Fluid-Object Interaction Modeling With Emphasis on Ship Hydrodynamics

DTIC Science & Technology

2012-01-01

0 on Cawt (21) in a weak sense. Equation (20) is the Eikonal partial differential equation subject to the interior constraint given by Eq. (21). To...tion, respectively. The formulation given by Eq. (22) is the SUPG method [30] applied to the Eikonal equation. At the steady state, the above problem

Planck satellite constraints on pseudo-Nambu-Goldstone boson quintessence

NASA Astrophysics Data System (ADS)

Smer-Barreto, Vanessa; Liddle, Andrew R.

2017-01-01

The pseudo-Nambu-Goldstone Boson (PNGB) potential, defined through the amplitude M4 and width f of its characteristic potential V(phi) = M4[1 + cos(phi/f)], is one of the best-suited models for the study of thawing quintessence. We analyse its present observational constraints by direct numerical solution of the scalar field equation of motion. Observational bounds are obtained using Supernovae data, cosmic microwave background temperature, polarization and lensing data from Planck, direct Hubble constant constraints, and baryon acoustic oscillations data. We find the parameter ranges for which PNGB quintessence gives a viable theory for dark energy. This exact approach is contrasted with the use of an approximate equation-of-state parametrization for thawing theories. We also discuss other possible parameterization choices, as well as commenting on the accuracy of the constraints imposed by Planck alone. Overall our analysis highlights a significant prior dependence to the outcome coming from the choice of modelling methodology, which current data are not sufficient to override.

Planck satellite constraints on pseudo-Nambu-Goldstone boson quintessence

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

Smer-Barreto, Vanessa; Liddle, Andrew R., E-mail: vsm@roe.ac.uk, E-mail: arl@roe.ac.uk

2017-01-01

The pseudo-Nambu-Goldstone Boson (PNGB) potential, defined through the amplitude M {sup 4} and width f of its characteristic potential V (φ) = M {sup 4}[1 + cos(φ/ f )], is one of the best-suited models for the study of thawing quintessence. We analyse its present observational constraints by direct numerical solution of the scalar field equation of motion. Observational bounds are obtained using Supernovae data, cosmic microwave background temperature, polarization and lensing data from Planck , direct Hubble constant constraints, and baryon acoustic oscillations data. We find the parameter ranges for which PNGB quintessence gives a viable theory for darkmore » energy. This exact approach is contrasted with the use of an approximate equation-of-state parametrization for thawing theories. We also discuss other possible parameterization choices, as well as commenting on the accuracy of the constraints imposed by Planck alone. Overall our analysis highlights a significant prior dependence to the outcome coming from the choice of modelling methodology, which current data are not sufficient to override.« less

An efficient and flexible Abel-inversion method for noisy data

NASA Astrophysics Data System (ADS)

Antokhin, Igor I.

2016-12-01

We propose an efficient and flexible method for solving the Abel integral equation of the first kind, frequently appearing in many fields of astrophysics, physics, chemistry, and applied sciences. This equation represents an ill-posed problem, thus solving it requires some kind of regularization. Our method is based on solving the equation on a so-called compact set of functions and/or using Tikhonov's regularization. A priori constraints on the unknown function, defining a compact set, are very loose and can be set using simple physical considerations. Tikhonov's regularization in itself does not require any explicit a priori constraints on the unknown function and can be used independently of such constraints or in combination with them. Various target degrees of smoothness of the unknown function may be set, as required by the problem at hand. The advantage of the method, apart from its flexibility, is that it gives uniform convergence of the approximate solution to the exact solution, as the errors of input data tend to zero. The method is illustrated on several simulated models with known solutions. An example of astrophysical application of the method is also given.

Introduction to neutron stars

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

Lattimer, James M.

Neutron stars contain the densest form of matter in the present universe. General relativity and causality set important constraints to their compactness. In addition, analytic GR solutions are useful in understanding the relationships that exist among the maximum mass, radii, moments of inertia, and tidal Love numbers of neutron stars, all of which are accessible to observation. Some of these relations are independent of the underlying dense matter equation of state, while others are very sensitive to the equation of state. Recent observations of neutron stars from pulsar timing, quiescent X-ray emission from binaries, and Type I X-ray bursts canmore » set important constraints on the structure of neutron stars and the underlying equation of state. In addition, measurements of thermal radiation from neutron stars has uncovered the possible existence of neutron and proton superfluidity/superconductivity in the core of a neutron star, as well as offering powerful evidence that typical neutron stars have significant crusts. These observations impose constraints on the existence of strange quark matter stars, and limit the possibility that abundant deconfined quark matter or hyperons exist in the cores of neutron stars.« less

Introduction to neutron stars

NASA Astrophysics Data System (ADS)

Lattimer, James M.

2015-02-01

Neutron stars contain the densest form of matter in the present universe. General relativity and causality set important constraints to their compactness. In addition, analytic GR solutions are useful in understanding the relationships that exist among the maximum mass, radii, moments of inertia, and tidal Love numbers of neutron stars, all of which are accessible to observation. Some of these relations are independent of the underlying dense matter equation of state, while others are very sensitive to the equation of state. Recent observations of neutron stars from pulsar timing, quiescent X-ray emission from binaries, and Type I X-ray bursts can set important constraints on the structure of neutron stars and the underlying equation of state. In addition, measurements of thermal radiation from neutron stars has uncovered the possible existence of neutron and proton superfluidity/superconductivity in the core of a neutron star, as well as offering powerful evidence that typical neutron stars have significant crusts. These observations impose constraints on the existence of strange quark matter stars, and limit the possibility that abundant deconfined quark matter or hyperons exist in the cores of neutron stars.

A mathematical solution for the parameters of three interfering resonances

NASA Astrophysics Data System (ADS)

Han, X.; Shen, C. P.

2018-04-01

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used. Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

Detecting chameleons through Casimir force measurements

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

Brax, Philippe; Bruck, Carsten van de; Davis, Anne-Christine

2007-12-15

The best laboratory constraints on strongly coupled chameleon fields come not from tests of gravity per se but from precision measurements of the Casimir force. The chameleonic force between two nearby bodies is more akin to a Casimir-like force than a gravitational one: The chameleon force behaves as an inverse power of the distance of separation between the surfaces of two bodies, just as the Casimir force does. Additionally, experimental tests of gravity often employ a thin metallic sheet to shield electrostatic forces; however, this sheet masks any detectable signal due to the presence of a strongly coupled chameleon field.more » As a result of this shielding, experiments that are designed to specifically test the behavior of gravity are often unable to place any constraint on chameleon fields with a strong coupling to matter. Casimir force measurements do not employ a physical electrostatic shield and as such are able to put tighter constraints on the properties of chameleons fields with a strong matter coupling than tests of gravity. Motivated by this, we perform a full investigation on the possibility of testing chameleon models with both present and future Casimir experiments. We find that present-day measurements are not able to detect the chameleon. However, future experiments have a strong possibility of detecting or rule out a whole class of chameleon models.« less

Generalized formulation of the interactions between soft spheres

NASA Astrophysics Data System (ADS)

Alonso-Marroquín, F.; McNamara, S.

2014-10-01

The goal of this paper is to identify the most general formulation that consistently links the different degrees of freedom in a contact between spherical soft particles. These contact laws have two parts: a set of "generalized contact velocities" that characterize the relative motion of the two particles, and a set of "generalized contact forces" that characterize the interparticle forces. One well known constraint on contact models is that the contact velocities must be objective. This requirement fixes the number of linearly independent contact velocities. We also present a previously unnoticed (in this context) constraint, namely, that the velocities and forces must be related in such a way that the stiffness matrix is symmetric. This constraint also places restrictions on the coupling between the contact forces. Within our generalized contact model, we discuss the expression for rolling velocity that need to be used in the calculation of rolling resistance, and the risk or producing perpetual mobile when other expressions of rolling velocity are using instead.

Future Cosmological Constraints From Fast Radio Bursts

NASA Astrophysics Data System (ADS)

Walters, Anthony; Weltman, Amanda; Gaensler, B. M.; Ma, Yin-Zhe; Witzemann, Amadeus

2018-03-01

We consider the possible observation of fast radio bursts (FRBs) with planned future radio telescopes, and investigate how well the dispersions and redshifts of these signals might constrain cosmological parameters. We construct mock catalogs of FRB dispersion measure (DM) data and employ Markov Chain Monte Carlo analysis, with which we forecast and compare with existing constraints in the flat ΛCDM model, as well as some popular extensions that include dark energy equation of state and curvature parameters. We find that the scatter in DM observations caused by inhomogeneities in the intergalactic medium (IGM) poses a big challenge to the utility of FRBs as a cosmic probe. Only in the most optimistic case, with a high number of events and low IGM variance, do FRBs aid in improving current constraints. In particular, when FRBs are combined with CMB+BAO+SNe+H 0 data, we find the biggest improvement comes in the {{{Ω }}}{{b}}{h}2 constraint. Also, we find that the dark energy equation of state is poorly constrained, while the constraint on the curvature parameter, Ω k , shows some improvement when combined with current constraints. When FRBs are combined with future baryon acoustic oscillation (BAO) data from 21 cm Intensity Mapping, we find little improvement over the constraints from BAOs alone. However, the inclusion of FRBs introduces an additional parameter constraint, {{{Ω }}}{{b}}{h}2, which turns out to be comparable to existing constraints. This suggests that FRBs provide valuable information about the cosmological baryon density in the intermediate redshift universe, independent of high-redshift CMB data.

The calculation of transport phenomena in electromagnetically levitated metal droplets

NASA Technical Reports Server (NTRS)

El-Kaddah, N.; Szekely, J.

1982-01-01

A mathematical representation has been developed for the electromagnetic force field, fluid flow field, and solute concentration field of levitation-melted metal specimens. The governing equations consist of the conventional transport equations combined with the appropriate expressions for the electromagnetic force field. The predictions obtained by solving the governing equations numerically on a digital computer are in good agreement with lifting force and average temperature measurements reported in the literature.

Numerical study of radiometric forces via the direct solution of the Boltzmann kinetic equation

NASA Astrophysics Data System (ADS)

Anikin, Yu. A.

2011-07-01

The two-dimensional rarefied gas motion in a Crookes radiometer and the resulting radiometric forces are studied by numerically solving the Boltzmann kinetic equation. The collision integral is directly evaluated using a projection method, and second-order accurate TVD schemes are used to solve the advection equation. The radiometric forces are found as functions of the Knudsen number and the temperatures, and their spatial distribution is analyzed.

Ensemble theory for slightly deformable granular matter.

PubMed

Tejada, Ignacio G

2014-09-01

Given a granular system of slightly deformable particles, it is possible to obtain different static and jammed packings subjected to the same macroscopic constraints. These microstates can be compared in a mathematical space defined by the components of the force-moment tensor (i.e. the product of the equivalent stress by the volume of the Voronoi cell). In order to explain the statistical distributions observed there, an athermal ensemble theory can be used. This work proposes a formalism (based on developments of the original theory of Edwards and collaborators) that considers both the internal and the external constraints of the problem. The former give the density of states of the points of this space, and the latter give their statistical weight. The internal constraints are those caused by the intrinsic features of the system (e.g. size distribution, friction, cohesion). They, together with the force-balance condition, determine which the possible local states of equilibrium of a particle are. Under the principle of equal a priori probabilities, and when no other constraints are imposed, it can be assumed that particles are equally likely to be found in any one of these local states of equilibrium. Then a flat sampling over all these local states turns into a non-uniform distribution in the force-moment space that can be represented with density of states functions. Although these functions can be measured, some of their features are explored in this paper. The external constraints are those macroscopic quantities that define the ensemble and are fixed by the protocol. The force-moment, the volume, the elastic potential energy and the stress are some examples of quantities that can be expressed as functions of the force-moment. The associated ensembles are included in the formalism presented here.

Partner symmetries and non-invariant solutions of four-dimensional heavenly equations

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2004-07-01

We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.

Maximum entropy and equations of state for random cellular structures

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

Rivier, N.

Random, space-filling cellular structures (biological tissues, metallurgical grain aggregates, foams, etc.) are investigated. Maximum entropy inference under a few constraints yields structural equations of state, relating the size of cells to their topological shape. These relations are known empirically as Lewis's law in Botany, or Desch's relation in Metallurgy. Here, the functional form of the constraints is now known as a priori, and one takes advantage of this arbitrariness to increase the entropy further. The resulting structural equations of state are independent of priors, they are measurable experimentally and constitute therefore a direct test for the applicability of MaxEnt inferencemore » (given that the structure is in statistical equilibrium, a fact which can be tested by another simple relation (Aboav's law)). 23 refs., 2 figs., 1 tab.« less

Calculation of a fluctuating entropic force by phase space sampling.

PubMed

Waters, James T; Kim, Harold D

2015-07-01

A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.

Hamiltonian structure of Dubrovin{close_quote}s equation of associativity in 2-d topological field theory

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

Galvao, C.A.; Nutku, Y.

1996-12-01

mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}

Augmenting the one-shot framework by additional constraints

DOE PAGES

Bosse, Torsten

2016-05-12

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. Finally, a retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

Augmenting the one-shot framework by additional constraints

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

Bosse, Torsten

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. Finally, a retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

A Variational Assimilation Method for Satellite and Conventional Data: Development of Basic Model for Diagnosis of Cyclone Systems

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Scott, Robert W.; Chen, J.

1991-01-01

A summary is presented of the progress toward the completion of a comprehensive diagnostic objective analysis system based upon the calculus of variations. The approach was to first develop the objective analysis subject to the constraints that the final product satisfies the five basic primitive equations for a dry inviscid atmosphere: the two nonlinear horizontal momentum equations, the continuity equation, the hydrostatic equation, and the thermodynamic equation. Then, having derived the basic model, there would be added to it the equations for moist atmospheric processes and the radiative transfer equation.

Spacecraft Constrained Maneuver Planning Using Positively Invariant Constraint Admissible Sets (Postprint)

DTIC Science & Technology

2013-08-14

Connectivity Graph; Graph Search; Bounded Disturbances; Linear Time-Varying (LTV); Clohessy - Wiltshire -Hill (CWH) 16. SECURITY CLASSIFICATION OF: 17...the linearization of the relative motion model given by the Hill- Clohessy - Wiltshire (CWH) equations is used [14]. A. Nonlinear equations of motion...equations can be used to describe the motion of the debris. B. Linearized HCW equations in discrete-time For δr << R, the linearized Hill- Clohessy

Experimental verification of theoretical equations for acoustic radiation force on compressible spherical particles in traveling waves.

PubMed

Johnson, Kennita A; Vormohr, Hannah R; Doinikov, Alexander A; Bouakaz, Ayache; Shields, C Wyatt; López, Gabriel P; Dayton, Paul A

2016-05-01

Acoustophoresis uses acoustic radiation force to remotely manipulate particles suspended in a host fluid for many scientific, technological, and medical applications, such as acoustic levitation, acoustic coagulation, contrast ultrasound imaging, ultrasound-assisted drug delivery, etc. To estimate the magnitude of acoustic radiation forces, equations derived for an inviscid host fluid are commonly used. However, there are theoretical predictions that, in the case of a traveling wave, viscous effects can dramatically change the magnitude of acoustic radiation forces, which make the equations obtained for an inviscid host fluid invalid for proper estimation of acoustic radiation forces. To date, experimental verification of these predictions has not been published. Experimental measurements of viscous effects on acoustic radiation forces in a traveling wave were conducted using a confocal optical and acoustic system and values were compared with available theories. Our results show that, even in a low-viscosity fluid such as water, the magnitude of acoustic radiation forces is increased manyfold by viscous effects in comparison with what follows from the equations derived for an inviscid fluid.

Experimental verification of theoretical equations for acoustic radiation force on compressible spherical particles in traveling waves

NASA Astrophysics Data System (ADS)

Johnson, Kennita A.; Vormohr, Hannah R.; Doinikov, Alexander A.; Bouakaz, Ayache; Shields, C. Wyatt; López, Gabriel P.; Dayton, Paul A.

2016-05-01

Acoustophoresis uses acoustic radiation force to remotely manipulate particles suspended in a host fluid for many scientific, technological, and medical applications, such as acoustic levitation, acoustic coagulation, contrast ultrasound imaging, ultrasound-assisted drug delivery, etc. To estimate the magnitude of acoustic radiation forces, equations derived for an inviscid host fluid are commonly used. However, there are theoretical predictions that, in the case of a traveling wave, viscous effects can dramatically change the magnitude of acoustic radiation forces, which make the equations obtained for an inviscid host fluid invalid for proper estimation of acoustic radiation forces. To date, experimental verification of these predictions has not been published. Experimental measurements of viscous effects on acoustic radiation forces in a traveling wave were conducted using a confocal optical and acoustic system and values were compared with available theories. Our results show that, even in a low-viscosity fluid such as water, the magnitude of acoustic radiation forces is increased manyfold by viscous effects in comparison with what follows from the equations derived for an inviscid fluid.

Improvements in GRACE Gravity Field Determination through Stochastic Observation Modeling

NASA Astrophysics Data System (ADS)

McCullough, C.; Bettadpur, S. V.

2016-12-01

Current unconstrained Release 05 GRACE gravity field solutions from the Center for Space Research (CSR RL05) assume random observation errors following an independent multivariate Gaussian distribution. This modeling of observations, a simplifying assumption, fails to account for long period, correlated errors arising from inadequacies in the background force models. Fully modeling the errors inherent in the observation equations, through the use of a full observation covariance (modeling colored noise), enables optimal combination of GPS and inter-satellite range-rate data and obviates the need for estimating kinematic empirical parameters during the solution process. Most importantly, fully modeling the observation errors drastically improves formal error estimates of the spherical harmonic coefficients, potentially enabling improved uncertainty quantification of scientific results derived from GRACE and optimizing combinations of GRACE with independent data sets and a priori constraints.

Brane junctions in the Randall-Sundrum scenario

NASA Astrophysics Data System (ADS)

Csáki, Csaba; Shirman, Yuri

2000-01-01

We present static solutions to Einstein's equations corresponding to branes at various angles intersecting in a single 3-brane. Such configurations may be useful for building models with localized gravity via the Randall-Sundrum mechanism. We find that such solutions may exist only if the mechanical forces acting on the junction exactly cancel. In addition to this constraint there are further conditions that the parameters of the theory have to satisfy. We find that at least one of these involves only the brane tensions and cosmological constants, and thus cannot have a dynamical origin. We present these conditions in detail for two simple examples. We discuss the nature of the cosmological constant problem in the framework of these scenarios, and outline the desired features of the brane configurations which may bring us closer towards a resolution of the cosmological constant problem.

Sensitivity of the model error parameter specification in weak-constraint four-dimensional variational data assimilation

NASA Astrophysics Data System (ADS)

Shaw, Jeremy A.; Daescu, Dacian N.

2017-08-01

This article presents the mathematical framework to evaluate the sensitivity of a forecast error aspect to the input parameters of a weak-constraint four-dimensional variational data assimilation system (w4D-Var DAS), extending the established theory from strong-constraint 4D-Var. Emphasis is placed on the derivation of the equations for evaluating the forecast sensitivity to parameters in the DAS representation of the model error statistics, including bias, standard deviation, and correlation structure. A novel adjoint-based procedure for adaptive tuning of the specified model error covariance matrix is introduced. Results from numerical convergence tests establish the validity of the model error sensitivity equations. Preliminary experiments providing a proof-of-concept are performed using the Lorenz multi-scale model to illustrate the theoretical concepts and potential benefits for practical applications.

HI Intensity Mapping with FAST

NASA Astrophysics Data System (ADS)

Bigot-Sazy, M.-A.; Ma, Y.-Z.; Battye, R. A.; Browne, I. W. A.; Chen, T.; Dickinson, C.; Harper, S.; Maffei, B.; Olivari, L. C.; Wilkinsondagger, P. N.

2016-02-01

We discuss the detectability of large-scale HI intensity fluctuations using the FAST telescope. We present forecasts for the accuracy of measuring the Baryonic Acoustic Oscillations and constraining the properties of dark energy. The FAST 19-beam L-band receivers (1.05-1.45 GHz) can provide constraints on the matter power spectrum and dark energy equation of state parameters (w0,wa) that are comparable to the BINGO and CHIME experiments. For one year of integration time we find that the optimal survey area is 6000 deg2. However, observing with larger frequency coverage at higher redshift (0.95-1.35 GHz) improves the projected errorbars on the HI power spectrum by more than 2 σ confidence level. The combined constraints from FAST, CHIME, BINGO and Planck CMB observations can provide reliable, stringent constraints on the dark energy equation of state.

Box compression analysis of world-wide data spanning 46 years

Treesearch

Thomas J. Urbanik; Benjamin Frank

2006-01-01

The state of the art among most industry citations of box compression estimation is the equation by McKee developed in 1963. Because of limitations in computing tools at the time the McKee equation was developed, the equation is a simplification, with many constraints, of a more general relationship. By applying the results of sophisticated finite element modeling, in...

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

DOE PAGES

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul; ...

2017-12-20

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

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

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

Laplace-Beltrami operator and exact solutions for branes

NASA Astrophysics Data System (ADS)

Zheltukhin, A. A.

2013-02-01

Proposed is a new approach to finding exact solutions of nonlinear p-brane equations in D-dimensional Minkowski space based on the use of various initial value constraints. It is shown that the constraints Δx→=0 and Δx→=-Λ(t,σr)x→ give two sets of exact solutions.

Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state

NASA Astrophysics Data System (ADS)

Alsing, Justin; Silva, Hector O.; Berti, Emanuele

2018-07-01

We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multimodality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be 2.0 M⊙ < mmax < 2.2 M⊙ (68 per cent), 2.0 M⊙ < mmax < 2.6 M⊙ (90 per cent), and evidence for a cut-off is robust against the choice of model for the mass distribution and to removing the most extreme (highest mass) neutron stars from the data set. If this sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts constraints on the equation of state. For a set of realistic equations of state that support >2 M⊙ neutron stars, our inference of mmax is able to distinguish between models at odds ratios of up to 12:1, whilst under a flexible piecewise polytropic equation-of-state model our maximum mass measurement improves constraints on the pressure at 3-7× the nuclear saturation density by ˜ 30-50 per cent compared to simply requiring mmax > 2 M⊙. We obtain a lower bound on the maximum sound speed attained inside the neutron star of c_ s^max > 0.63c (99.8 per cent), ruling out c_ s^max < c/√{3} at high significance. Our constraints on the maximum neutron star mass strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.

Constraining the equation of state of neutron stars from binary mergers.

PubMed

Takami, Kentaro; Rezzolla, Luciano; Baiotti, Luca

2014-08-29

Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we find that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the total compactness of the stars in the binary. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We test our approach with simulated data and verify it works well for all the equations of state considered.

Algebraic solution for the forward displacement analysis of the general 6-6 stewart mechanism

NASA Astrophysics Data System (ADS)

Wei, Feng; Wei, Shimin; Zhang, Ying; Liao, Qizheng

2016-01-01

The solution for the forward displacement analysis(FDA) of the general 6-6 Stewart mechanism(i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane) has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra(CGA). The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Gröbner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Gröbner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9´9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

NASA Astrophysics Data System (ADS)

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-01

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field.

PubMed

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-28

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

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

Reister, D.B.; Unseren, M.A.

When a vehicle with two or more steerable drive wheels is traveling in a circle, the motion of the wheels is constrained. The wheel translational velocity divided by the radius to the center of rotation must be the same for all wheels. When the drive wheels are controlled independently using position control, the motion of the wheels may violate the constraints and the wheels may slip. Consequently, substantial errors can occur in the orientation of the vehicle. A vehicle with N drive wheels has (N - 1) constraints and one degree of freedom. We have developed a new approach tomore » the control of a vehicle with N steerable drive wheels. The novel aspect of our approach is the use of force control. To control the vehicle, we have one degree of freedom for the position on the circle and (N - 1) forces that can be used to reduce errors. Recently, Kankaanranta and Koivo developed a control architecture that allows the force and position degrees of freedom to be decoupled. In the work of Kankaanranta and Koivo the force is an exogenous input. We have made the force endogenous by defining the force in terms of the errors in satisfying the rigid body kinematic constraints. We have applied the control architecture to the HERMIES-III robot and have measured a dramatic reduction in error (more than a factor of 20) compared to motions without force control.« less

Governing equations for electro-conjugate fluid flow

NASA Astrophysics Data System (ADS)

Hosoda, K.; Takemura, K.; Fukagata, K.; Yokota, S.; Edamura, K.

2013-12-01

An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

Muscle function in glenohumeral joint stability during lifting task.

PubMed

Blache, Yoann; Begon, Mickaël; Michaud, Benjamin; Desmoulins, Landry; Allard, Paul; Dal Maso, Fabien

2017-01-01

Ensuring glenohumeral stability during repetitive lifting tasks is a key factor to reduce the risk of shoulder injuries. Nevertheless, the literature reveals some lack concerning the assessment of the muscles that ensure glenohumeral stability during specific lifting tasks. Therefore, the purpose of this study was to assess the stabilization function of shoulder muscles during a lifting task. Kinematics and muscle electromyograms (n = 9) were recorded from 13 healthy adults during a bi-manual lifting task performed from the hip to the shoulder level. A generic upper-limb OpenSim model was implemented to simulate glenohumeral stability and instability by performing static optimizations with and without glenohumeral stability constraints. This procedure enabled to compute the level of shoulder muscle activity and forces in the two conditions. Without the stability constraint, the simulated movement was unstable during 74%±16% of the time. The force of the supraspinatus was significantly increased of 107% (p<0.002) when the glenohumeral stability constraint was implemented. The increased supraspinatus force led to greater compressive force (p<0.001) and smaller shear force (p<0.001), which contributed to improved glenohumeral stability. It was concluded that the supraspinatus may be the main contributor to glenohumeral stability during lifting task.

Muscle function in glenohumeral joint stability during lifting task

PubMed Central

Begon, Mickaël; Michaud, Benjamin; Desmoulins, Landry; Allard, Paul

2017-01-01

Ensuring glenohumeral stability during repetitive lifting tasks is a key factor to reduce the risk of shoulder injuries. Nevertheless, the literature reveals some lack concerning the assessment of the muscles that ensure glenohumeral stability during specific lifting tasks. Therefore, the purpose of this study was to assess the stabilization function of shoulder muscles during a lifting task. Kinematics and muscle electromyograms (n = 9) were recorded from 13 healthy adults during a bi-manual lifting task performed from the hip to the shoulder level. A generic upper-limb OpenSim model was implemented to simulate glenohumeral stability and instability by performing static optimizations with and without glenohumeral stability constraints. This procedure enabled to compute the level of shoulder muscle activity and forces in the two conditions. Without the stability constraint, the simulated movement was unstable during 74%±16% of the time. The force of the supraspinatus was significantly increased of 107% (p<0.002) when the glenohumeral stability constraint was implemented. The increased supraspinatus force led to greater compressive force (p<0.001) and smaller shear force (p<0.001), which contributed to improved glenohumeral stability. It was concluded that the supraspinatus may be the main contributor to glenohumeral stability during lifting task. PMID:29244838

Wind Wave Behavior in Fetch and Depth Limited Estuaries

NASA Astrophysics Data System (ADS)

Karimpour, Arash; Chen, Qin; Twilley, Robert R.

2017-01-01

Wetland dominated estuaries serve as one of the most productive natural ecosystems through their ecological, economic and cultural services, such as nursery grounds for fisheries, nutrient sequestration, and ecotourism. The ongoing deterioration of wetland ecosystems in many shallow estuaries raises concerns about the contributing erosive processes and their roles in restraining coastal restoration efforts. Given the combination of wetlands and shallow bays as landscape components that determine the function of estuaries, successful restoration strategies require knowledge of wind wave behavior in fetch and depth limited water as a critical design feature. We experimentally evaluate physics of wind wave growth in fetch and depth limited estuaries. We demonstrate that wave growth rate in shallow estuaries is a function of wind fetch to water depth ratio, which helps to develop a new set of parametric wave growth equations. We find that the final stage of wave growth in shallow estuaries can be presented by a product of water depth and wave number, whereby their product approaches 1.363 as either depth or wave energy increases. Suggested wave growth equations and their asymptotic constraints establish the magnitude of wave forces acting on wetland erosion that must be included in ecosystem restoration design.

Wind Wave Behavior in Fetch and Depth Limited Estuaries

PubMed Central

Karimpour, Arash; Chen, Qin; Twilley, Robert R.

2017-01-01

Wetland dominated estuaries serve as one of the most productive natural ecosystems through their ecological, economic and cultural services, such as nursery grounds for fisheries, nutrient sequestration, and ecotourism. The ongoing deterioration of wetland ecosystems in many shallow estuaries raises concerns about the contributing erosive processes and their roles in restraining coastal restoration efforts. Given the combination of wetlands and shallow bays as landscape components that determine the function of estuaries, successful restoration strategies require knowledge of wind wave behavior in fetch and depth limited water as a critical design feature. We experimentally evaluate physics of wind wave growth in fetch and depth limited estuaries. We demonstrate that wave growth rate in shallow estuaries is a function of wind fetch to water depth ratio, which helps to develop a new set of parametric wave growth equations. We find that the final stage of wave growth in shallow estuaries can be presented by a product of water depth and wave number, whereby their product approaches 1.363 as either depth or wave energy increases. Suggested wave growth equations and their asymptotic constraints establish the magnitude of wave forces acting on wetland erosion that must be included in ecosystem restoration design. PMID:28098236

Traversable wormholes satisfying the weak energy condition in third-order Lovelock gravity

NASA Astrophysics Data System (ADS)

Zangeneh, Mahdi Kord; Lobo, Francisco S. N.; Dehghani, Mohammad Hossein

2015-12-01

In this paper, we consider third-order Lovelock gravity with a cosmological constant term in an n -dimensional spacetime M4×Kn -4, where Kn -4 is a constant curvature space. We decompose the equations of motion to four and higher dimensional ones and find wormhole solutions by considering a vacuum Kn -4 space. Applying the latter constraint, we determine the second- and third-order Lovelock coefficients and the cosmological constant in terms of specific parameters of the model, such as the size of the extra dimensions. Using the obtained Lovelock coefficients and Λ , we obtain the four-dimensional matter distribution threading the wormhole. Furthermore, by considering the zero tidal force case and a specific equation of state, given by ρ =(γ p -τ )/[ω (1 +γ )], we find the exact solution for the shape function which represents both asymptotically flat and nonflat wormhole solutions. We show explicitly that these wormhole solutions in addition to traversibility satisfy the energy conditions for suitable choices of parameters and that the existence of a limited spherically symmetric traversable wormhole with normal matter in a four-dimensional spacetime implies a negative effective cosmological constant.

Wind Wave Behavior in Fetch and Depth Limited Estuaries.

PubMed

Karimpour, Arash; Chen, Qin; Twilley, Robert R

2017-01-18

Wetland dominated estuaries serve as one of the most productive natural ecosystems through their ecological, economic and cultural services, such as nursery grounds for fisheries, nutrient sequestration, and ecotourism. The ongoing deterioration of wetland ecosystems in many shallow estuaries raises concerns about the contributing erosive processes and their roles in restraining coastal restoration efforts. Given the combination of wetlands and shallow bays as landscape components that determine the function of estuaries, successful restoration strategies require knowledge of wind wave behavior in fetch and depth limited water as a critical design feature. We experimentally evaluate physics of wind wave growth in fetch and depth limited estuaries. We demonstrate that wave growth rate in shallow estuaries is a function of wind fetch to water depth ratio, which helps to develop a new set of parametric wave growth equations. We find that the final stage of wave growth in shallow estuaries can be presented by a product of water depth and wave number, whereby their product approaches 1.363 as either depth or wave energy increases. Suggested wave growth equations and their asymptotic constraints establish the magnitude of wave forces acting on wetland erosion that must be included in ecosystem restoration design.

Forced Convection Heat Transfer in Circular Pipes

ERIC Educational Resources Information Center

Tosun, Ismail

2007-01-01

One of the pitfalls of engineering education is to lose the physical insight of the problem while tackling the mathematical part. Forced convection heat transfer (the Graetz-Nusselt problem) certainly falls into this category. The equation of energy together with the equation of motion leads to a partial differential equation subject to various…

Position and force control of a vehicle with two or more steerable drive wheels

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

Reister, D.B.; Unseren, M.A.

1992-10-01

When a vehicle with two or more steerable drive wheels is traveling in a circle, the motion of the wheels is constrained. The wheel translational velocity divided by the radius to the center of rotation must be the same for all wheels. When the drive wheels are controlled independently using position control, the motion of the wheels may violate the constraints and the wheels may slip. Consequently, substantial errors can occur in the orientation of the vehicle. A vehicle with N drive wheels has (N - 1) constraints and one degree of freedom. We have developed a new approach tomore » the control of a vehicle with N steerable drive wheels. The novel aspect of our approach is the use of force control. To control the vehicle, we have one degree of freedom for the position on the circle and (N - 1) forces that can be used to reduce errors. Recently, Kankaanranta and Koivo developed a control architecture that allows the force and position degrees of freedom to be decoupled. In the work of Kankaanranta and Koivo the force is an exogenous input. We have made the force endogenous by defining the force in terms of the errors in satisfying the rigid body kinematic constraints. We have applied the control architecture to the HERMIES-III robot and have measured a dramatic reduction in error (more than a factor of 20) compared to motions without force control.« less

Confronting the Uncertainty in Aerosol Forcing Using Comprehensive Observational Data

NASA Astrophysics Data System (ADS)

Johnson, J. S.; Regayre, L. A.; Yoshioka, M.; Pringle, K.; Sexton, D.; Lee, L.; Carslaw, K. S.

2017-12-01

The effect of aerosols on cloud droplet concentrations and radiative properties is the largest uncertainty in the overall radiative forcing of climate over the industrial period. In this study, we take advantage of a large perturbed parameter ensemble of simulations from the UK Met Office HadGEM-UKCA model (the aerosol component of the UK Earth System Model) to comprehensively sample uncertainty in aerosol forcing. Uncertain aerosol and atmospheric parameters cause substantial aerosol forcing uncertainty in climatically important regions. As the aerosol radiative forcing itself is unobservable, we investigate the potential for observations of aerosol and radiative properties to act as constraints on the large forcing uncertainty. We test how eight different theoretically perfect aerosol and radiation observations can constrain the forcing uncertainty over Europe. We find that the achievable constraint is weak unless many diverse observations are used simultaneously. This is due to the complex relationships between model output responses and the multiple interacting parameter uncertainties: compensating model errors mean there are many ways to produce the same model output (known as model equifinality) which impacts on the achievable constraint. However, using all eight observable quantities together we show that the aerosol forcing uncertainty can potentially be reduced by around 50%. This reduction occurs as we reduce a large sample of model variants (over 1 million) that cover the full parametric uncertainty to around 1% that are observationally plausible.Constraining the forcing uncertainty using real observations is a more complex undertaking, in which we must account for multiple further uncertainties including measurement uncertainties, structural model uncertainties and the model discrepancy from reality. Here, we make a first attempt to determine the true potential constraint on the forcing uncertainty from our model that is achievable using a comprehensive set of real aerosol and radiation observations taken from ground stations, flight campaigns and satellite. This research has been supported by the UK-China Research & Innovation Partnership Fund through the Met Office Climate Science for Service Partnership (CSSP) China as part of the Newton Fund, and by the NERC funded GASSP project.

On the extraction of pressure fields from PIV velocity measurements in turbines

NASA Astrophysics Data System (ADS)

Villegas, Arturo; Diez, Fancisco J.

2012-11-01

In this study, the pressure field for a water turbine is derived from particle image velocimetry (PIV) measurements. Measurements are performed in a recirculating water channel facility. The PIV measurements include calculating the tangential and axial forces applied to the turbine by solving the integral momentum equation around the airfoil. The results are compared with the forces obtained from the Blade Element Momentum theory (BEMT). Forces are calculated by using three different methods. In the first method, the pressure fields are obtained from PIV velocity fields by solving the Poisson equation. The boundary conditions are obtained from the Navier-Stokes momentum equations. In the second method, the pressure at the boundaries is determined by spatial integration of the pressure gradients along the boundaries. In the third method, applicable only to incompressible, inviscid, irrotational, and steady flow, the pressure is calculated using the Bernoulli equation. This approximated pressure is known to be accurate far from the airfoil and outside of the wake for steady flows. Additionally, the pressure is used to solve for the force from the integral momentum equation on the blade. From the three methods proposed to solve for pressure and forces from PIV measurements, the first one, which is solved by using the Poisson equation, provides the best match to the BEM theory calculations.

On redundant variables in Lagrangian mechanics, with applications to perturbation theory and KS regularization. [Kustaanheimo-Stiefel two body problem

NASA Technical Reports Server (NTRS)

Broucke, R.; Lass, H.

1975-01-01

It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange multipliers). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel regularization. Some interesting applications to perturbation theory are also described.

Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state

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

Sharov, G.S., E-mail: german.sharov@mail.ru

Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H ( z ) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale r {sub s} ( z {sub d} ). Among the considered models the best value of χ{sup 2} is achieved formore » the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.« less

Prestack density inversion using the Fatti equation constrained by the P- and S-wave impedance and density

NASA Astrophysics Data System (ADS)

Liang, Li-Feng; Zhang, Hong-Bing; Dan, Zhi-Wei; Xu, Zi-Qiang; Liu, Xiu-Juan; Cao, Cheng-Hao

2017-03-01

Simultaneous prestack inversion is based on the modified Fatti equation and uses the ratio of the P- and S-wave velocity as constraints. We use the relation of P-wave impedance and density (PID) and S-wave impedance and density (SID) to replace the constant Vp/Vs constraint, and we propose the improved constrained Fatti equation to overcome the effect of P-wave impedance on density. We compare the sensitivity of both methods using numerical simulations and conclude that the density inversion sensitivity improves when using the proposed method. In addition, the random conjugate-gradient method is used in the inversion because it is fast and produces global solutions. The use of synthetic and field data suggests that the proposed inversion method is effective in conventional and nonconventional lithologies.

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

The fundamental equation of eddy covariance and its application in flux measurements

Treesearch

Lianhong Gu; William J. Massman; Ray Leuning; Stephen G. Pallardy; Tilden Meyers; Paul J. Hanson; Jeffery S. Riggs; Kevin P. Hosman; Bai Yang

2012-01-01

A fundamental equation of eddy covariance (FQEC) is derived that allows the net ecosystem exchange (NEE) Ns of a specified atmospheric constituent s to be measured with the constraint of conservation of any other atmospheric constituent (e.g. N2, argon, or dry air). It is shown that if the condition [equation, see PDF] is true, the conservation of mass can be applied...

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1990-09-18

to be published Proceedings: conference Chaos in Australia (February 1990). 5. On the Kadomtsev Petviashvili Equation and Associated Constraints by...Scattering Transfoni (IST). IST is a method which alows one to’solve nonlinear wave equations by solving certain related direct and inverse scattering...problems. We use these results to find solutions to nonlinear wave equations much like one uses Fourier analysis for linear problems. Moreover the

Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

NASA Astrophysics Data System (ADS)

Antonowicz, Marek; Szczyrba, Wiktor

1985-06-01

We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.

Conformal invariance and conserved quantities of mechanical system with unilateral constraints

NASA Astrophysics Data System (ADS)

Wang, Peng

2018-06-01

By distinguishing the different constraint cases, the whole course and piecewise conserved quantities, which deduced from conformal invariance of mechanical systems with unilateral constraints, are given. The determining equation of conformal invariance of the system is obtained. The sufficient and necessary conditions for the conformal invariance must be Lie symmetry of the system are given. The forms of conformal factors are obtained. An example is given to illustrate the results in this paper.

Fiber-reinforced materials: finite elements for the treatment of the inextensibility constraint

NASA Astrophysics Data System (ADS)

Auricchio, Ferdinando; Scalet, Giulia; Wriggers, Peter

2017-12-01

The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.

New dynamic variables for rotating spacecraft

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1993-01-01

This paper introduces two new seven-parameter representations for spacecraft attitude dynamics modeling. The seven parameters are the three components of the total system angular momentum in the spacecraft body frame; the three components of the angular momentum in the inertial reference frame; and an angle variable. These obey a single constraint as do parameterizations that include a quaternion; in this case the constraint is the equality of the sum of the squares of the angular momentum components in the two frames. The two representations are nonsingular if the system angular momentum is non-zero and obeys certain orientation constraints. The new parameterizations of the attitude matrix, the equations of motion, and the relation of the solution of these equations to Euler angles for torque-free motion are developed and analyzed. The superiority of the new parameterizations for numerical integration is shown in a specific example.

Influence of flow constraints on the properties of the critical endpoint of symmetric nuclear matter

NASA Astrophysics Data System (ADS)

Ivanytskyi, A. I.; Bugaev, K. A.; Sagun, V. V.; Bravina, L. V.; Zabrodin, E. E.

2018-06-01

We propose a novel family of equations of state for symmetric nuclear matter based on the induced surface tension concept for the hard-core repulsion. It is shown that having only four adjustable parameters the suggested equations of state can, simultaneously, reproduce not only the main properties of the nuclear matter ground state, but the proton flow constraint up its maximal particle number densities. Varying the model parameters we carefully examine the range of values of incompressibility constant of normal nuclear matter and its critical temperature, which are consistent with the proton flow constraint. This analysis allows us to show that the physically most justified value of nuclear matter critical temperature is 15.5-18 MeV, the incompressibility constant is 270-315 MeV and the hard-core radius of nucleons is less than 0.4 fm.

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

Finite BRST-BFV transformations for dynamical systems with second-class constraints

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2015-06-01

We study finite field-dependent BRST-BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

Learning in Context: Linguistic and Attentional Constraints on Children's Color Term Learning

ERIC Educational Resources Information Center

O'Hanlon, Catherine G.; Roberson, Debi

2006-01-01

Three experiments investigated whether linguistic and/or attentional constraints might account for preschoolers' difficulties when learning color terms. Task structure and demands were equated across experiments, and both speed and degree of learning were compared. In Experiment 1, 3-year-olds who were matched on vocabulary score were taught new…

Divergence Boundary Conditions for Vector Helmholtz Equations with Divergence Constraints

NASA Technical Reports Server (NTRS)

Kangro, Urve; Nicolaides, Roy

1997-01-01

The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.

Oscillation theorems for second order nonlinear forced differential equations.

PubMed

Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md

2014-01-01

In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature.

Implications for Climate Sensitivity from the Response to Individual Forcings

NASA Technical Reports Server (NTRS)

Marvel, Kate; Schmidt, Gavin A.; Miller, Ron L.; Nazarenko, Larissa

2015-01-01

Climate sensitivity to doubled CO2 is a widely-used metric of the large-scale response to external forcing. Climate models predict a wide range for two commonly used definitions: the transient climate response (TCR: the warming after 70 years of CO2 concentrations that riseat 1 per year), and the equilibrium climate sensitivity (ECS: the equilibrium temperature change following a doubling of CO2 concentrations). Many observational datasets have been used to constrain these values, including temperature trends over the recent past 16, inferences from paleo-climate and process-based constraints from the modern satellite eras. However, as the IPCC recently reported different classes of observational constraints produce somewhat incongruent ranges. Here we show that climate sensitivity estimates derived from recent observations must account for the efficacy of each forcing active during the historical period. When we use single forcing experiments to estimate these efficacies and calculate climate sensitivity from the observed twentieth-century warming, our estimates of both TCR and ECS are revised upward compared to previous studies, improving the consistency with independent constraints.

Optimal multi-floor plant layout based on the mathematical programming and particle swarm optimization.

PubMed

Lee, Chang Jun

2015-01-01

In the fields of researches associated with plant layout optimization, the main goal is to minimize the costs of pipelines and pumping between connecting equipment under various constraints. However, what is the lacking of considerations in previous researches is to transform various heuristics or safety regulations into mathematical equations. For example, proper safety distances between equipments have to be complied for preventing dangerous accidents on a complex plant. Moreover, most researches have handled single-floor plant. However, many multi-floor plants have been constructed for the last decade. Therefore, the proper algorithm handling various regulations and multi-floor plant should be developed. In this study, the Mixed Integer Non-Linear Programming (MINLP) problem including safety distances, maintenance spaces, etc. is suggested based on mathematical equations. The objective function is a summation of pipeline and pumping costs. Also, various safety and maintenance issues are transformed into inequality or equality constraints. However, it is really hard to solve this problem due to complex nonlinear constraints. Thus, it is impossible to use conventional MINLP solvers using derivatives of equations. In this study, the Particle Swarm Optimization (PSO) technique is employed. The ethylene oxide plant is illustrated to verify the efficacy of this study.

The Forced van der Pol Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2009-01-01

We report on a study of the forced van der Pol equation x + [epsilon](x[superscript 2] - 1)x + x = F cos[omega]t, by solving numerically the differential equation for a variety of values of the parameters [epsilon], F and [omega]. In doing so, many striking and interesting trajectories can be discovered and phenomena such as frequency entrainment,…

Integrated force method versus displacement method for finite element analysis

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Berke, L.; Gallagher, R. H.

1991-01-01

A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EEs) are integrated with the global compatibility conditions (CCs) to form the governing set of equations. In IFM the CCs are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

Integrated force method versus displacement method for finite element analysis

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.

1990-01-01

A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

Application of the method of steepest descent to laminated shield weight optimization with several constraints: Theory

NASA Technical Reports Server (NTRS)

Lahti, G. P.

1971-01-01

The method of steepest descent used in optimizing one-dimensional layered radiation shields is extended to multidimensional, multiconstraint situations. The multidimensional optimization algorithm and equations are developed for the case of a dose constraint in any one direction being dependent only on the shield thicknesses in that direction and independent of shield thicknesses in other directions. Expressions are derived for one-, two-, and three-dimensional cases (one, two, and three constraints). The precedure is applicable to the optimization of shields where there are different dose constraints and layering arrangements in the principal directions.

An integrable family of Monge-Ampère equations and their multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sarioǧlu, Ö.

1993-02-01

We have identified a completely integrable family of Monge-Ampère equations through an examination of their Hamiltonian structure. Starting with a variational formulation of the Monge-Ampère equations we have constructed the first Hamiltonian operator through an application of Dirac's theory of constraints. The completely integrable class of Monge-Ampère equations are then obtained by solving the Jacobi identities for a sufficiently general form of the second Hamiltonian operator that is compatible with the first.

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

Complementary Constrains on Component based Multiphase Flow Problems, Should It Be Implemented Locally or Globally?

NASA Astrophysics Data System (ADS)

Shao, H.; Huang, Y.; Kolditz, O.

2015-12-01

Multiphase flow problems are numerically difficult to solve, as it often contains nonlinear Phase transition phenomena A conventional technique is to introduce the complementarity constraints where fluid properties such as liquid saturations are confined within a physically reasonable range. Based on such constraints, the mathematical model can be reformulated into a system of nonlinear partial differential equations coupled with variational inequalities. They can be then numerically handled by optimization algorithms. In this work, two different approaches utilizing the complementarity constraints based on persistent primary variables formulation[4] are implemented and investigated. The first approach proposed by Marchand et.al[1] is using "local complementary constraints", i.e. coupling the constraints with the local constitutive equations. The second approach[2],[3] , namely the "global complementary constrains", applies the constraints globally with the mass conservation equation. We will discuss how these two approaches are applied to solve non-isothermal componential multiphase flow problem with the phase change phenomenon. Several benchmarks will be presented for investigating the overall numerical performance of different approaches. The advantages and disadvantages of different models will also be concluded. References[1] E.Marchand, T.Mueller and P.Knabner. Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: formulation and properties of the mathematical model, Computational Geosciences 17(2): 431-442, (2013). [2] A. Lauser, C. Hager, R. Helmig, B. Wohlmuth. A new approach for phase transitions in miscible multi-phase flow in porous media. Water Resour., 34,(2011), 957-966. [3] J. Jaffré, and A. Sboui. Henry's Law and Gas Phase Disappearance. Transp. Porous Media. 82, (2010), 521-526. [4] A. Bourgeat, M. Jurak and F. Smaï. Two-phase partially miscible flow and transport modeling in porous media : application to gas migration in a nuclear waste repository, Comp.Geosciences. (2009), Volume 13, Number 1, 29-42.

Topological constraints and the existence of force-free fields

NASA Technical Reports Server (NTRS)

Antiochos, S. K.

1986-01-01

A fundamental problem in plasma theory is the question of the existence of MHD equilibria. The issue of topological constraints is of crucial importance for the problem of the existence of equilibria. Heuristic methods are used to discuss the coronal wrapping pattern. It is concluded that for a given set of footpoint positions the wrapping pattern in the corona is completely fixed. The topological constraints are included in the boundary conditions on the Euler potentials and impost no additional restrictions on possible equilibria. Although this does not prove that equilibria always exist, it does show that the force-free problem is not overdetermined and that existence of equilibria is still an open question.

Constraints on flavor-dependent long range forces from solar neutrinos and KamLAND

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Abhijit; Dighe, Amol; Joshipura, Anjan S.

2007-05-01

Flavor-dependent long range (LR) leptonic forces, like those mediated by the Le-Lμ or Le-Lτ gauge bosons, constitute a minimal extension of the standard model that preserves its renormalizability. We study the impact of such interactions on the solar neutrino oscillations when the interaction range RLR is much larger than the Earth-Sun distance. The LR potential can dominate over the standard charged current potential inside the Sun in spite of strong constraints on the coupling α of the LR force coming from the atmospheric neutrino data and laboratory search for new forces. We demonstrate that the solar and atmospheric neutrino mass scales do not get trivially decoupled even if θ13 is vanishingly small. In addition, for α≳10-52 and normal hierarchy, resonant enhancement of θ13 results in nontrivial energy dependent effects on the νe survival probability. We perform a complete three generation analysis, and obtain constraints on α through a global fit to the solar neutrino and KamLAND data. We get the 3σ limits αeμ<3.4×10-53 and αeτ<2.5×10-53 when RLR is much smaller than our distance from the galactic center. With larger RLR, the collective LR potential due to all the electrons in the galaxy becomes significant and the constraints on α become stronger by up to two orders of magnitude.

Some Properties of Estimated Scale Invariant Covariance Structures.

ERIC Educational Resources Information Center

Dijkstra, T. K.

1990-01-01

An example of scale invariance is provided via the LISREL model that is subject only to classical normalizations and zero constraints on the parameters. Scale invariance implies that the estimated covariance matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. (TJH)

Guiding-center equations for electrons in ultraintense laser fields

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

Moore, J.E.; Fisch, N.J.

1994-01-01

The guiding-center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increase of the oscillating electrons, a simple frame-invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation.

Dynamically Consistent Shallow-Atmosphere Equations with a Complete Coriolis force

NASA Astrophysics Data System (ADS)

Tort, Marine; Dubos, Thomas; Bouchut, François; Zeitlin, Vladimir

2014-05-01

Dynamically Consistent Shallow-Atmosphere Equations with a Complete Coriolis force Marine Tort1, Thomas Dubos1, François Bouchut2 & Vladimir Zeitlin1,3 1 Laboratoire of Dynamical Meteorology, Univ. P. and M. Curie, Ecole Normale Supérieure, and Ecole Polytechnique, FRANCE 2 Université Paris-Est, Laboratoire d'Analyse et de Mathématiques Appliquées, FRANCE 3 Institut Universitaire de France Atmospheric and oceanic motion are usually modeled within the shallow-fluid approximation, which simplifies the 3D spherical geometry. For dynamical consistency, i.e. to ensure conservation laws for potential vorticity, energy and angular momentum, the horizontal component of the Coriolis force is neglected. Here new equation sets combining consistently a simplified shallow-fluid geometry with a complete Coriolis force is presented. The derivation invokes Hamilton's principle of least action with an approximate Lagrangian capturing the small increase with height of the solid-body entrainment velocity due to planetary rotation. A three-dimensional compressible model and a one-layer shallow-water model are obtained. The latter extends previous work done on the f-plane and β-plane. Preliminary numerical results confirm the accuracy of the 3D model within the range of parameters for which the equations are relevant. These new models could be useful to incorporate a full Coriolis force into existing numerical models and to disentangle the effects of the shallow-atmosphere approximation from those of the traditional approximation. Related papers: Tort M., Dubos T., Bouchut F. and Zeitlin V. Consistent shallow-water equations on the rotating sphere with complete Coriolis force and topography. J. Fluid Mech. (under revisions) Tort M. and Dubos T. Dynamically consistent shallow-atmosphere equations with a complete Coriolis force. Q.J.R. Meteorol. Soc. (DOI: 10.1002/qj.2274)

A coordinate free description of magnetohydrostatic equilibria

NASA Technical Reports Server (NTRS)

Martens, P. C. H.

1986-01-01

The question what geometrical restrictions are imposed on static magnetic fields by the magnetohydrostatic (MHS) equation is addressed. The general mathematical problem is therefore to determine the solutions of the MHS equations in the corona subject to an arbitrary normal component of the magnetic field at the boundary and arbitrary connectivity. What constraints the MHS equations impose on the geometry of the solutions, expressed in metric tensors, will be determined.

Sachs' free data in real connection variables

NASA Astrophysics Data System (ADS)

De Paoli, Elena; Speziale, Simone

2017-11-01

We discuss the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and use the Newman-Penrose formalism to shed light on the geometric meaning of the various constraints. We identify the equivalent of Sachs' constraint-free initial data as projections of connection components related to null rotations, i.e. the translational part of the ISO(2) group stabilising the internal null direction soldered to the hypersurface. A pair of second-class constraints reduces these connection components to the shear of a null geodesic congruence, thus establishing equivalence with the second-order formalism, which we show in details at the level of symplectic potentials. A special feature of the first-order formulation is that Sachs' propagating equations for the shear, away from the initial hypersurface, are turned into tertiary constraints; their role is to preserve the relation between connection and shear under retarded time evolution. The conversion of wave-like propagating equations into constraints is possible thanks to an algebraic Bianchi identity; the same one that allows one to describe the radiative data at future null infinity in terms of a shear of a (non-geodesic) asymptotic null vector field in the physical spacetime. Finally, we compute the modification to the spin coefficients and the null congruence in the presence of torsion.

Advanced data assimilation in strongly nonlinear dynamical systems

NASA Technical Reports Server (NTRS)

Miller, Robert N.; Ghil, Michael; Gauthiez, Francois

1994-01-01

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Inverts permittivity and conductivity with structural constraint in GPR FWI based on truncated Newton method

NASA Astrophysics Data System (ADS)

Ren, Qianci

2018-04-01

Full waveform inversion (FWI) of ground penetrating radar (GPR) is a promising technique to quantitatively evaluate the permittivity and conductivity of near subsurface. However, these two parameters are simultaneously inverted in the GPR FWI, increasing the difficulty to obtain accurate inversion results for both parameters. In this study, I present a structural constrained GPR FWI procedure to jointly invert the two parameters, aiming to force a structural relationship between permittivity and conductivity in the process of model reconstruction. The structural constraint is enforced by a cross-gradient function. In this procedure, the permittivity and conductivity models are inverted alternately at each iteration and updated with hierarchical frequency components in the frequency domain. The joint inverse problem is solved by the truncated Newton method which considering the effect of Hessian operator and using the approximated solution of Newton equation to be the perturbation model in the updating process. The joint inversion procedure is tested by three synthetic examples. The results show that jointly inverting permittivity and conductivity in GPR FWI effectively increases the structural similarities between the two parameters, corrects the structures of parameter models, and significantly improves the accuracy of conductivity model, resulting in a better inversion result than the individual inversion.

Robust H∞ control of active vehicle suspension under non-stationary running

NASA Astrophysics Data System (ADS)

Guo, Li-Xin; Zhang, Li-Ping

2012-12-01

Due to complexity of the controlled objects, the selection of control strategies and algorithms in vehicle control system designs is an important task. Moreover, the control problem of automobile active suspensions has been become one of the important relevant investigations due to the constrained peculiarity and parameter uncertainty of mathematical models. In this study, after establishing the non-stationary road surface excitation model, a study on the active suspension control for non-stationary running condition was conducted using robust H∞ control and linear matrix inequality optimization. The dynamic equation of a two-degree-of-freedom quarter car model with parameter uncertainty was derived. The H∞ state feedback control strategy with time-domain hard constraints was proposed, and then was used to design the active suspension control system of the quarter car model. Time-domain analysis and parameter robustness analysis were carried out to evaluate the proposed controller stability. Simulation results show that the proposed control strategy has high systemic stability on the condition of non-stationary running and parameter uncertainty (including suspension mass, suspension stiffness and tire stiffness). The proposed control strategy can achieve a promising improvement on ride comfort and satisfy the requirements of dynamic suspension deflection, dynamic tire loads and required control forces within given constraints, as well as non-stationary running condition.

Free Vibration Analysis of DWCNTs Using CDM and Rayleigh-Schmidt Based on Nonlocal Euler-Bernoulli Beam Theory

PubMed Central

2014-01-01

The free vibration response of double-walled carbon nanotubes (DWCNTs) is investigated. The DWCNTs are modelled as two beams, interacting between them through the van der Waals forces, and the nonlocal Euler-Bernoulli beam theory is used. The governing equations of motion are derived using a variational approach and the free frequencies of vibrations are obtained employing two different approaches. In the first method, the two double-walled carbon nanotubes are discretized by means of the so-called “cell discretization method” (CDM) in which each nanotube is reduced to a set of rigid bars linked together by elastic cells. The resulting discrete system takes into account nonlocal effects, constraint elasticities, and the van der Waals forces. The second proposed approach, belonging to the semianalytical methods, is an optimized version of the classical Rayleigh quotient, as proposed originally by Schmidt. The resulting conditions are solved numerically. Numerical examples end the paper, in which the two approaches give lower-upper bounds to the true values, and some comparisons with existing results are offered. Comparisons of the present numerical results with those from the open literature show an excellent agreement. PMID:24715807

A numerical method for simulations of rigid fiber suspensions

NASA Astrophysics Data System (ADS)

Tornberg, Anna-Karin; Gustavsson, Katarina

2006-06-01

In this paper, we present a numerical method designed to simulate the challenging problem of the dynamics of slender fibers immersed in an incompressible fluid. Specifically, we consider microscopic, rigid fibers, that sediment due to gravity. Such fibers make up the micro-structure of many suspensions for which the macroscopic dynamics are not well understood. Our numerical algorithm is based on a non-local slender body approximation that yields a system of coupled integral equations, relating the forces exerted on the fibers to their velocities, which takes into account the hydrodynamic interactions of the fluid and the fibers. The system is closed by imposing the constraints of rigid body motions. The fact that the fibers are straight have been further exploited in the design of the numerical method, expanding the force on Legendre polynomials to take advantage of the specific mathematical structure of a finite-part integral operator, as well as introducing analytical quadrature in a manner possible only for straight fibers. We have carefully treated issues of accuracy, and present convergence results for all numerical parameters before we finally discuss the results from simulations including a larger number of fibers.

SENSITIVITY OF HELIOSEISMIC TRAVEL TIMES TO THE IMPOSITION OF A LORENTZ FORCE LIMITER IN COMPUTATIONAL HELIOSEISMOLOGY

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

Moradi, Hamed; Cally, Paul S., E-mail: hamed.moradi@monash.edu

The rapid exponential increase in the Alfvén wave speed with height above the solar surface presents a serious challenge to physical modeling of the effects of magnetic fields on solar oscillations, as it introduces a significant Courant-Friedrichs-Lewy time-step constraint for explicit numerical codes. A common approach adopted in computational helioseismology, where long simulations in excess of 10 hr (hundreds of wave periods) are often required, is to cap the Alfvén wave speed by artificially modifying the momentum equation when the ratio between the Lorentz and hydrodynamic forces becomes too large. However, recent studies have demonstrated that the Alfvén wave speedmore » plays a critical role in the MHD mode conversion process, particularly in determining the reflection height of the upwardly propagating helioseismic fast wave. Using numerical simulations of helioseismic wave propagation in constant inclined (relative to the vertical) magnetic fields we demonstrate that the imposition of such artificial limiters significantly affects time-distance travel times unless the Alfvén wave-speed cap is chosen comfortably in excess of the horizontal phase speeds under investigation.« less

Numerical Simulation of Forced and Free-to-Roll Delta-Wing Motions

NASA Technical Reports Server (NTRS)

Chaderjian, Neal M.; Schiff, Lewis B.

1996-01-01

The three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) equations are used to numerically simulate nonsteady vortical flow about a 65-deg sweep delta wing at 30-deg angle of attack. Two large-amplitude, high-rate, forced-roll motions, and a damped free-to-roll motion are presented. The free-to-roll motion is computed by coupling the time-dependent RANS equations to the flight dynamic equation of motion. The computed results are in good agreement with the forces, moments, and roll-angle time histories. Vortex breakdown is present in each case. Significant time lags in the vortex breakdown motions relative to the body motions strongly influence the dynamic forces and moments.

The electromagnetic force field, fluid flow field and temperature profiles in levitated metal droplets

NASA Technical Reports Server (NTRS)

El-Kaddah, N.; Szekely, J.

1982-01-01

A mathematical representation was developed for the electromagnetic force field, the flow field, the temperature field (and for transport controlled kinetics), in a levitation melted metal droplet. The technique of mutual inductances was employed for the calculation of the electromagnetic force field, while the turbulent Navier - Stokes equations and the turbulent convective transport equations were used to represent the fluid flow field, the temperature field and the concentration field. The governing differential equations, written in spherical coordinates, were solved numerically. The computed results were in good agreement with measurements, regarding the lifting force, and the average temperature of the specimen and carburization rates, which were transport controlled.

An integrated control scheme for space robot after capturing non-cooperative target

NASA Astrophysics Data System (ADS)

Wang, Mingming; Luo, Jianjun; Yuan, Jianping; Walter, Ulrich

2018-06-01

How to identify the mass properties and eliminate the unknown angular momentum of space robotic system after capturing a non-cooperative target is of great challenge. This paper focuses on designing an integrated control framework which includes detumbling strategy, coordination control and parameter identification. Firstly, inverted and forward chain approaches are synthesized for space robot to obtain dynamic equation in operational space. Secondly, a detumbling strategy is introduced using elementary functions with normalized time, while the imposed end-effector constraints are considered. Next, a coordination control scheme for stabilizing both base and end-effector based on impedance control is implemented with the target's parameter uncertainty. With the measurements of the forces and torques exerted on the target, its mass properties are estimated during the detumbling process accordingly. Simulation results are presented using a 7 degree-of-freedom kinematically redundant space manipulator, which verifies the performance and effectiveness of the proposed method.

A revised version of the transfer matrix method to analyze one-dimensional structures

NASA Technical Reports Server (NTRS)

Nitzsche, F.

1983-01-01

A new and general method to analyze both free and forced vibration characteristics of one-dimensional structures is discussed in this paper. This scheme links for the first time the classical transfer matrix method with the recently developed integrating matrix technique to integrate systems of differential equations. Two alternative approaches to the problem are presented. The first is based upon the lumped parameter model to account for the inertia properties of the structure. The second releases that constraint allowing a more precise description of the physical system. The free vibration of a straight uniform beam under different support conditions is analyzed to test the accuracy of the two models. Finally some results for the free vibration of a 12th order system representing a curved, rotating beam prove that the present method is conveniently extended to more complicated structural dynamics problems.

Restoration of the contact surface in FORCE-type centred schemes I: Homogeneous two-dimensional shallow water equations

NASA Astrophysics Data System (ADS)

Canestrelli, Alberto; Toro, Eleuterio F.

2012-10-01

Recently, the FORCE centred scheme for conservative hyperbolic multi-dimensional systems has been introduced in [34] and has been applied to Euler and relativistic MHD equations, solved on unstructured meshes. In this work we propose a modification of the FORCE scheme, named FORCE-Contact, that provides improved resolution of contact and shear waves. This paper presents the technique in full detail as applied to the two-dimensional homogeneous shallow water equations. The improvements due to the new method are particularly evident when an additional equation is solved for a tracer, since the modified scheme exactly resolves isolated and steady contact discontinuities. The improvement is considerable also for slowly moving contact discontinuities, for shear waves and for steady states in meandering channels. For these types of flow fields, the numerical results provided by the new FORCE-Contact scheme are comparable with, and sometimes better than, the results obtained from upwind schemes, such as Roes scheme for example. In a companion paper, a similar approach to restoring the missing contact wave and preserving well-balanced properties for non-conservative one- and two-layer shallow water equations is introduced. However, the procedure is general and it is in principle applicable to other multidimensional hyperbolic systems in conservative and non-conservative form, such as the Euler equations for compressible gas dynamics.

Time variant analysis of large scale constrained rotorcraft systems dynamics - An exploitation of IBM-3090 vector-processor's pipe-lining feature

NASA Technical Reports Server (NTRS)

Amirouche, F. M. L.; Shareef, N. H.; Xie, M.

1991-01-01

A generalized algorithmic procedure is presented for handling the constraints in transmissions, which are treated as a multibody system of interconnected rigid/flexible bodies. The type of constraints are classified based on the interconnection of the bodies, assuming one or more points of contact to exist between them. The method is explained through flow charts and configuration/interaction tables. A significant increase in speed of execution is achieved by vectorizing the developed code in computationally intensive areas. The study of an example consisting of two meshing disks rotating at high angular velocity is carried out. The dynamic behavior of the constraint forces associated with the generalized coordinates of the system are plotted by selecting various modes. Applications are intended for the study of dynamic and subsequent prediction of constraint forces at the gear teeth contacting points in helicopter transmissions with the aim of improving performance dependability.

Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2017-12-01

In this paper, the generalized variable-coefficient forced Kadomtsev-Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

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

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE PAGES

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

2016-07-26

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Gravity-driven groundwater flow and slope failure potential: 1. Elastic effective-stress model

USGS Publications Warehouse

Iverson, Richard M.; Reid, Mark E.

1992-01-01

Hilly or mountainous topography influences gravity-driven groundwater flow and the consequent distribution of effective stress in shallow subsurface environments. Effective stress, in turn, influences the potential for slope failure. To evaluate these influences, we formulate a two-dimensional, steady state, poroelastic model. The governing equations incorporate groundwater effects as body forces, and they demonstrate that spatially uniform pore pressure changes do not influence effective stresses. We implement the model using two finite element codes. As an illustrative case, we calculate the groundwater flow field, total body force field, and effective stress field in a straight, homogeneous hillslope. The total body force and effective stress fields show that groundwater flow can influence shear stresses as well as effective normal stresses. In most parts of the hillslope, groundwater flow significantly increases the Coulomb failure potential Φ, which we define as the ratio of maximum shear stress to mean effective normal stress. Groundwater flow also shifts the locus of greatest failure potential toward the slope toe. However, the effects of groundwater flow on failure potential are less pronounced than might be anticipated on the basis of a simpler, one-dimensional, limit equilibrium analysis. This is a consequence of continuity, compatibility, and boundary constraints on the two-dimensional flow and stress fields, and it points to important differences between our elastic continuum model and limit equilibrium models commonly used to assess slope stability.

Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck

NASA Astrophysics Data System (ADS)

Kumar, Suresh; Xu, Lixin

2014-10-01

In this paper, we study a cosmological model in general relativity within the framework of spatially flat Friedmann-Robertson-Walker space-time filled with ordinary matter (baryonic), radiation, dark matter and dark energy, where the latter two components are described by Chevallier-Polarski-Linder equation of state parameters. We utilize the observational data sets from SNLS3, BAO and Planck + WMAP9 + WiggleZ measurements of matter power spectrum to constrain the model parameters. We find that the current observational data offer tight constraints on the equation of state parameter of dark matter. We consider the perturbations and study the behavior of dark matter by observing its effects on CMB and matter power spectra. We find that the current observational data favor the cold dark matter scenario with the cosmological constant type dark energy at the present epoch.

Inertial torque during reaching directly impacts grip-force adaptation to weightless objects.

PubMed

Giard, T; Crevecoeur, F; McIntyre, J; Thonnard, J-L; Lefèvre, P

2015-11-01

A hallmark of movement control expressed by healthy humans is the ability to gradually improve motor performance through learning. In the context of object manipulation, previous work has shown that the presence of a torque load has a direct impact on grip-force control, characterized by a significantly slower grip-force adjustment across lifting movements. The origin of this slower adaptation rate remains unclear. On the one hand, information about tangential constraints during stationary holding may be difficult to extract in the presence of a torque. On the other hand, inertial torque experienced during movement may also potentially disrupt the grip-force adjustments, as the dynamical constraints clearly differ from the situation when no torque load is present. To address the influence of inertial torque loads, we instructed healthy adults to perform visually guided reaching movements in weightlessness while holding an unbalanced object relative to the grip axis. Weightlessness offered the possibility to remove gravitational constraints and isolate the effect of movement-related feedback on grip force adjustments. Grip-force adaptation rates were compared with a control group who manipulated a balanced object without any torque load and also in weightlessness. Our results clearly show that grip-force adaptation in the presence of a torque load is significantly slower, which suggests that the presence of torque loads experienced during movement may alter our internal estimates of how much force is required to hold an unbalanced object stable. This observation may explain why grasping objects around the expected location of the center of mass is such an important component of planning and control of manipulation tasks.

Extension of Murray's law using a non-Newtonian model of blood flow.

PubMed

Revellin, Rémi; Rousset, François; Baud, David; Bonjour, Jocelyn

2009-05-15

So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. MODELING: In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. SigmaR(c) = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n. We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature. It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

Constrained Maximum Likelihood Estimation for Two-Level Mean and Covariance Structure Models

ERIC Educational Resources Information Center

Bentler, Peter M.; Liang, Jiajuan; Tang, Man-Lai; Yuan, Ke-Hai

2011-01-01

Maximum likelihood is commonly used for the estimation of model parameters in the analysis of two-level structural equation models. Constraints on model parameters could be encountered in some situations such as equal factor loadings for different factors. Linear constraints are the most common ones and they are relatively easy to handle in…

Analysis of the pen pressure and grip force signal during basic drawing tasks: The timing and speed changes impact drawing characteristics.

PubMed

Gatouillat, Arthur; Dumortier, Antoine; Perera, Subashan; Badr, Youakim; Gehin, Claudine; Sejdić, Ervin

2017-08-01

Writing is a complex fine and trained motor skill, involving complex biomechanical and cognitive processes. In this paper, we propose the study of writing kinetics using three angles: the pen-tip normal force, the total grip force signal and eventually writing quality assessment. In order to collect writing kinetics data, we designed a sensor collecting these characteristics simultaneously. Ten healthy right-handed adults were recruited and were asked to perform four tasks: first, they were instructed to draw circles at a speed they considered comfortable; they then were instructed to draw circles at a speed they regarded as fast; afterwards, they repeated the comfortable task compelled to follow the rhythm of a metronome; and eventually they performed the fast task under the same timing constraints. Statistical differences between the tasks were computed, and while pen-tip normal force and total grip force signal were not impacted by the changes introduced in each task, writing quality features were affected by both the speed changes and timing constraint changes. This verifies the already-studied speed-accuracy trade-off and suggest the existence of a timing constraints-accuracy trade-off. Copyright © 2017 Elsevier Ltd. All rights reserved.

Determination of gas & liquid two-phase flow regime transitions in wellbore annulus by virtual mass force coefficient when gas cut

NASA Astrophysics Data System (ADS)

Qu, Junbo; Yan, Tie; Sun, Xiaofeng; Chen, Ye; Pan, Yi

2017-10-01

With the development of drilling technology to deeper stratum, overflowing especially gas cut occurs frequently, and then flow regime in wellbore annulus is from the original drilling fluid single-phase flow into gas & liquid two-phase flow. By using averaged two-fluid model equations and the basic principle of fluid mechanics to establish the continuity equations and momentum conservation equations of gas phase & liquid phase respectively. Relationship between pressure and density of gas & liquid was introduced to obtain hyperbolic equation, and get the expression of the dimensionless eigenvalue of the equation by using the characteristic line method, and analyze wellbore flow regime to get the critical gas content under different virtual mass force coefficients. Results show that the range of equation eigenvalues is getting smaller and smaller with the increase of gas content. When gas content reaches the critical point, the dimensionless eigenvalue of equation has no real solution, and the wellbore flow regime changed from bubble flow to bomb flow. When virtual mass force coefficients are 0.50, 0.60, 0.70 and 0.80 respectively, the critical gas contents are 0.32, 0.34, 0.37 and 0.39 respectively. The higher the coefficient of virtual mass force, the higher gas content in wellbore corresponding to the critical point of transition flow regime, which is in good agreement with previous experimental results. Therefore, it is possible to determine whether there is a real solution of the dimensionless eigenvalue of equation by virtual mass force coefficient and wellbore gas content, from which we can obtain the critical condition of wellbore flow regime transformation. It can provide theoretical support for the accurate judgment of the annular flow regime.

Piezoresistive Cantilever Performance—Part II: Optimization

PubMed Central

Park, Sung-Jin; Doll, Joseph C.; Rastegar, Ali J.; Pruitt, Beth L.

2010-01-01

Piezoresistive silicon cantilevers fabricated by ion implantation are frequently used for force, displacement, and chemical sensors due to their low cost and electronic readout. However, the design of piezoresistive cantilevers is not a straightforward problem due to coupling between the design parameters, constraints, process conditions, and performance. We systematically analyzed the effect of design and process parameters on force resolution and then developed an optimization approach to improve force resolution while satisfying various design constraints using simulation results. The combined simulation and optimization approach is extensible to other doping methods beyond ion implantation in principle. The optimization results were validated by fabricating cantilevers with the optimized conditions and characterizing their performance. The measurement results demonstrate that the analytical model accurately predicts force and displacement resolution, and sensitivity and noise tradeoff in optimal cantilever performance. We also performed a comparison between our optimization technique and existing models and demonstrated eight times improvement in force resolution over simplified models. PMID:20333323

Exact solutions in 3D new massive gravity.

PubMed

Ahmedov, Haji; Aliev, Alikram N

2011-01-14

We show that the field equations of new massive gravity (NMG) consist of a massive (tensorial) Klein-Gordon-type equation with a curvature-squared source term and a constraint equation. We also show that, for algebraic type D and N spacetimes, the field equations of topologically massive gravity (TMG) can be thought of as the "square root" of the massive Klein-Gordon-type equation. Using this fact, we establish a simple framework for mapping all types D and N solutions of TMG into NMG. Finally, we present new examples of types D and N solutions to NMG.

Exact Solutions in 3D New Massive Gravity

NASA Astrophysics Data System (ADS)

Ahmedov, Haji; Aliev, Alikram N.

2011-01-01

We show that the field equations of new massive gravity (NMG) consist of a massive (tensorial) Klein-Gordon-type equation with a curvature-squared source term and a constraint equation. We also show that, for algebraic type D and N spacetimes, the field equations of topologically massive gravity (TMG) can be thought of as the “square root” of the massive Klein-Gordon-type equation. Using this fact, we establish a simple framework for mapping all types D and N solutions of TMG into NMG. Finally, we present new examples of types D and N solutions to NMG.

CCM Continuity Constraint Method: A finite-element computational fluid dynamics algorithm for incompressible Navier-Stokes fluid flows

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

Williams, P. T.

1993-09-01

As the field of computational fluid dynamics (CFD) continues to mature, algorithms are required to exploit the most recent advances in approximation theory, numerical mathematics, computing architectures, and hardware. Meeting this requirement is particularly challenging in incompressible fluid mechanics, where primitive-variable CFD formulations that are robust, while also accurate and efficient in three dimensions, remain an elusive goal. This dissertation asserts that one key to accomplishing this goal is recognition of the dual role assumed by the pressure, i.e., a mechanism for instantaneously enforcing conservation of mass and a force in the mechanical balance law for conservation of momentum. Provingmore » this assertion has motivated the development of a new, primitive-variable, incompressible, CFD algorithm called the Continuity Constraint Method (CCM). The theoretical basis for the CCM consists of a finite-element spatial semi-discretization of a Galerkin weak statement, equal-order interpolation for all state-variables, a 0-implicit time-integration scheme, and a quasi-Newton iterative procedure extended by a Taylor Weak Statement (TWS) formulation for dispersion error control. Original contributions to algorithmic theory include: (a) formulation of the unsteady evolution of the divergence error, (b) investigation of the role of non-smoothness in the discretized continuity-constraint function, (c) development of a uniformly H 1 Galerkin weak statement for the Reynolds-averaged Navier-Stokes pressure Poisson equation, (d) derivation of physically and numerically well-posed boundary conditions, and (e) investigation of sparse data structures and iterative methods for solving the matrix algebra statements generated by the algorithm.« less

Eulerian Formulation of Spatially Constrained Elastic Rods

NASA Astrophysics Data System (ADS)

Huynen, Alexandre

Slender elastic rods are ubiquitous in nature and technology. For a vast majority of applications, the rod deflection is restricted by an external constraint and a significant part of the elastic body is in contact with a stiff constraining surface. The research work presented in this doctoral dissertation formulates a computational model for the solution of elastic rods constrained inside or around frictionless tube-like surfaces. The segmentation strategy adopted to cope with this complex class of problems consists in sequencing the global problem into, comparatively simpler, elementary problems either in continuous contact with the constraint or contact-free between their extremities. Within the conventional Lagrangian formulation of elastic rods, this approach is however associated with two major drawbacks. First, the boundary conditions specifying the locations of the rod centerline at both extremities of each elementary problem lead to the establishment of isoperimetric constraints, i.e., integral constraints on the unknown length of the rod. Second, the assessment of the unilateral contact condition requires, in principle, the comparison of two curves parametrized by distinct curvilinear coordinates, viz. the rod centerline and the constraint axis. Both conspire to burden the computations associated with the method. To streamline the solution along the elementary problems and rationalize the assessment of the unilateral contact condition, the rod governing equations are reformulated within the Eulerian framework of the constraint. The methodical exploration of both types of elementary problems leads to specific formulations of the rod governing equations that stress the profound connection between the mechanics of the rod and the geometry of the constraint surface. The proposed Eulerian reformulation, which restates the rod local equilibrium in terms of the curvilinear coordinate associated with the constraint axis, describes the rod deformed configuration by means of either its relative position with respect to the constraint axis (contact-free segments) or its angular position on the constraint surface (continuous contacts.) This formulation circumvents both drawbacks that afflict the conventional Lagrangian approach associated with the segmentation strategy. As the a priori unknown domain, viz. the rod length, is substituted for the known constraint axis, the free boundary problem and the associated isoperimetric constraints are converted into a classical two-point boundary value problem. Additionally, the description of the rod deflection by means of its eccentricity with respect to the constraint axis trivializes the assessment of the unilateral contact condition. Along continuous contacts, this formulation expresses the strain variables, measuring the rod change of shape, in terms of the geometric invariants of the constraint surface, and emphasizes the influence of the constraint local geometry on the reaction pressure. Formalizing the segmentation strategy, a computational model that exploits the Eulerian formulation of the rod governing equations is devised. To solve the quasi-static deflection of elastic rods constrained inside or around a tube-like surface, this computational model identifies the number of contacts, their nature (either discrete or continuous), and the rod configuration at the connections that satisfies the unilateral contact condition and preserves the rod integrity along the sequence of elementary problems.

Phase-field model of vapor-liquid-solid nanowire growth

NASA Astrophysics Data System (ADS)

Wang, Nan; Upmanyu, Moneesh; Karma, Alain

2018-03-01

We present a multiphase-field model to describe quantitatively nanowire growth by the vapor-liquid-solid (VLS) process. The free-energy functional of this model depends on three nonconserved order parameters that distinguish the vapor, liquid, and solid phases and describe the energetic properties of various interfaces, including arbitrary forms of anisotropic γ plots for the solid-vapor and solid-liquid interfaces. The evolution equations for those order parameters describe basic kinetic processes including the rapid (quasi-instantaneous) equilibration of the liquid catalyst to a droplet shape with constant mean curvature, the slow incorporation of growth atoms at the droplet surface, and crystallization within the droplet. The standard constraint that the sum of the phase fields equals unity and the conservation of the number of catalyst atoms, which relates the catalyst volume to the concentration of growth atoms inside the droplet, are handled via separate Lagrange multipliers. An analysis of the model is presented that rigorously maps the phase-field equations to a desired set of sharp-interface equations for the evolution of the phase boundaries under the constraint of force balance at three-phase junctions (triple points) given by the Young-Herring relation that includes torque term related to the anisotropy of the solid-liquid and solid-vapor interface excess free energies. Numerical examples of growth in two dimensions are presented for the simplest case of vanishing crystalline anisotropy and the more realistic case of a solid-liquid γ plot with cusped minima corresponding to two sets of (10 ) and (11 ) facets. The simulations reproduce many of the salient features of nanowire growth observed experimentally, including growth normal to the substrate with tapering of the side walls, transitions between different growth orientations, and crawling growth along the substrate. They also reproduce different observed relationships between the nanowire growth velocity and radius depending on the growth condition. For the basic normal growth mode, the steady-state solid-liquid interface tip shape consists of a main facet intersected by two truncated side facets ending at triple points. The ratio of truncated and main facet lengths are in quantitative agreement with the prediction of sharp-interface theory that is developed here for faceted nanowire growth in two dimensions.

Development of multidisciplinary design optimization procedures for smart composite wings and turbomachinery blades

NASA Astrophysics Data System (ADS)

Jha, Ratneshwar

Multidisciplinary design optimization (MDO) procedures have been developed for smart composite wings and turbomachinery blades. The analysis and optimization methods used are computationally efficient and sufficiently rigorous. Therefore, the developed MDO procedures are well suited for actual design applications. The optimization procedure for the conceptual design of composite aircraft wings with surface bonded piezoelectric actuators involves the coupling of structural mechanics, aeroelasticity, aerodynamics and controls. The load carrying member of the wing is represented as a single-celled composite box beam. Each wall of the box beam is analyzed as a composite laminate using a refined higher-order displacement field to account for the variations in transverse shear stresses through the thickness. Therefore, the model is applicable for the analysis of composite wings of arbitrary thickness. Detailed structural modeling issues associated with piezoelectric actuation of composite structures are considered. The governing equations of motion are solved using the finite element method to analyze practical wing geometries. Three-dimensional aerodynamic computations are performed using a panel code based on the constant-pressure lifting surface method to obtain steady and unsteady forces. The Laplace domain method of aeroelastic analysis produces root-loci of the system which gives an insight into the physical phenomena leading to flutter/divergence and can be efficiently integrated within an optimization procedure. The significance of the refined higher-order displacement field on the aeroelastic stability of composite wings has been established. The effect of composite ply orientations on flutter and divergence speeds has been studied. The Kreisselmeier-Steinhauser (K-S) function approach is used to efficiently integrate the objective functions and constraints into a single envelope function. The resulting unconstrained optimization problem is solved using the Broyden-Fletcher-Goldberg-Shanno algorithm. The optimization problem is formulated with the objective of simultaneously minimizing wing weight and maximizing its aerodynamic efficiency. Design variables include composite ply orientations, ply thicknesses, wing sweep, piezoelectric actuator thickness and actuator voltage. Constraints are placed on the flutter/divergence dynamic pressure, wing root stresses and the maximum electric field applied to the actuators. Numerical results are presented showing significant improvements, after optimization, compared to reference designs. The multidisciplinary optimization procedure for the design of turbomachinery blades integrates aerodynamic and heat transfer design objective criteria along with various mechanical and geometric constraints on the blade geometry. The airfoil shape is represented by Bezier-Bernstein polynomials, which results in a relatively small number of design variables for the optimization. Thin shear layer approximation of the Navier-Stokes equation is used for the viscous flow calculations. Grid generation is accomplished by solving Poisson equations. The maximum and average blade temperatures are obtained through a finite element analysis. Total pressure and exit kinetic energy losses are minimized, with constraints on blade temperatures and geometry. The constrained multiobjective optimization problem is solved using the K-S function approach. The results for the numerical example show significant improvements after optimization.

78 FR 63208 - UPDATE-Meeting of the Community Preventive Services Task Force (Task Force)

Federal Register 2010, 2011, 2012, 2013, 2014

2013-10-23

..., and issues recommendations. These recommendations provide evidence-based options from which decision makers in communities, companies, health departments, health plans and healthcare systems, non..., available resources, and constraints of their constituents. The Task Force's recommendations, along with the...

Lepton flavorful fifth force and depth-dependent neutrino matter interactions

NASA Astrophysics Data System (ADS)

Wise, Mark B.; Zhang, Yue

2018-06-01

We consider a fifth force to be an interaction that couples to matter with a strength that grows with the number of atoms. In addition to competing with the strength of gravity a fifth force can give rise to violations of the equivalence principle. Current long range constraints on the strength and range of fifth forces are very impressive. Amongst possible fifth forces are those that couple to lepton flavorful charges L e - L μ or L e - L τ . They have the property that their range and strength are also constrained by neutrino interactions with matter. In this brief note we review the existing constraints on the allowed parameter space in gauged U{(1)}_{L_e-{L}_{μ },{L}_{τ }} . We find two regions where neutrino oscillation experiments are at the frontier of probing such a new force. In particular, there is an allowed range of parameter space where neutrino matter interactions relevant for long baseline oscillation experiments depend on the depth of the neutrino beam below the surface of the earth.

Cosmology with galaxy cluster phase spaces

NASA Astrophysics Data System (ADS)

Stark, Alejo; Miller, Christopher J.; Huterer, Dragan

2017-07-01

We present a novel approach to constrain accelerating cosmologies with galaxy cluster phase spaces. With the Fisher matrix formalism we forecast constraints on the cosmological parameters that describe the cosmological expansion history. We find that our probe has the potential of providing constraints comparable to, or even stronger than, those from other cosmological probes. More specifically, with 1000 (100) clusters uniformly distributed in the redshift range 0 ≤z ≤0.8 , after applying a conservative 80% mass scatter prior on each cluster and marginalizing over all other parameters, we forecast 1 σ constraints on the dark energy equation of state w and matter density parameter ΩM of σw=0.138 (0.431 ) and σΩM=0.007(0.025 ) in a flat universe. Assuming 40% mass scatter and adding a prior on the Hubble constant we can achieve a constraint on the Chevallier-Polarski-Linder parametrization of the dark energy equation of state parameters w0 and wa with 100 clusters in the same redshift range: σw 0=0.191 and σwa=2.712. Dropping the assumption of flatness and assuming w =-1 we also attain competitive constraints on the matter and dark energy density parameters: σΩ M=0.101 and σΩ Λ=0.197 for 100 clusters uniformly distributed in the range 0 ≤z ≤0.8 after applying a prior on the Hubble constant. We also discuss various observational strategies for tightening constraints in both the near and far future.

The Identities Hidden in the Matching Laws, and Their Uses

ERIC Educational Resources Information Center

Thorne, David R.

2010-01-01

Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help…

Radiation from Accelerating Electric Charges: The Third Derivative of Position

NASA Astrophysics Data System (ADS)

Butterworth, Edward

2010-03-01

While some textbooks appear to suggest that acceleration of an electric charge is both a necessary and sufficient cause for the generation of electromagnetic radiation, the question has in fact had an intricate and involved history. In particular, the acceleration of a charge in hyperbolic motion, the behavior of a charge supported against a gravitational force (and its implications for the Equivalence Principle), and a charge accelerated by a workless constraint have been the subject of repeated investigation. The present paper examines specifically the manner in which the third derivative of position enters into the equations of motion, and the implications this has for the emission of radiation. Plass opens his review article with the statement that ``A fundamental property of all charged particles is that electromagnetic energy is radiated whenever they are accelerated'' (Plass 1961; emphasis mine). His treatment of the equations of motion, however, emphasizes the importance of the occurrence of the third derivative of position therein, present in linear motion only when the rate of acceleration is increasing or decreasing. There appears to be general agreement that the presence of a nonzero third derivative indicates that this charge is radiating; but does its absence preclude radiation? This question leads back to the issues of charges accelerated by a uniform gravitational field. We will examine the equations of motion as presented in Fulton & Rohrlich (1960), Plass (1961), Barut (1964), Teitelboim (1970) and Mo & Papas (1971) in the light of more recent literature in an attempt to clarify this question.

Theory of equilibria of elastic 2-braids with interstrand interaction

NASA Astrophysics Data System (ADS)

Starostin, E. L.; van der Heijden, G. H. M.

2014-03-01

Motivated by continuum models for DNA supercoiling we formulate a theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. No assumption is made on the shape of the contact curve. The theory is developed in terms of a moving frame of directors attached to one of the strands. The other strand is tracked by including in this frame the normalised closest-approach chord connecting the two strands. The kinematic constant-distance constraint is formulated at strain level through the introduction of what we call braid strains. As a result the total potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Hard contact models are used to obtain the normal contact pressure between strands that has to be non-negative for a physically realisable solution without the need for external devices such as clamps or glue to keep the strands together. The theory is first illustrated by a number of problems that can be solved analytically and then applied to several new problems that have not hitherto been treated.

Quasivariational Solutions for First Order Quasilinear Equations with Gradient Constraint

NASA Astrophysics Data System (ADS)

Rodrigues, José Francisco; Santos, Lisa

2012-08-01

We prove the existence of solutions for a quasi-variational inequality of evolution with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable a priori estimates. We also obtain the existence of stationary solutions by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results.

Virasoro constraints and polynomial recursion for the linear Hodge integrals

NASA Astrophysics Data System (ADS)

Guo, Shuai; Wang, Gehao

2017-04-01

The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the Virasoro equations. The expression of our Virasoro constraints is simply a linear combination of the Virasoro operators, where the coefficients are restored from a power series for the Lambert W function. Then, using this result, we deduce a simple version of the Virasoro constraints for the linear Hodge partition function, where the coefficients are restored from the Gamma function. Finally, we establish the equivalence relation between the Virasoro constraints and polynomial recursion formula for the linear Hodge integrals.

Forcing function modeling for flow induced vibration

NASA Technical Reports Server (NTRS)

Fleeter, Sanford

1993-01-01

The fundamental forcing function unsteady aerodynamics for application to turbomachine blade row forced response are considered, accomplished through a series of experiments performed in a rotating annular cascade and a research axial flow turbine. In particular, the unsteady periodic flowfields downstream of rotating rows of perforated plates, airfoils and turbine blade rows are measured with a cross hot-wire and an unsteady total pressure probe. The unsteady velocity and static pressure fields were then analyzed harmonically and split into vortical and potential gusts, accomplished by developing a gust splitting analysis which includes both gust unsteady static pressure and velocity data. The perforated plate gusts closely were found to be linear theory vortical gusts, satisfying the vortical gust constraints. The airfoil and turbine blade row generated velocity perturbations did not satisfy the vortical gust constraints. However, the decomposition of the unsteady flow field separated the data into a propagating vortical component which satisfied these vortical gust constraints and a decaying potential component.

The Forced Soft Spring Equation

ERIC Educational Resources Information Center

Fay, T. H.

2006-01-01

Through numerical investigations, this paper studies examples of the forced Duffing type spring equation with [epsilon] negative. By performing trial-and-error numerical experiments, the existence is demonstrated of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions. Subharmonic boundaries are…

Parabola solitons for the nonautonomous KP equation in fluids and plasmas

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

Yu, Xin, E-mail: yuxin@buaa.edu.cn; Sun, Zhi-Yuan

Under investigation in this paper is a nonautonomous Kadomtsev–Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.

Final Technical Report for "Applied Mathematics Research: Simulation Based Optimization and Application to Electromagnetic Inverse Problems"

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

Haber, Eldad

2014-03-17

The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequality constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.

Parabola solitons for the nonautonomous KP equation in fluids and plasmas

NASA Astrophysics Data System (ADS)

Yu, Xin; Sun, Zhi-Yuan

2016-04-01

Under investigation in this paper is a nonautonomous Kadomtsev-Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.

Optical solitons to the resonance nonlinear Schrödinger equation by Sine-Gordon equation method

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru

2018-01-01

In this paper, we examined the optical solitons to the resonant nonlinear Schrödinger equation (R-NLSE) which describes the propagation of solitons through optical fibers. Three types of nonlinear media fibers are studied. They are; quadratic-cubic law, Kerr law and parabolic law. Dark, bright, dark-bright or combined optical and singular soliton solutions are derived using the sine-Gordon equation method (SGEM). The constraint conditions that naturally fall out of the solution structure which guarantee the existence of these solitons are also reported.

Notes on implementation of Coulomb friction in coupled dynamical simulations

NASA Technical Reports Server (NTRS)

Vandervoort, R. J.; Singh, R. P.

1987-01-01

A coupled dynamical system is defined as an assembly of rigid/flexible bodies that may be coupled by kinematic connections. The interfaces between bodies are modeled using hinges having 0 to 6 degrees of freedom. The equations of motion are presented for a mechanical system of n flexible bodies in a topological tree configuration. The Lagrange form of the D'Alembert principle was employed to derive the equations. The equations of motion are augmented by the kinematic constraint equations. This augmentation is accomplished via the method of singular value decomposition.

Analysis of stability for stochastic delay integro-differential equations.

PubMed

Zhang, Yu; Li, Longsuo

2018-01-01

In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

Importance of Force Decomposition for Local Stress Calculations in Biomembrane Molecular Simulations.

PubMed

Vanegas, Juan M; Torres-Sánchez, Alejandro; Arroyo, Marino

2014-02-11

Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.

Conformal and covariant Z4 formulation of the Einstein equations: Strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Guercilena, Federico; Köppel, Sven; Rezzolla, Luciano; Zanotti, Olindo

2018-04-01

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of standard gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in nonconservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

Solitary waves in the nonlinear Dirac equation in the presence of external driving forces

DOE PAGES

Mertens, Franz G.; Cooper, Fred; Quintero, Niurka R.; ...

2016-01-05

In this paper, we consider the nonlinear Dirac (NLD) equation in (1 + 1) dimensions with scalar–scalar self interaction g 2/κ + 1 (Ψ¯Ψ) κ + 1 in the presence of external forces as well as damping of the form f(x) - iμγ 0Ψ, where both f and Ψ are two-component spinors. We develop an approximate variational approach using collective coordinates (CC) for studying the time dependent response of the solitary waves to these external forces. This approach predicts intrinsic oscillations of the solitary waves, i.e. the amplitude, width and phase all oscillate with the same frequency. The translational motionmore » is also affected, because the soliton position oscillates around a mean trajectory. For κ = 1 we solve explicitly the CC equations of the variational approximation for slow moving solitary waves in a constant external force without damping and find reasonable agreement with solving numerically the CC equations. Finally, we then compare the results of the variational approximation with no damping with numerical simulations of the NLD equation for κ = 1, when the components of the external force are of the form f j = r j exp(–iΚx) and again find agreement if we take into account a certain linear excitation with specific wavenumber that is excited together with the intrinsic oscillations such that the momentum in a transformed NLD equation is conserved.« less

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

A robust, efficient equidistribution 2D grid generation method

NASA Astrophysics Data System (ADS)

Chacon, Luis; Delzanno, Gian Luca; Finn, John; Chung, Jeojin; Lapenta, Giovanni

2007-11-01

We present a new cell-area equidistribution method for two- dimensional grid adaptation [1]. The method is able to satisfy the equidistribution constraint to arbitrary precision while optimizing desired grid properties (such as isotropy and smoothness). The method is based on the minimization of the grid smoothness integral, constrained to producing a given positive-definite cell volume distribution. The procedure gives rise to a single, non-linear scalar equation with no free-parameters. We solve this equation numerically with the Newton-Krylov technique. The ellipticity property of the linearized scalar equation allows multigrid preconditioning techniques to be effectively used. We demonstrate a solution exists and is unique. Therefore, once the solution is found, the adapted grid cannot be folded due to the positivity of the constraint on the cell volumes. We present several challenging tests to show that our new method produces optimal grids in which the constraint is satisfied numerically to arbitrary precision. We also compare the new method to the deformation method [2] and show that our new method produces better quality grids. [1] G.L. Delzanno, L. Chac'on, J.M. Finn, Y. Chung, G. Lapenta, A new, robust equidistribution method for two-dimensional grid generation, in preparation. [2] G. Liao and D. Anderson, A new approach to grid generation, Appl. Anal. 44, 285--297 (1992).

Downhill cycling symmetry breaking: how the rider foils experiment

NASA Astrophysics Data System (ADS)

Ben Abu, Yuval; Wolfson, Ira; Bran, Gil; Yizhaq, Hezi

2017-11-01

In high-school teaching of mechanics, we deal, among other things, with the nature of static and kinetic friction, forces that are proportional to the normal force. Under the influence of frictional forces, a body moves down a rough sloped decline at a fixed rate of acceleration that is independent of its mass. This situation does not apply to cases where the frictional force is dependent upon velocity, such as bodies which are moving through a streaming fluid (such as raindrops falling to the ground). In this case the body moves with a continuously decreasing acceleration, eventually reaching a terminal velocity when the frictional and gravitational forces balance out. This velocity constraint is determined by the dependence of the frictional force on velocity and geometric parameters that determine the strength of the frictional force. We show here that a similar situation takes place when bicycles descend an incline with a fixed slope. We also investigated the dependence of the velocity constraint with mass, using bicycles equipped with sophisticated sensors that metamorphose them into data-processing laboratories.

Theoretical Pressure Distribution, Apparent Mass, and Moment of Inertia of a Disk Pendulum Oscillating at Low Frequency. M.S. Thesis - George Washington Univ., Washington, D. C.

NASA Technical Reports Server (NTRS)

Dunning, R. S.

1973-01-01

Equations are developed which give the pressure profile, the forces and torques on a disk pendulum by means of point source wave theory from acoustics. The pressure, force and torque equations for an unbaffled disk are developed. These equations are then used to calculate the apparent mass and apparent inertia for the pendulum.

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

NASA Astrophysics Data System (ADS)

Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.

2013-12-01

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.

INTEGRATION OF PARTICLE-GAS SYSTEMS WITH STIFF MUTUAL DRAG INTERACTION

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

Yang, Chao-Chin; Johansen, Anders, E-mail: ccyang@astro.lu.se, E-mail: anders@astro.lu.se

2016-06-01

Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff—particularly because of small particles and/or strong local solid concentration—that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct,more » we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force, and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force, as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can, for example, be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.« less

Chameleon vector bosons

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

Nelson, Ann E.; Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias, C-XVI Universidad Autonoma de Madrid Cantoblanco, Madrid 28049; Walsh, Jonathan

2008-05-01

We show that for a force mediated by a vector particle coupled to a conserved U(1) charge, the apparent range and strength can depend on the size and density of the source, and the proximity to other sources. This chameleon effect is due to screening from a light charged scalar. Such screening can weaken astrophysical constraints on new gauge bosons. As an example we consider the constraints on chameleonic gauged B-L. We show that although Casimir measurements greatly constrain any B-L force much stronger than gravity with range longer than 0.1 {mu}m, there remains an experimental window for a long-rangemore » chameleonic B-L force. Such a force could be much stronger than gravity, and long or infinite range in vacuum, but have an effective range near the surface of the earth which is less than a micron.« less

Multilevel algorithms for nonlinear optimization

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia; Dennis, J. E., Jr.

1994-01-01

Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

Automated Kinematics Equations Generation and Constrained Motion Planning Resolution for Modular and Reconfigurable Robots

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

Pin, Francois G.; Love, Lonnie L.; Jung, David L.

2004-03-29

Contrary to the repetitive tasks performed by industrial robots, the tasks in most DOE missions such as environmental restoration or Decontamination and Decommissioning (D&D) can be characterized as ''batches-of-one'', in which robots must be capable of adapting to changes in constraints, tools, environment, criteria and configuration. No commercially available robot control code is suitable for use with such widely varying conditions. In this talk we present our development of a ''generic code'' to allow real time (at loop rate) robot behavior adaptation to changes in task objectives, tools, number and type of constraints, modes of controls or kinematics configuration. Wemore » present the analytical framework underlying our approach and detail the design of its two major modules for the automatic generation of the kinematics equations when the robot configuration or tools change and for the motion planning under time-varying constraints. Sample problems illustrating the capabilities of the developed system are presented.« less

A Method for Optimal Load Dispatch of a Multi-zone Power System with Zonal Exchange Constraints

NASA Astrophysics Data System (ADS)

Hazarika, Durlav; Das, Ranjay

2018-04-01

This paper presented a method for economic generation scheduling of a multi-zone power system having inter zonal operational constraints. For this purpose, the generator rescheduling for a multi area power system having inter zonal operational constraints has been represented as a two step optimal generation scheduling problem. At first, the optimal generation scheduling has been carried out for the zone having surplus or deficient generation with proper spinning reserve using co-ordination equation. The power exchange required for the deficit zones and zones having no generation are estimated based on load demand and generation for the zone. The incremental transmission loss formulas for the transmission lines participating in the power transfer process among the zones are formulated. Using these, incremental transmission loss expression in co-ordination equation, the optimal generation scheduling for the zonal exchange has been determined. Simulation is carried out on IEEE 118 bus test system to examine the applicability and validity of the method.

Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.

MagIC: Fluid dynamics in a spherical shell simulator

NASA Astrophysics Data System (ADS)

Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.

2017-09-01

MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.

Path following control of planar snake robots using virtual holonomic constraints: theory and experiments.

PubMed

Rezapour, Ehsan; Pettersen, Kristin Y; Liljebäck, Pål; Gravdahl, Jan T; Kelasidi, Eleni

This paper considers path following control of planar snake robots using virtual holonomic constraints. In order to present a model-based path following control design for the snake robot, we first derive the Euler-Lagrange equations of motion of the system. Subsequently, we define geometric relations among the generalized coordinates of the system, using the method of virtual holonomic constraints. These appropriately defined constraints shape the geometry of a constraint manifold for the system, which is a submanifold of the configuration space of the robot. Furthermore, we show that the constraint manifold can be made invariant by a suitable choice of feedback. In particular, we analytically design a smooth feedback control law to exponentially stabilize the constraint manifold. We show that enforcing the appropriately defined virtual holonomic constraints for the configuration variables implies that the robot converges to and follows a desired geometric path. Numerical simulations and experimental results are presented to validate the theoretical approach.

Implication of adaptive smoothness constraint and Helmert variance component estimation in seismic slip inversion

NASA Astrophysics Data System (ADS)

Fan, Qingbiao; Xu, Caijun; Yi, Lei; Liu, Yang; Wen, Yangmao; Yin, Zhi

2017-10-01

When ill-posed problems are inverted, the regularization process is equivalent to adding constraint equations or prior information from a Bayesian perspective. The veracity of the constraints (or the regularization matrix R) significantly affects the solution, and a smoothness constraint is usually added in seismic slip inversions. In this paper, an adaptive smoothness constraint (ASC) based on the classic Laplacian smoothness constraint (LSC) is proposed. The ASC not only improves the smoothness constraint, but also helps constrain the slip direction. A series of experiments are conducted in which different magnitudes of noise are imposed and different densities of observation are assumed, and the results indicated that the ASC was superior to the LSC. Using the proposed ASC, the Helmert variance component estimation method is highlighted as the best for selecting the regularization parameter compared with other methods, such as generalized cross-validation or the mean squared error criterion method. The ASC may also benefit other ill-posed problems in which a smoothness constraint is required.

Stability analysis solutions and optical solitons in extended nonlinear Schrödinger equation with higher-order odd and even terms

NASA Astrophysics Data System (ADS)

Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

2018-01-01

In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.

Field equations from Killing spinors

NASA Astrophysics Data System (ADS)

Açık, Özgür

2018-02-01

From the Killing spinor equation and the equations satisfied by their bilinears, we deduce some well-known bosonic and fermionic field equations of mathematical physics. Aside from the trivially satisfied Dirac equation, these relativistic wave equations in curved spacetimes, respectively, are Klein-Gordon, Maxwell, Proca, Duffin-Kemmer-Petiau, Kähler, twistor, and Rarita-Schwinger equations. This result shows that, besides being special kinds of Dirac fermions, Killing fermions can be regarded as physically fundamental. For the Maxwell case, the problem of motion is analysed in a reverse manner with respect to the studies of Einstein-Groemer-Infeld-Hoffmann and Jean Marie Souriau. In the analysis of the gravitino field, a generalised 3-ψ rule is found which is termed the vanishing trace constraint.

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

Chow, Edmond

Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.

Constraints on Non-Newtonian Gravity From the Experiment on Neutron Quantum States in the Earth's Gravitational Field.

PubMed

Nesvizhevsky, V V; Protasov, K V

2005-01-01

An upper limit to non-Newtonian attractive forces is obtained from the measurement of quantum states of neutrons in the Earth's gravitational field. This limit improves the existing constraints in the nanometer range.

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

NASA Astrophysics Data System (ADS)

Agresti, Juri; De Pietri, Roberto; Lusanna, Luca; Martucci, Luca

2004-05-01

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy {\\hat E}ADM, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) r_{\\bar a}(\\tau ,\\vec \\sigma ), \\pi_{\\bar a}(\\tau ,\\vec \\sigma ), \\bar a = 1,2. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in {\\hat E}ADM. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's r_{\\bar a}(\\tau ,\\vec \\sigma ), which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.

A Higher Harmonic Optimal Controller to Optimise Rotorcraft Aeromechanical Behaviour

NASA Technical Reports Server (NTRS)

Leyland, Jane Anne

1996-01-01

Three methods to optimize rotorcraft aeromechanical behavior for those cases where the rotorcraft plant can be adequately represented by a linear model system matrix were identified and implemented in a stand-alone code. These methods determine the optimal control vector which minimizes the vibration metric subject to constraints at discrete time points, and differ from the commonly used non-optimal constraint penalty methods such as those employed by conventional controllers in that the constraints are handled as actual constraints to an optimization problem rather than as just additional terms in the performance index. The first method is to use a Non-linear Programming algorithm to solve the problem directly. The second method is to solve the full set of non-linear equations which define the necessary conditions for optimality. The third method is to solve each of the possible reduced sets of equations defining the necessary conditions for optimality when the constraints are pre-selected to be either active or inactive, and then to simply select the best solution. The effects of maneuvers and aeroelasticity on the systems matrix are modelled by using a pseudo-random pseudo-row-dependency scheme to define the systems matrix. Cases run to date indicate that the first method of solution is reliable, robust, and easiest to use, and that it was superior to the conventional controllers which were considered.

Forces on nuclei moving on autoionizing molecular potential energy surfaces.

PubMed

Moiseyev, Nimrod

2017-01-14

Autoionization of molecular systems occurs in diatomic molecules and in small biochemical systems. Quantum chemistry packages enable calculation of complex potential energy surfaces (CPESs). The imaginary part of the CPES is associated with the autoionization decay rate, which is a function of the molecular structure. Molecular dynamics simulations, within the framework of the Born-Oppenheimer approximation, require the definition of a force field. The ability to calculate the forces on the nuclei in bio-systems when autoionization takes place seems to rely on an understanding of radiative damages in RNA and DNA arising from the release of slow moving electrons which have long de Broglie wavelengths. This work addresses calculation of the real forces on the nuclei moving on the CPES. By using the transformation of the time-dependent Schrödinger equation, previously used by Madelung, we proved that the classical forces on nuclei moving on the CPES correlated with the gradient of the real part of the CPES. It was proved that the force on the nuclei of the metastable molecules is time independent although the probability to detect metastable molecules exponentially decays. The classical force is obtained from the transformed Schrödinger equation when ℏ=0 and the Schrödinger equation is reduced to the classical (Newtonian) equations of motion. The forces on the nuclei regardless on what potential energy surface they move (parent CPES or product real PESs) vary in time due to the autoionization process.

Resonant Tidal Excitation of Internal Waves in the Earth's Fluid Core

NASA Technical Reports Server (NTRS)

Tyler, Robert H.; Kuang, Weijia

2014-01-01

It has long been speculated that there is a stably stratified layer below the core-mantle boundary, and two recent studies have improved the constraints on the parameters describing this stratification. Here we consider the dynamical implications of this layer using a simplified model. We first show that the stratification in this surface layer has sensitive control over the rate at which tidal energy is transferred to the core. We then show that when the stratification parameters from the recent studies are used in this model, a resonant configuration arrives whereby tidal forces perform elevated rates of work in exciting core flow. Specifically, the internal wave speed derived from the two independent studies (150 and 155 m/s) are in remarkable agreement with the speed (152 m/s) required for excitation of the primary normal mode of oscillation as calculated from full solutions of the Laplace Tidal Equations applied to a reduced-gravity idealized model representing the stratified layer. In evaluating this agreement it is noteworthy that the idealized model assumed may be regarded as the most reduced representation of the stratified dynamics of the layer, in that there are no non-essential dynamical terms in the governing equations assumed. While it is certainly possible that a more realistic treatment may require additional dynamical terms or coupling, it is also clear that this reduced representation includes no freedom for coercing the correlation described. This suggests that one must accept either (1) that tidal forces resonantly excite core flow and this is predicted by a simple model or (2) that either the independent estimates or the dynamical model does not accurately portray the core surface layer and there has simply been an unlikely coincidence between three estimates of a stratification parameter which would otherwise have a broad plausible range.

New optical solitons of space-time conformable fractional perturbed Gerdjikov-Ivanov equation by sine-Gordon equation method

NASA Astrophysics Data System (ADS)

Yaşar, Elif; Yıldırım, Yakup; Yaşar, Emrullah

2018-06-01

This paper devotes to conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation which appears in nonlinear fiber optics and photonic crystal fibers (PCF). We consider the model with full nonlinearity in order to give a generalized flavor. The sine-Gordon equation approach is carried out to model equation for retrieving the dark, bright, dark-bright, singular and combined singular optical solitons. The constraint conditions are also reported for guaranteeing the existence of these solitons. We also present some graphical simulations of the solutions for better understanding the physical phenomena of the behind the considered model.

Constrained dynamics approach for motion synchronization and consensus

NASA Astrophysics Data System (ADS)

Bhatia, Divya

In this research we propose to develop constrained dynamical systems based stable attitude synchronization, consensus and tracking (SCT) control laws for the formation of rigid bodies. The generalized constrained dynamics Equations of Motion (EOM) are developed utilizing constraint potential energy functions that enforce communication constraints. Euler-Lagrange equations are employed to develop the non-linear constrained dynamics of multiple vehicle systems. The constraint potential energy is synthesized based on a graph theoretic formulation of the vehicle-vehicle communication. Constraint stabilization is achieved via Baumgarte's method. The performance of these constrained dynamics based formations is evaluated for bounded control authority. The above method has been applied to various cases and the results have been obtained using MATLAB simulations showing stability, synchronization, consensus and tracking of formations. The first case corresponds to an N-pendulum formation without external disturbances, in which the springs and the dampers connected between the pendulums act as the communication constraints. The damper helps in stabilizing the system by damping the motion whereas the spring acts as a communication link relaying relative position information between two connected pendulums. Lyapunov stabilization (energy based stabilization) technique is employed to depict the attitude stabilization and boundedness. Various scenarios involving different values of springs and dampers are simulated and studied. Motivated by the first case study, we study the formation of N 2-link robotic manipulators. The governing EOM for this system is derived using Euler-Lagrange equations. A generalized set of communication constraints are developed for this system using graph theory. The constraints are stabilized using Baumgarte's techniques. The attitude SCT is established for this system and the results are shown for the special case of three 2-link robotic manipulators. These methods are then applied to the formation of N-spacecraft. Modified Rodrigues Parameters (MRP) are used for attitude representation of the spacecraft because of their advantage of being a minimum parameter representation. Constrained non-linear equations of motion for this system are developed and stabilized using a Proportional-Derivative (PD) controller derived based on Baumgarte's method. A system of 3 spacecraft is simulated and the results for SCT are shown and analyzed. Another problem studied in this research is that of maintaining SCT under unknown external disturbances. We use an adaptive control algorithm to derive control laws for the actuator torques and develop an estimation law for the unknown disturbance parameters to achieve SCT. The estimate of the disturbance is added as a feed forward term in the actual control law to obtain the stabilization of a 3-spacecraft formation. The disturbance estimates are generated via a Lyapunov analysis of the closed loop system. In summary, the constrained dynamics method shows a lot of potential in formation control, achieving stabilization, synchronization, consensus and tracking of a set of dynamical systems.

'Footballs', conical singularities, and the Liouville equation

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

Redi, Michele

We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints.

Braneworld gravity within non-conservative gravitational theory

NASA Astrophysics Data System (ADS)

Fabris, J. C.; Caramês, Thiago R. P.; da Silva, J. M. Hoff

2018-05-01

We investigate the braneworld gravity starting from the non-conservative gravitational field equations in a five-dimensional bulk. The approach is based on the Gauss-Codazzi formalism along with the study of the braneworld consistency conditions. The effective gravitational equations on the brane are obtained and the constraint leading to a brane energy-momentum conservation is analyzed.

Modifiying shallow-water equations as a model for wave-vortex turbulence

NASA Astrophysics Data System (ADS)

Mohanan, A. V.; Augier, P.; Lindborg, E.

2017-12-01

The one-layer shallow-water equations is a simple two-dimensional model to study the complex dynamics of the oceans and the atmosphere. We carry out forced-dissipative numerical simulations, either by forcing medium-scale wave modes, or by injecting available potential energy (APE). With pure wave forcing in non-rotating cases, a statistically stationary regime is obtained for a range of forcing Froude numbers Ff = ɛ /(kf c), where ɛ is the energy dissipation rate, kf the forcing wavenumber and c the wave speed. Interestingly, the spectra scale as k-2 and third and higher order structure functions scale as r. Such statistics is a manifestation of shock turbulence or Burgulence, which dominate the flow. Rotating cases exhibit some inverse energy cascade, along with a stronger forward energy cascade, dominated by wave-wave interactions. We also propose two modifications to the classical shallow-water equations to construct a toy model. The properties of the model are explored by forcing in APE at a small and a medium wavenumber. The toy model simulations are then compared with results from shallow-water equations and a full General Circulation Model (GCM) simulation. The most distinctive feature of this model is that, unlike shallow-water equations, it avoids shocks and conserves quadratic energy. In Fig. 1, for the shallow-water equations, shocks appear as thin dark lines in the divergence (∇ .{u}) field, and as discontinuities in potential temperature (θ ) field; whereas only waves appear in the corresponding fields from toy model simulation. Forward energy cascade results in a wave field with k-5/3 spectrum, along with equipartition of KE and APE at small scales. The vortical field develops into a k-3 spectrum. With medium forcing wavenumber, at large scales, energy converted from APE to KE undergoes inverse cascade as a result of nonlinear fluxes composed of vortical modes alone. Gradually, coherent vortices emerge with a strong preference for anticyclonic motion. The model can serve as a closer representation of real geophysical turbulence than the classical shallow-water equations. Fig 1. Divergence and potential temperature fields of shallow-water (top row) and toy model (bottom row) simulations.

Comprehensive evaluation of long-term hydrological data sets: Constraints of the Budyko framework

NASA Astrophysics Data System (ADS)

Greve, Peter; Orlowsky, Boris; Seneviratne, Sonia I.

2013-04-01

An accurate estimate of the climatological land water balance is essential for a wide range of socio-economical issues. Despite the simplicity of the underlying water balance equation, its individual variables are of complex nature. Global estimates, either derived from observations or from models, of precipitation (P ) and especially evapotranspiration (ET) are characterized by high uncertainties. This leads to inconsistent results in determining conditions related to the land water balance and its components. In this study, we consider the Budyko framework as a constraint to evaluate long-term hydrological data sets within the period from 1984 to 2005. The Budyko framework is a well established empirically based relationsship between ET-P and Ep-P , with Ep being the potential evaporation. We use estimates of ET associated with the LandFlux-EVAL initiative (Mueller et. al., 2012), either derived from observations, CMIP5 models or land-surface models (LSMs) driven with observation-based forcing or atmospheric reanalyses. Data sets of P comprise all commonly used global observation-based estimates. Ep is determined by methods of differing complexity with recent global temperature and radiation data sets. Based on this comprehensive synthesis of data sets and methods to determine Ep, more than 2000 possible combinations for ET-P in conjunction with Ep-P are created. All combinations are validated against the Budyko curve and against physical limits within the Budyko phase space. For this purpose we develop an error measure based on the root mean square error which combines both constraints. We find that uncertainties are mainly induced by the ET data sets. In particular, reanalysis and CMIP5 data sets are characterized by low realism. The realism of LSMs is further not primarily controlled by the forcing, as different LSMs driven with the same forcing show significantly different error measures. Our comprehensive approach is thus suitable to detect uncertainties associated with individual data sets. Furthermore, combinations performing well within the Budyko phase space are identified and could be used for future studies, like e.g. to investigate decadal changes of the land water balance. B. MUELLER, M. HIRSCHI, C. JIMENEZ, P. CIAIS, P.A. DIRMEYER, A.J. DOLMAN, J.B. FISHER, Z. GUO, M. JUNG, F. LUDWIG, F. MAIGNAN, D. MIRALLES, M.F. MCCABE, M. REICHSTEIN, J. SHEELD, K. WANG, E.F.WOOD, Y. ZHANG, S.I. SENEVIRATNE (2012): Benchmark products for land evapotranspiration: LandFlux-EVAL multi-dataset synthesis, Hydrol. Earth Syst. Sci., submitted.

Weak Galilean invariance as a selection principle for coarse-grained diffusive models.

PubMed

Cairoli, Andrea; Klages, Rainer; Baule, Adrian

2018-05-29

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

Variational Lagrangian data assimilation in open channel networks

NASA Astrophysics Data System (ADS)

Wu, Qingfang; Tinka, Andrew; Weekly, Kevin; Beard, Jonathan; Bayen, Alexandre M.

2015-04-01

This article presents a data assimilation method in a tidal system, where data from both Lagrangian drifters and Eulerian flow sensors were fused to estimate water velocity. The system is modeled by first-order, hyperbolic partial differential equations subject to periodic forcing. The estimation problem can then be formulated as the minimization of the difference between the observed variables and model outputs, and eventually provide the velocity and water stage of the hydrodynamic system. The governing equations are linearized and discretized using an implicit discretization scheme, resulting in linear equality constraints in the optimization program. Thus, the flow estimation can be formed as an optimization problem and efficiently solved. The effectiveness of the proposed method was substantiated by a large-scale field experiment in the Sacramento-San Joaquin River Delta in California. A fleet of 100 sensors developed at the University of California, Berkeley, were deployed in Walnut Grove, CA, to collect a set of Lagrangian data, a time series of positions as the sensors moved through the water. Measurements were also taken from Eulerian sensors in the region, provided by the United States Geological Survey. It is shown that the proposed method can effectively integrate Lagrangian and Eulerian measurement data, resulting in a suited estimation of the flow variables within the hydraulic system.

River velocities from sequential multispectral remote sensing images

NASA Astrophysics Data System (ADS)

Chen, Wei; Mied, Richard P.

2013-06-01

We address the problem of extracting surface velocities from a pair of multispectral remote sensing images over rivers using a new nonlinear multiple-tracer form of the global optimal solution (GOS). The derived velocity field is a valid solution across the image domain to the nonlinear system of equations obtained by minimizing a cost function inferred from the conservation constraint equations for multiple tracers. This is done by deriving an iteration equation for the velocity, based on the multiple-tracer displaced frame difference equations, and a local approximation to the velocity field. The number of velocity equations is greater than the number of velocity components, and thus overly constrain the solution. The iterative technique uses Gauss-Newton and Levenberg-Marquardt methods and our own algorithm of the progressive relaxation of the over-constraint. We demonstrate the nonlinear multiple-tracer GOS technique with sequential multispectral Landsat and ASTER images over a portion of the Potomac River in MD/VA, and derive a dense field of accurate velocity vectors. We compare the GOS river velocities with those from over 12 years of data at four NOAA reference stations, and find good agreement. We discuss how to find the appropriate spatial and temporal resolutions to allow optimization of the technique for specific rivers.

Centripetal and centrifugal forces in the moral circle: Competing constraints on moral learning.

PubMed

Graham, Jesse; Waytz, Adam; Meindl, Peter; Iyer, Ravi; Young, Liane

2017-10-01

The idea of the moral circle pictures the self in the center, surrounded by concentric circles encompassing increasingly distant possible targets of moral concern, including family, local community, nation, all humans, all mammals, all living things including plants, and all things including inanimate objects. The authors develop the idea of two opposing forces in people's moral circles, with centripetal forces pulling inward, urging greater concern for close others than for distant others, and centrifugal forces pushing outward, resisting "drawing the line" anywhere as a form of prejudice and urging egalitarian concern for all regardless of social distance. Review of the developmental literature shows very early emergence of both moral forces, suggesting at least partly intuitive bases for each. Moral education approaches favoring one force over the other are compared, to show how these forces can provide constraints on moral learning. Finally, the centripetal/centrifugal forces view is applied to current moral debates about empathy and about politics. The authors argue that this view helps us see how intercultural and interpersonal disagreements about morality are based in intrapersonal conflicts shared by all people. Copyright © 2016. Published by Elsevier B.V.

Indian summer monsoon rainfall: Dancing with the tunes of the sun

NASA Astrophysics Data System (ADS)

Hiremath, K. M.; Manjunath, Hegde; Soon, Willie

2015-02-01

There is strong statistical evidence that solar activity influences the Indian summer monsoon rainfall. To search for a physical link between the two, we consider the coupled cloud hydrodynamic equations, and derive an equation for the rate of precipitation that is similar to the equation of a forced harmonic oscillator, with cloud and rain water mixing ratios as forcing variables. Those internal forcing variables are parameterized in terms of the combined effect of external forcing as measured by sunspot and coronal hole activities with several well known solar periods (9, 13 and 27 days; 1.3, 5, 11 and 22 years). The equation is then numerically solved and the results show that the variability of the simulated rate of precipitation captures very well the actual variability of the Indian monsoon rainfall, yielding vital clues for a physical understanding that has so far eluded analyses based on statistical correlations alone. We also solved the precipitation equation by allowing for the effects of long-term variation of aerosols. We tentatively conclude that the net effects of aerosols variation are small, when compared to the solar factors, in terms of explaining the observed rainfall variability covering the full Indian monsoonal geographical domains.

Determining the Probability of Violating Upper-Level Wind Constraints for the Launch of Minuteman Ill Ballistic Missiles At Vandenberg Air Force Base

NASA Technical Reports Server (NTRS)

Shafer, Jaclyn A.; Brock, Tyler M.

2013-01-01

The 30th Operational Support Squadron Weather Flight (30 OSSWF) provides comprehensive weather services to the space program at Vandenberg Air Force Base (VAFB) in California. One of their responsibilities is to monitor upper-level winds to ensure safe launch operations of the Minuteman Ill ballistic missile. The 30 OSSWF requested the Applied Meteorology Unit (AMU) analyze VAFB sounding data to determine the probability of violating (PoV) upper-level thresholds for wind speed and shear constraints specific to this launch vehicle, and to develop a graphical user interface (GUI) that will calculate the PoV of each constraint on the day of launch. The AMU suggested also including forecast sounding data from the Rapid Refresh (RAP) model. This would provide further insight for the launch weather officers (LWOs) when determining if a wind constraint violation will occur over the next few hours, and help to improve the overall upper winds forecast on launch day.

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

NASA Astrophysics Data System (ADS)

Majima, H.; Suzuki, A.

2011-12-01

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity ( -γẋ) and a time-dependent external force ( K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: ℒ=mẋẏ-U(x+{1}/{2}y)+U(x-{1}/{2}y)+{γ}/{2}(xẏ-yẋ)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x±y/2)={1}/{2}k( specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian ℋ. The Heisenberg equations of motion utilizing the quantized Hamiltonian ℋ̂ surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force.

6Li in a three-body model with realistic Forces: Separable versus nonseparable approach

NASA Astrophysics Data System (ADS)

Hlophe, L.; Lei, Jin; Elster, Ch.; Nogga, A.; Nunes, F. M.

2017-12-01

Background: Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d ,p ) reactions may be viewed as three-body reactions and described with Faddeev techniques. Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that their solution based on separable interactions agrees exactly with solutions based on nonseparable forces. Methods: Momentum space Faddeev equations are solved with nonseparable and separable forces as coupled integral equations. Results: The ground state of 6Li is calculated via momentum space Faddeev equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-4He force. For the latter the Pauli-forbidden S -wave bound state is projected out. This result is compared to a calculation in which the interactions in the two-body subsystems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. Conclusions: We find that calculations based on the separable representation of the interactions and the original interactions give results that agree to four significant figures for the binding energy, provided that energy and momentum support points of the EST expansion are chosen independently. The momentum distributions computed in both approaches also fully agree with each other.

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

How Well Do We Know The Supernova Equation of State?

NASA Astrophysics Data System (ADS)

Hempel, Matthias; Oertel, Micaela; Typel, Stefan; Klähn, Thomas

We give an overview about equations of state (EOS) which are currently available for simulations of core-collapse supernovae and neutron star mergers. A few selected important aspects of the EOS, such as the symmetry energy, the maximum mass of neutron stars, and cluster formation, are confronted with constraints from experiments and astrophysical observations. There are just very few models which are compatible even with this very restricted set of constraints. These remaining models illustrate the uncertainty of the uniform nuclear matter EOS at high densities. In addition, at finite temperatures the medium modifications of nuclear clusters represent a conceptual challenge. In conclusion, there has been significant development in the recent years, but there is still need for further improved general purpose EOS tables.

Rigorous derivation of electromagnetic self-force

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

Gralla, Samuel E.; Harte, Abraham I.; Wald, Robert M.

2009-07-15

During the past century, there has been considerable discussion and analysis of the motion of a point charge in an external electromagnetic field in special relativity, taking into account 'self-force' effects due to the particle's own electromagnetic field. We analyze the issue of 'particle motion' in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density J{sup a}({lambda}) and stress-energy tensor T{sub ab}({lambda}) scale to zero size in an asymptotically self-similar manner about a worldline {gamma} as {lambda}{yields}0. In thismore » limit, the charge, q, and total mass, m, of the body go to zero, and q/m goes to a well-defined limit. The Maxwell field F{sub ab}({lambda}) is assumed to be the retarded solution associated with J{sup a}({lambda}) plus a homogeneous solution (the 'external field') that varies smoothly with {lambda}. We prove that the worldline {gamma} must be a solution to the Lorentz force equations of motion in the external field F{sub ab}({lambda}=0). We then obtain self-force, dipole forces, and spin force as first-order perturbative corrections to the center-of-mass motion of the body. We believe that this is the first rigorous derivation of the complete first-order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the 'reduction of order' procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. (There is no corresponding justification for the non-reduced-order equations.) We restrict consideration in this paper to classical electrodynamics in flat spacetime, but there should be no difficulty in extending our results to the motion of a charged body in an arbitrary globally hyperbolic curved spacetime.« less

Time domain convergence properties of Lyapunov stable penalty methods

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Sunkel, John

1991-01-01

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

Aerodynamic optimization by simultaneously updating flow variables and design parameters with application to advanced propeller designs

NASA Technical Reports Server (NTRS)

Rizk, Magdi H.

1988-01-01

A scheme is developed for solving constrained optimization problems in which the objective function and the constraint function are dependent on the solution of the nonlinear flow equations. The scheme updates the design parameter iterative solutions and the flow variable iterative solutions simultaneously. It is applied to an advanced propeller design problem with the Euler equations used as the flow governing equations. The scheme's accuracy, efficiency and sensitivity to the computational parameters are tested.

Dispersion relations with crossing symmetry for {pi}{pi}D- and F1-wave amplitudes

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

Kaminski, R.

Results of implementation of dispersion relations with imposed crossing symmetry condition to description of {pi}{pi}D and F1 wave amplitudes are presented. We use relations with only one subtraction what leads to small uncertainties of results and to strong constraints for tested {pi}{pi} amplitudes. Presented equations are similar to those with one subtraction (so called GKPY equations) and to those with two subtractions (the Roy's equations) for the S and P waves. Numerical calculations are done with the S and P wave input amplitudes tested already with use of the Roy's and GKPY equations.

The ESS and replicator equation in matrix games under time constraints.

PubMed

Garay, József; Cressman, Ross; Móri, Tamás F; Varga, Tamás

2018-06-01

Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model. Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games.

Entanglement in Quantum-Classical Hybrid

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, non-classical systems such as quantum-classical hybrids, and covers the concept of entanglement as a special type of global constraint imposed upon a broad class of dynamical systems. Application of hybrid systems for physics of life, as well as for quantum-inspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the Hamilton-Jacobi equation in the form of the quantum potential. Preserving the same topology, the innovators replaced the quantum potential with other types of feedback, and investigated the property of these hybrid systems. A function of probability density has been introduced. Non-locality associated with a global geometrical constraint that leads to an entanglement effect was demonstrated. Despite such a quantum like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement sheds light on the concept of non-locality in physics.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Force sensing using 3D displacement measurements in linear elastic bodies

NASA Astrophysics Data System (ADS)

Feng, Xinzeng; Hui, Chung-Yuen

2016-07-01

In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.

Early and Forced Child Marriage on Girls' Education, in Migori County, Kenya: Constraints, Prospects and Policy

ERIC Educational Resources Information Center

Ganira, Lilian K.; Inda, Nancy A.; Odundo, Paul A.; Akondo, Joseph Ochieng; Ngaruiya, Boniface

2015-01-01

Early and forced marriage infringes rights of women and girls globally, undermining initiatives to raise involvement in education, reduce maternal mortality, increase employment and enterprise levels. Parental and Communal involvement in Early and Forced Child Marriage negatively influence Girls' Education, which hinders their participation in…

Lepton Flavorful Fifth Force and Depth-Dependent Neutrino Matter Interactions

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

Wise, Mark B.; Zhang, Yue

We consider a fifth force to be an interaction that couples to matter with a strength that grows with the number of atoms. In addition to competing with the strength of gravity a fifth force can give rise to violations of the equivalence principle. Current long range constraints on the strength and range of fifth forces are very impressive. Amongst possible fifth forces are those that couple to lepton flavorful chargesmore » $$L_e-L_{\\mu}$$ or $$L_e-L_{\\tau}$$. They have the property that their range and strength are also constrained by neutrino interactions with matter. In this brief note we review the existing constraints on the allowed parameter space in gauged $$U(1)_{L_e-L_{\\mu}, L_{\\tau}}$$. We find two regions where neutrino oscillation experiments are at the frontier of probing such a new force. In particular, there is an allowed range of parameter space where neutrino matter interactions relevant for long baseline oscillation experiments depend on the depth of the neutrino beam below the surface of the earth.« less

Multifractal analysis of time series generated by discrete Ito equations

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

Telesca, Luciano; Czechowski, Zbigniew; Lovallo, Michele

2015-06-15

In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.

Revised Chapman-Enskog analysis for a class of forcing schemes in the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Li, Q.; Zhou, P.; Yan, H. J.

2016-10-01

In the lattice Boltzmann (LB) method, the forcing scheme, which is used to incorporate an external or internal force into the LB equation, plays an important role. It determines whether the force of the system is correctly implemented in an LB model and affects the numerical accuracy. In this paper we aim to clarify a critical issue about the Chapman-Enskog analysis for a class of forcing schemes in the LB method in which the velocity in the equilibrium density distribution function is given by u =∑αeαfα / ρ , while the actual fluid velocity is defined as u ̂=u +δtF / (2 ρ ) . It is shown that the usual Chapman-Enskog analysis for this class of forcing schemes should be revised so as to derive the actual macroscopic equations recovered from these forcing schemes. Three forcing schemes belonging to the above class are analyzed, among which Wagner's forcing scheme [A. J. Wagner, Phys. Rev. E 74, 056703 (2006), 10.1103/PhysRevE.74.056703] is shown to be capable of reproducing the correct macroscopic equations. The theoretical analyses are examined and demonstrated with two numerical tests, including the simulation of Womersley flow and the modeling of flat and circular interfaces by the pseudopotential multiphase LB model.

Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor

NASA Astrophysics Data System (ADS)

Beyer, Florian; Paetz, Tim-Torben

2018-02-01

The Mars-Simon tensor (MST), which, e.g., plays a crucial role to provide gauge invariant characterizations of the Kerr-NUT-(A)(dS) family, satisfies a Bianchi-like equation. In this paper, we analyze this equation in close analogy to the Bianchi equation, in particular it will be shown that the constraints are preserved supposing that a generalized Buchdahl condition holds. This permits the systematic construction of solutions to this equation in terms of a well-posed Cauchy problem. A particular emphasis lies on the asymptotic Cauchy problem, where data are prescribed on a space-like I (i.e., for ∧ > 0). In contrast to the Bianchi equation, the MST equation is of Fuchsian type at I , for which existence and uniqueness results are derived.

[Addictions: Motivated or forced care].

PubMed

Cottencin, Olivier; Bence, Camille

2016-12-01

Patients presenting with addictions are often obliged to consult. This constraint can be explicit (partner, children, parents, doctor, police, justice) or can be implicit (for their children, for their families, or for their health). Thus, beyond the fact that the caregiver faces the paradox of caring for subjects who do not ask treatment, he faces as well a double bind considered to be supporter of the social order or helper of patients. The transtheoretical model of change is complex showing us that it was neither fixed in time, nor perpetual for a given individual. This model includes ambivalence, resistance and even relapse, but it still considers constraint as a brake than an effective tool. Therapist must have adequate communication tools to enable everyone (forced or not) understand that involvement in care will enable him/her to regain his free will, even though it took to go through coercion. We propose in this article to detail the first steps with the patient presenting with addiction looking for constraint (implicit or explicit), how to work with constraint, avoid making resistances ourselves and make of constraint a powerful motivator for change. Copyright © 2016 Elsevier Masson SAS. All rights reserved.

Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

Vibration control of a ship engine system using high-load magnetorheological mounts associated with a new indirect fuzzy sliding mode controller

NASA Astrophysics Data System (ADS)

Phu, Do Xuan; Choi, Seung-Bok

2015-02-01

In this work, a new high-load magnetorheological (MR) fluid mount system is devised and applied to control vibration in a ship engine. In the investigation of vibration-control performance, a new modified indirect fuzzy sliding mode controller is formulated and realized. The design of the proposed MR mount is based on the flow mode of MR fluid, and it includes two separated coils for generating a magnetic field. An optimization process is carried out to achieve maximal damping force under certain design constraints, such as the allowable height of the mount. As an actuating smart fluid, a new plate-like iron-particle-based MR fluid is used, instead of the conventional spherical iron-particle-based MR fluid. After evaluating the field-dependent yield stress of the MR fluid, the field-dependent damping force required to control unwanted vibration in the ship engine is determined. Subsequently, an appropriate-sized MR mount is manufactured and its damping characteristics are evaluated. After confirming the sufficient damping force level of the manufactured MR mount, a medium-sized ship engine mount system consisting of eight MR mounts is established, and its dynamic governing equations are derived. A new modified indirect fuzzy sliding mode controller is then formulated and applied to the engine mount system. The displacement and velocity responses show that the unwanted vibrations of the ship engine system can be effectively controlled in both the axial and radial directions by applying the proposed control methodology.

Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

PubMed Central

Omar, Mohamed A.

2014-01-01

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations. PMID:25045732

Geometric Implications of Maxwell's Equations

NASA Astrophysics Data System (ADS)

Smith, Felix T.

2015-03-01

Maxwell's synthesis of the varied results of the accumulated knowledge of electricity and magnetism, based largely on the searching insights of Faraday, still provide new issues to explore. A case in point is a well recognized anomaly in the Maxwell equations: The laws of electricity and magnetism require two 3-vector and two scalar equations, but only six dependent variables are available to be their solutions, the 3-vectors E and B. This leaves an apparent redundancy of two degrees of freedom (J. Rosen, AJP 48, 1071 (1980); Jiang, Wu, Povinelli, J. Comp. Phys. 125, 104 (1996)). The observed self-consistency of the eight equations suggests that they contain additional information. This can be sought as a previously unnoticed constraint connecting the space and time variables, r and t. This constraint can be identified. It distorts the otherwise Euclidean 3-space of r with the extremely slight, time dependent curvature k (t) =Rcurv-2 (t) of the 3-space of a hypersphere whose radius has the time dependence dRcurv / dt = +/- c nonrelativistically, or dRcurvLor / dt = +/- ic relativistically. The time dependence is exactly that of the Hubble expansion. Implications of this identification will be explored.

A molecular model for cohesive slip at polymer melt/solid interfaces.

PubMed

Tchesnokov, M A; Molenaar, J; Slot, J J M; Stepanyan, R

2005-06-01

A molecular model is proposed which predicts wall slip by disentanglement of polymer chains adsorbed on a wall from those in the polymer bulk. The dynamics of the near-wall boundary layer is found to be governed by a nonlinear equation of motion, which accounts for such mechanisms on surface chains as convection, retraction, constraint release, and thermal fluctuations. This equation is valid over a wide range of grafting regimes, including those in which interactions between neighboring adsorbed molecules become essential. It is not closed since the dynamics of adsorbed chains is shown to be coupled to that of polymer chains in the bulk via constraint release. The constitutive equations for the layer and bulk, together with continuity of stress and velocity, are found to form a closed system of equations which governs the dynamics of the whole "bulk+boundary layer" ensemble. Its solution provides a stick-slip law in terms of the molecular parameters and extruder geometry. The model is quantitative and contains only those parameters that can be measured directly, or extracted from independent rheological measurements. The model predictions show a good agreement with available experimental data.

Static analysis of large-scale multibody system using joint coordinates and spatial algebra operator.

PubMed

Omar, Mohamed A

2014-01-01

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.

A diagnostic study of the forcing of the Ferrel cell by eddies, with latent heat effects included

NASA Technical Reports Server (NTRS)

Salustri, G.; Stone, P. H.

1983-01-01

A diagnostic study of the forcing of the Ferrel cell by eddy fluxes in the Northern Hemisphere is carried out. The quasi-geostrophic omega equation, and Oort and Rasmusson's (1971) data set, are used. The effects of condensation associated with the large scale motions are introduced to the omega equation by using the quasi-geostrophic moisture conservation equation. Thus, the dry static stability is replaced by a moist static stability, and the forcing of the Ferrel cell by eddy latent heat fluxes as well as sensible heat and momentum fluxes is included. Both effects tend to enhance the forcing of the Ferrel cell. The numerical analysis indicates that the effects are small in January, but in July the maximum vertical velocities are enhanced by about 30 percent.

Constraint Optimization Problem For The Cutting Of A Cobalt Chrome Refractory Material

NASA Astrophysics Data System (ADS)

Lebaal, Nadhir; Schlegel, Daniel; Folea, Milena

2011-05-01

This paper shows a complete approach to solve a given problem, from the experimentation to the optimization of different cutting parameters. In response to an industrial problem of slotting FSX 414, a Cobalt-based refractory material, we have implemented a design of experiment to determine the most influent parameters on the tool life, the surface roughness and the cutting forces. After theses trials, an optimization approach has been implemented to find the lowest manufacturing cost while respecting the roughness constraints and cutting force limitation constraints. The optimization approach is based on the Response Surface Method (RSM) using the Sequential Quadratic programming algorithm (SQP) for a constrained problem. To avoid a local optimum and to obtain an accurate solution at low cost, an efficient strategy, which allows improving the RSM accuracy in the vicinity of the global optimum, is presented. With these models and these trials, we could apply and compare our optimization methods in order to get the lowest cost for the best quality, i.e. a satisfying surface roughness and limited cutting forces.

Hour-glass ceilings: Work-hour thresholds, gendered health inequities.

PubMed

Dinh, Huong; Strazdins, Lyndall; Welsh, Jennifer

2017-03-01

Long workhours erode health, which the setting of maximum weekly hours aims to avert. This 48-h limit, and the evidence base to support it, has evolved from a workforce that was largely male, whose time in the labour force was enabled by women's domestic work and care giving. The gender composition of the workforce has now changed, and many women (as well as some men) combine care-giving with paid work, a change viewed as fundamental for gender equality. However, it raises questions on the suitability of the work time limit and the extent it is protective of health. We estimate workhour-mental health thresholds, testing if they vary for men and women due to gendered workloads and constraints on and off the job. Using six waves of data from a nationally representative sample of Australian adults (24-65 years), surveyed in the Household Income Labour Dynamics of Australia Survey (N = 3828 men; 4062 women), our study uses a longitudinal, simultaneous equation approach to address endogeneity. Averaging over the sample, we find an overall threshold of 39 h per week beyond which mental health declines. Separate curves then estimate thresholds for men and women, by high or low care and domestic time constraints, using stratified and pooled samples. We find gendered workhour-health limits (43.5 for men, 38 for women) which widen further once differences in resources on and off the job are considered. Only when time is 'unencumbered' and similar time constraints and contexts are assumed, do gender gaps narrow and thresholds approximate the 48-h limit. Our study reveals limits to contemporary workhour regulation which may be systematically disadvantaging women's health. Copyright © 2017 Elsevier Ltd. All rights reserved.

A methodology for analysing lateral coupled behavior of high speed railway vehicles and structures

NASA Astrophysics Data System (ADS)

Antolín, P.; Goicolea, J. M.; Astiz, M. A.; Alonso, A.

2010-06-01

Continuous increment of the speed of high speed trains entails the increment of kinetic energy of the trains. The main goal of this article is to study the coupled lateral behavior of vehicle-structure systems for high speed trains. Non linear finite element methods are used for structures whereas multibody dynamics methods are employed for vehicles. Special attention must be paid when dealing with contact rolling constraints for coupling bridge decks and train wheels. The dynamic models must include mixed variables (displacements and creepages). Additionally special attention must be paid to the contact algorithms adequate to wheel-rail contact. The coupled vehicle-structure system is studied in a implicit dynamic framework. Due to the presence of very different systems (trains and bridges), different frequencies are involved in the problem leading to stiff systems. Regarding to contact methods, a main branch is studied in normal contact between train wheels and bridge decks: penalty method. According to tangential contact FastSim algorithm solves the tangential contact at each time step solving a differential equation involving relative displacements and creepage variables. Integration for computing the total forces in the contact ellipse domain is performed for each train wheel and each solver iteration. Coupling between trains and bridges requires a special treatment according to the kinetic constraints imposed in the wheel-rail pair and the load transmission. A numerical example is performed.

Optimization of cascade blade mistuning under flutter and forced response constraints

NASA Technical Reports Server (NTRS)

Murthy, D. V.; Haftka, R. T.

1984-01-01

In the development of modern turbomachinery, problems of flutter instabilities and excessive forced response of a cascade of blades that were encountered have often turned out to be extremely difficult to eliminate. The study of these instabilities and the forced response is complicated by the presence of mistuning; that is, small differences among the individual blades. The theory of mistuned cascade behavior shows that mistuning can have a beneficial effect on the stability of the rotor. This beneficial effect is produced by the coupling between the more stable and less stable flutter modes introduced by mistuning. The effect of mistuning on the forced response can be either beneficial or adverse. Kaza and Kielb have studied the effects of two types of mistuning on the flutter and forced response: alternate mistuning where alternte blades are identical and random mistuning. The objective is to investigate other patterns of mistuning which maximize the beneficial effects on the flutter and forced response of the cascade. Numerical optimization techniques are employed to obtain optimal mistuning patterns. The optimization program seeks to minimize the amount of mistuning required to satisfy constraints on flutter speed and forced response.

Automation for Primary Processing of Hardwoods

Treesearch

Daniel L. Schmoldt

1992-01-01

Hardwood sawmills critically need to incorporate automation and computer technology into their operations. Social constraints, forest biology constraints, forest product market changes, and financial necessity are forcing primary processors to boost their productivity and efficiency to higher levels. The locations, extent, and types of defects found in logs and on...

Model-independent cosmological constraints from growth and expansion

NASA Astrophysics Data System (ADS)

L'Huillier, Benjamin; Shafieloo, Arman; Kim, Hyungjin

2018-05-01

Reconstructing the expansion history of the Universe from Type Ia supernovae data, we fit the growth rate measurements and put model-independent constraints on some key cosmological parameters, namely, Ωm, γ, and σ8. The constraints are consistent with those from the concordance model within the framework of general relativity, but the current quality of the data is not sufficient to rule out modified gravity models. Adding the condition that dark energy density should be positive at all redshifts, independently of its equation of state, further constrains the parameters and interestingly supports the concordance model.

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.

Possibilities of the free-complement methodology for solving the Schrödinger equation of atoms and molecules

NASA Astrophysics Data System (ADS)

Nakatsuji, Hiroshi

Chemistry is a science of complex subjects that occupy this universe and biological world and that are composed of atoms and molecules. Its essence is diversity. However, surprisingly, whole of this science is governed by simple quantum principles like the Schrödinger and the Dirac equations. Therefore, if we can find a useful general method of solving these quantum principles under the fermionic and/or bosonic constraints accurately in a reasonable speed, we can replace somewhat empirical methodologies of this science with purely quantum theoretical and computational logics. This is the purpose of our series of studies - called ``exact theory'' in our laboratory. Some of our documents are cited below. The key idea was expressed as the free complement (FC) theory (originally called ICI theory) that was introduced to solve the Schrödinger and Dirac equations analytically. For extending this methodology to larger systems, order N methodologies are essential, but actually the antisymmetry constraints for electronic wave functions become big constraints. Recently, we have shown that the antisymmetry rule or `dogma' can be very much relaxed when our subjects are large molecular systems. In this talk, I want to present our recent progress in our FC methodology. The purpose is to construct ``predictive quantum chemistry'' that is useful in chemical and physical researches and developments in institutes and industries

Linear spin-2 fields in most general backgrounds

NASA Astrophysics Data System (ADS)

Bernard, Laura; Deffayet, Cédric; Schmidt-May, Angnis; von Strauss, Mikael

2016-04-01

We derive the full perturbative equations of motion for the most general background solutions in ghost-free bimetric theory in its metric formulation. Clever field redefinitions at the level of fluctuations enable us to circumvent the problem of varying a square-root matrix appearing in the theory. This greatly simplifies the expressions for the linear variation of the bimetric interaction terms. We show that these field redefinitions exist and are uniquely invertible if and only if the variation of the square-root matrix itself has a unique solution, which is a requirement for the linearized theory to be well defined. As an application of our results we examine the constraint structure of ghost-free bimetric theory at the level of linear equations of motion for the first time. We identify a scalar combination of equations which is responsible for the absence of the Boulware-Deser ghost mode in the theory. The bimetric scalar constraint is in general not manifestly covariant in its nature. However, in the massive gravity limit the constraint assumes a covariant form when one of the interaction parameters is set to zero. For that case our analysis provides an alternative and almost trivial proof of the absence of the Boulware-Deser ghost. Our findings generalize previous results in the metric formulation of massive gravity and also agree with studies of its vielbein version.

Cauchy problem as a two-surface based ‘geometrodynamics’

NASA Astrophysics Data System (ADS)

Rácz, István

2015-01-01

Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1 + (1 + 2) decomposition, the canonical form of the spacetime metric and a suitable specification of the conformal structure of the foliating two-surfaces, a gauge fixing is introduced. It is shown that, in terms of the chosen geometrically distinguished variables, the 1 + 3 Hamiltonian and momentum constraints can be recast into the form of a parabolic equation and a first order symmetric hyperbolic system, respectively. Initial data to this system can be given on one of the two-surfaces foliating the three-dimensional initial data surface. The 1 + 3 reduced Einstein's equations are also determined. By combining the 1 + 3 momentum constraint with the reduced system of the secondary 1 + 2 decomposition, a mixed hyperbolic-hyperbolic system is formed. It is shown that solutions to this mixed hyperbolic-hyperbolic system are also solutions to the full set of Einstein's equations provided that the 1 + 3 Hamiltonian constraint is solved on the initial data surface {{Σ }0} and the 1 + 2 Hamiltonian and momentum type expressions vanish on a world-tube yielded by the Lie transport of one of the two-surfaces foliating {{Σ }0} along the time evolution vector field. Whenever the foliating two-surfaces are compact without boundary in the spacetime and a regular origin exists on the time-slices—this is the location where the foliating two-surfaces smoothly reduce to a point—it suffices to guarantee that the 1 + 3 Hamiltonian constraint holds on the initial data surface. A short discussion on the use of the geometrically distinguished variables in identifying the degrees of freedom of gravity are also included. Dedicated to Zoltán Cseke on the occasion of his 70th birthday.

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Maximum Principle in the Optimal Design of Plates with Stratified Thickness

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

Roubicek, Tomas

2005-03-15

An optimal design problem for a plate governed by a linear, elliptic equation with bounded thickness varying only in a single prescribed direction and with unilateral isoperimetrical-type constraints is considered. Using Murat-Tartar's homogenization theory for stratified plates and Young-measure relaxation theory, smoothness of the extended cost and constraint functionals is proved, and then the maximum principle necessary for an optimal relaxed design is derived.

Elasto-limited plastic analysis of structures for probabilistic conditions

NASA Astrophysics Data System (ADS)

Movahedi Rad, M.

2018-06-01

With applying plastic analysis and design methods, significant saving in material can be obtained. However, as a result of this benefit excessive plastic deformations and large residual displacements might develop, which in turn might lead to unserviceability and collapse of the structure. In this study, for deterministic problem the residual deformation of structures is limited by considering a constraint on the complementary strain energy of the residual forces. For probabilistic problem the constraint for the complementary strain energy of the residual forces is given randomly and critical stresses updated during the iteration. Limit curves are presented for the plastic limit load factors. The results show that these constraints have significant effects on the load factors. The formulations of the deterministic and probabilistic problems lead to mathematical programming which are solved by the use of nonlinear algorithm.

A variational approach to probing extreme events in turbulent dynamical systems

PubMed Central

Farazmand, Mohammad; Sapsis, Themistoklis P.

2017-01-01

Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large-scale networks, and biological systems. We propose a variational framework for probing conditions that trigger intermittent extreme events in high-dimensional nonlinear dynamical systems. We seek the triggers as the probabilistically feasible solutions of an appropriately constrained optimization problem, where the function to be maximized is a system observable exhibiting intermittent extreme bursts. The constraints are imposed to ensure the physical admissibility of the optimal solutions, that is, significant probability for their occurrence under the natural flow of the dynamical system. We apply the method to a body-forced incompressible Navier-Stokes equation, known as the Kolmogorov flow. We find that the intermittent bursts of the energy dissipation are independent of the external forcing and are instead caused by the spontaneous transfer of energy from large scales to the mean flow via nonlinear triad interactions. The global maximizer of the corresponding variational problem identifies the responsible triad, hence providing a precursor for the occurrence of extreme dissipation events. Specifically, monitoring the energy transfers within this triad allows us to develop a data-driven short-term predictor for the intermittent bursts of energy dissipation. We assess the performance of this predictor through direct numerical simulations. PMID:28948226

Was That Assumption Necessary? Reconsidering Boundary Conditions for Analytical Solutions to Estimate Streambed Fluxes

NASA Astrophysics Data System (ADS)

Luce, Charles H.; Tonina, Daniele; Applebee, Ralph; DeWeese, Timothy

2017-11-01

Two common refrains about using the one-dimensional advection diffusion equation to estimate fluid fluxes and thermal conductivity from temperature time series in streambeds are that the solution assumes that (1) the surface boundary condition is a sine wave or nearly so, and (2) there is no gradient in mean temperature with depth. Although the mathematical posing of the problem in the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we develop a mathematical proof demonstrating the equivalence of the solution as developed based on an arbitrary (Fourier integral) surface temperature forcing when evaluated at a single given frequency versus that derived considering a single frequency from the beginning. The implication is that any single frequency can be used in the frequency-domain solutions to estimate thermal diffusivity and 1-D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes or gradients in the mean temperature with depth are not actually assumptions, and deviations from them should not cause errors in estimates. Given this clarification, we further explore the potential for using information at multiple frequencies to augment the information derived from time series of temperature.

Physically weighted approximations of unsteady aerodynamic forces using the minimum-state method

NASA Technical Reports Server (NTRS)

Karpel, Mordechay; Hoadley, Sherwood Tiffany

1991-01-01

The Minimum-State Method for rational approximation of unsteady aerodynamic force coefficient matrices, modified to allow physical weighting of the tabulated aerodynamic data, is presented. The approximation formula and the associated time-domain, state-space, open-loop equations of motion are given, and the numerical procedure for calculating the approximation matrices, with weighted data and with various equality constraints are described. Two data weighting options are presented. The first weighting is for normalizing the aerodynamic data to maximum unit value of each aerodynamic coefficient. The second weighting is one in which each tabulated coefficient, at each reduced frequency value, is weighted according to the effect of an incremental error of this coefficient on aeroelastic characteristics of the system. This weighting yields a better fit of the more important terms, at the expense of less important ones. The resulting approximate yields a relatively low number of aerodynamic lag states in the subsequent state-space model. The formulation forms the basis of the MIST computer program which is written in FORTRAN for use on the MicroVAX computer and interfaces with NASA's Interaction of Structures, Aerodynamics and Controls (ISAC) computer program. The program structure, capabilities and interfaces are outlined in the appendices, and a numerical example which utilizes Rockwell's Active Flexible Wing (AFW) model is given and discussed.

The Effects of Earth's Outer Core's Viscosity on Geodynamo Models

NASA Astrophysics Data System (ADS)

Dong, C.; Jiao, L.; Zhang, H.

2017-12-01

Geodynamo process is controlled by mathematic equations and input parameters. To study effects of parameters on geodynamo system, MoSST model has been used to simulate geodynamo outputs under different outer core's viscosity ν. With spanning ν for nearly three orders when other parameters fixed, we studied the variation of each physical field and its typical length scale. We find that variation of ν affects the velocity field intensely. The magnetic field almost decreases monotonically with increasing of ν, while the variation is no larger than 30%. The temperature perturbation increases monotonically with ν, but by a very small magnitude (6%). The averaged velocity field (u) of the liquid core increases with ν as a simple fitted scaling relation: u∝ν0.49. The phenomenon that u increases with ν is essentially that increasing of ν breaks the Taylor-Proudman constraint and drops the critical Rayleigh number, and thus u increases under the same thermal driving force. Forces balance is analyzed and balance mode shifts with variation of ν. When compared with former studies of scaling laws, this study supports the conclusion that in a certain parameter range, the magnetic field strength doesn't vary much with the viscosity, but opposes to the assumption that the velocity field has nothing to do with the outer core viscosity.

A Simulation Study of the Overdetermined Geodetic Boundary Value Problem Using Collocation

DTIC Science & Technology

1989-03-01

9 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED GEOPHYSICS LABORATORY AIR FORCE SYSTEMS COMMAND UNITED STATES AIR FORCE HANSCOM AIR FORCE BASE...linearized integral equation is obtained through an infinite system of integral equations which is solved step by step by means of Stokes’ function. The...computed. Since 9 and W = W(9) 4 are known on the boundary, then the boundary is known in the new coordinate system . The serious disadvantage of this

Generalized cable equation model for myelinated nerve fiber.

PubMed

Einziger, Pinchas D; Livshitz, Leonid M; Mizrahi, Joseph

2005-10-01

Herein, the well-known cable equation for nonmyelinated axon model is extended analytically for myelinated axon formulation. The myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonmyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the nerve fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the nerve fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a myelinated nerve fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.

Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics

NASA Astrophysics Data System (ADS)

Webb, G. M.; Anco, S. C.

2016-02-01

The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.

The Dynamic Force Table

ERIC Educational Resources Information Center

Geddes, John B.; Black, Kelly

2008-01-01

We examine an experimental apparatus that is used to motivate the connections between the basic properties of vectors, potential functions, systems of nonlinear equations, and Newton's method for nonlinear systems of equations. The apparatus is an adaptation of a force table where we remove the center-pin and allow the center-ring to move freely.…

Exact solution of a quantum forced time-dependent harmonic oscillator

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN

1992-01-01

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Application of a soft computing technique in predicting the percentage of shear force carried by walls in a rectangular channel with non-homogeneous roughness.

PubMed

Khozani, Zohreh Sheikh; Bonakdari, Hossein; Zaji, Amir Hossein

2016-01-01

Two new soft computing models, namely genetic programming (GP) and genetic artificial algorithm (GAA) neural network (a combination of modified genetic algorithm and artificial neural network methods) were developed in order to predict the percentage of shear force in a rectangular channel with non-homogeneous roughness. The ability of these methods to estimate the percentage of shear force was investigated. Moreover, the independent parameters' effectiveness in predicting the percentage of shear force was determined using sensitivity analysis. According to the results, the GP model demonstrated superior performance to the GAA model. A comparison was also made between the GP program determined as the best model and five equations obtained in prior research. The GP model with the lowest error values (root mean square error ((RMSE) of 0.0515) had the best function compared with the other equations presented for rough and smooth channels as well as smooth ducts. The equation proposed for rectangular channels with rough boundaries (RMSE of 0.0642) outperformed the prior equations for smooth boundaries.

p-Euler equations and p-Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Linear force and moment equations for an annular smooth shaft seal perturbed both angularly and laterally

NASA Technical Reports Server (NTRS)

Fenwick, J.; Dijulio, R.; Ek, M. C.; Ehrgott, R.

1982-01-01

Coefficients are derived for equations expressing the lateral force and pitching moments associated with both planar translation and angular perturbations from a nominally centered rotating shaft with respect to a stationary seal. The coefficients for the lowest order and first derivative terms emerge as being significant and are of approximately the same order of magnitude as the fundamental coefficients derived by means of Black's equations. Second derivative, shear perturbation, and entrance coefficient variation effects are adjudged to be small.

Quasi-periodic solutions of a quasi-periodically forced nonlinear beam equation

NASA Astrophysics Data System (ADS)

Wang, Yi

2012-06-01

In this paper, one quasi-periodically forced nonlinear beam equation utt+uxxxx+μu+ɛg(ωt,x)u3=0,μ>0,x∈[0,π] with hinged boundary conditions is considered. Here ɛ is a small positive parameter, g( ωt, x) is real analytic in all variables and quasi-periodic in t with a frequency vector ω = ( ω1, ω2, … , ωm). It is proved that the above equation admits small-amplitude quasi-periodic solutions.

On the synchrotron radiation reaction in external magnetic field

NASA Astrophysics Data System (ADS)

Tursunov, Arman; Kološ, Martin

2017-12-01

We study the dynamics of point electric charges undergoing radiation reaction force due to synchrotron radiation in the presence of external uniform magnetic field. The radiation reaction force cannot be neglected in many physical situations and its presence modifies the equations of motion significantly. The exact form of the equation of motion known as the Lorentz-Dirac equation contains higher order Schott term which leads to the appearance of the runaway solutions. We demonstrate effective computational ways to avoid such unphysical solutions and perform numerical integration of the dynamical equations. We show that in the ultrarelativistic case the Schott term is small and does not have considerable effect to the trajectory of a particle. We compare results with the covariant Landau-Lifshitz equation which is the first iteration of the Lorentz-Dirac equation. Even though the Landau-Lifshitz equation is thought to be approximative solution, we show that in realistic scenarios both approaches lead to identical results.

Incompressible Navier-Stokes Computations with Heat Transfer

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan; Rogers, Stuart; Kutler, Paul (Technical Monitor)

1994-01-01

The existing pseudocompressibility method for the system of incompressible Navier-Stokes equations is extended to heat transfer problems by including the energy equation. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. Both forced and natural convection problems are examined. Numerical results from turbulent reattaching flow behind a backward-facing step will be compared against experimental measurements for the forced convection case. The validity of Boussinesq approximation to simplify the buoyancy force term will be investigated. The natural convective flow structure generated by heat transfer in a vertical rectangular cavity will be studied. The numerical results will be compared by experimental measurements by Morrison and Tran.

Analysis of the vibratory excitation arising from spiral bevel gears

NASA Technical Reports Server (NTRS)

Mark, William D.

1987-01-01

Tools required to understand and predict in terms of its underlying causes the vibratory excitation arising from meshing spiral bevel gears are developed. A generalized three component transmission error of meshing spiral bevel gears is defined. Equations are derived that yield the three components of the generalized transmission error in terms of deviations of tooth running surfaces from equispaced perfect spherical involute surfaces and tooth/gearbody elastic deformations arising from the three components of the generalized force transmitted by the meshing gears. A method for incorporating these equations into the equations of motion of a gear system is described. Equations are derived for the three components of the generalized force transmitted by the gears which are valid whenever inertial effects of the meshing gears and their supports are negligible. Bearing offsets from the positions occupied by the shaft centerlines of perfect spherical involute bevel gears and bearing/bearing support flexibilities enter into the computation of these forces.

Implicit Motives and Men’s Perceived Constraint in Fatherhood

PubMed Central

Ruppen, Jessica; Waldvogel, Patricia; Ehlert, Ulrike

2016-01-01

Research shows that implicit motives influence social relationships. However, little is known about their role in fatherhood and, particularly, how men experience their paternal role. Therefore, this study examined the association of implicit motives and fathers’ perceived constraint due to fatherhood. Furthermore, we explored their relation to fathers’ life satisfaction. Participants were fathers with biological children (N = 276). They were asked to write picture stories, which were then coded for implicit affiliation and power motives. Perceived constraint and life satisfaction were assessed on a visual analog scale. A higher implicit need for affiliation was significantly associated with lower perceived constraint, whereas the implicit need for power had the opposite effect. Perceived constraint had a negative influence on life satisfaction. Structural equation modeling revealed significant indirect effects of implicit affiliation and power motives on life satisfaction mediated by perceived constraint. Our findings indicate that men with a higher implicit need for affiliation experience less constraint due to fatherhood, resulting in higher life satisfaction. The implicit need for power, however, results in more perceived constraint and is related to decreased life satisfaction. PMID:27933023

Multi-dimensional multi-species modeling of transient electrodeposition in LIGA microfabrication.

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

Evans, Gregory Herbert; Chen, Ken Shuang

2004-06-01

This report documents the efforts and accomplishments of the LIGA electrodeposition modeling project which was headed by the ASCI Materials and Physics Modeling Program. A multi-dimensional framework based on GOMA was developed for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electro-chemical reactions on moving deposition surfaces. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation that explicitly describes the electrolyte potential was derived. The set of coupled, nonlinear equations governing species transport, electric potential, velocity, hydrodynamic pressure, and mesh motion were solved in GOMA, using themore » finite-element method and a fully-coupled implicit solution scheme via Newton's method. By treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and by repeatedly performing re-meshing with CUBIT and re-mapping with MAPVAR, the moving deposition surfaces were tracked explicitly from start of deposition until the trenches were filled with metal, thus enabling the computation of local current densities that potentially influence the microstructure and frictional/mechanical properties of the deposit. The multi-dimensional, multi-species, transient computational framework was demonstrated in case studies of two-dimensional nickel electrodeposition in single and multiple trenches, without and with bath stirring or forced flow. Effects of buoyancy-induced convection on deposition were also investigated. To further illustrate its utility, the framework was employed to simulate deposition in microscreen-based LIGA molds. Lastly, future needs for modeling LIGA electrodeposition are discussed.« less

Planck 2015 results. XIV. Dark energy and modified gravity

NASA Astrophysics Data System (ADS)

Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartolo, N.; Battaner, E.; Battye, R.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H. C.; Christensen, P. R.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Désert, F.-X.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A. A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J. E.; Hansen, F. K.; Hanson, D.; Harrison, D. L.; Heavens, A.; Helou, G.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huang, Z.; Huffenberger, K. M.; Hurier, G.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T. S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C. R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Lewis, A.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Ma, Y.-Z.; Macías-Pérez, J. F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marchini, A.; Maris, M.; Martin, P. G.; Martinelli, M.; Martínez-González, E.; Masi, S.; Matarrese, S.; McGehee, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Narimani, A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Pearson, T. J.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Reach, W. T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubiño-Martín, J. A.; Rusholme, B.; Salvatelli, V.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Schaefer, B. M.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Spencer, L. D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Viel, M.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; Wehus, I. K.; White, M.; Yvon, D.; Zacchei, A.; Zonca, A.

2016-09-01

We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state w(a), as well as principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints and find that it has to be below ~2% (at 95% confidence) of the critical density, even when forced to play a role for z < 50 only. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories, and coupled DE. In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations (expansion of the equation of state, early DE, general potentials in minimally-coupled scalar fields or principal component analysis) are in agreement with ΛCDM. When testing models that also change perturbations (even when the background is fixed to ΛCDM), some tensions appear in a few scenarios: the maximum one found is ~2σ for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to, at most, 3σ when external data sets are included. It however disappears when including CMB lensing.

Identification of potential compensatory muscle strategies in a breast cancer survivor population: A combined computational and experimental approach.

PubMed

Chopp-Hurley, Jaclyn N; Brookham, Rebecca L; Dickerson, Clark R

2016-12-01

Biomechanical models are often used to estimate the muscular demands of various activities. However, specific muscle dysfunctions typical of unique clinical populations are rarely considered. Due to iatrogenic tissue damage, pectoralis major capability is markedly reduced in breast cancer population survivors, which could influence arm internal and external rotation muscular strategies. Accordingly, an optimization-based muscle force prediction model was systematically modified to emulate breast cancer population survivors through adjusting pectoralis capability and enforcing an empirical muscular co-activation relationship. Model permutations were evaluated through comparisons between predicted muscle forces and empirically measured muscle activations in survivors. Similarities between empirical data and model outputs were influenced by muscle type, hand force, pectoralis major capability and co-activation constraints. Differences in magnitude were lower when the co-activation constraint was enforced (-18.4% [31.9]) than unenforced (-23.5% [27.6]) (p<0.0001). This research demonstrates that muscle dysfunction in breast cancer population survivors can be reflected through including a capability constraint for pectoralis major. Further refinement of the co-activation constraint for survivors could improve its generalizability across this population and activities. Improving biomechanical models to more accurately represent clinical populations can provide novel information that can help in the development of optimal treatment programs for breast cancer population survivors. Copyright © 2016 Elsevier Ltd. All rights reserved.

Nonlinear Mechanisms for the Generation of Nearshore Wave Phenomena.

DTIC Science & Technology

1988-04-01

Kadomtsev - Petviashvili equation . Numerical solutions of this equation indicate that steady state is reached only if dispersion is negative; otherwise...leads to a forced Kadomtsev - Petviashvili equation . Numerical solutions of this equation indicate that steady state is reached only if dispersion is

Limitations to maximum running speed on flat curves.

PubMed

Chang, Young-Hui; Kram, Rodger

2007-03-01

Why is maximal running speed reduced on curved paths? The leading explanation proposes that an increase in lateral ground reaction force necessitates a decrease in peak vertical ground reaction force, assuming that maximum leg extension force is the limiting factor. Yet, no studies have directly measured these forces or tested this critical assumption. We measured maximum sprint velocities and ground reaction forces for five male humans sprinting along a straight track and compared them to sprints along circular tracks of 1, 2, 3, 4 and 6 m radii. Circular track sprint trials were performed either with or without a tether that applied centripetal force to the center of mass. Sprinters generated significantly smaller peak resultant ground reaction forces during normal curve sprinting compared to straight sprinting. This provides direct evidence against the idea that maximum leg extension force is always achieved and is the limiting factor. Use of the tether increased sprint speed, but not to expected values. During curve sprinting, the inside leg consistently generated smaller peak forces compared to the outside leg. Several competing biomechanical constraints placed on the stance leg during curve sprinting likely make the inside leg particularly ineffective at generating the ground reaction forces necessary to attain maximum velocities comparable to straight path sprinting. The ability of quadrupeds to redistribute function across multiple stance legs and decouple these multiple constraints may provide a distinct advantage for turning performance.

The centripetal force law and the equation of motion for a particle on a curved hypersurface

NASA Astrophysics Data System (ADS)

Hu, L. D.; Lian, D. K.; Liu, Q. H.

2016-12-01

It is pointed out that the current form of the extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version; for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once this fact is taken into consideration, the equation takes the same form as that for the centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is preferable.

Observational constraints on extended Chaplygin gas cosmologies

NASA Astrophysics Data System (ADS)

Paul, B. C.; Thakur, P.; Saha, A.

2017-08-01

We investigate cosmological models with extended Chaplygin gas (ECG) as a candidate for dark energy and determine the equation of state parameters using observed data namely, observed Hubble data, baryon acoustic oscillation data and cosmic microwave background shift data. Cosmological models are investigated considering cosmic fluid which is an extension of Chaplygin gas, however, it reduces to modified Chaplygin gas (MCG) and also to generalized Chaplygin gas (GCG) in special cases. It is found that in the case of MCG and GCG, the best-fit values of all the parameters are positive. The distance modulus agrees quite well with the experimental Union2 data. The speed of sound obtained in the model is small, necessary for structure formation. We also determine the observational constraints on the constants of the ECG equation.

Chapman-Enskog Analyses on the Gray Lattice Boltzmann Equation Method for Fluid Flow in Porous Media

NASA Astrophysics Data System (ADS)

Chen, Chen; Li, Like; Mei, Renwei; Klausner, James F.

2018-03-01

The gray lattice Boltzmann equation (GLBE) method has recently been used to simulate fluid flow in porous media. It employs a partial bounce-back of populations (through a fractional coefficient θ, which represents the fraction of populations being reflected by the solid phase) in the evolution equation to account for the linear drag of the medium. Several particular GLBE schemes have been proposed in the literature and these schemes are very easy to implement; but there exists uncertainty about the need for redefining the macroscopic velocity as there has been no systematic analysis to recover the Brinkman equation from the various GLBE schemes. Rigorous Chapman-Enskog analyses are carried out to show that the momentum equation recovered from these schemes can satisfy Brinkman equation to second order in ɛ only if θ = O( ɛ ) in which ɛ is the ratio of the lattice spacing to the characteristic length of physical dimension. The need for redefining macroscopic velocity is shown to be scheme-dependent. When a body force is encountered such as the gravitational force or that caused by a pressure gradient, different forms of forcing redefinitions are required for each GLBE scheme.

Correlation of embryonic skeletal muscle myotube physical characteristics with contractile force generation on an atomic force microscope-based bio-microelectromechanical systems device

NASA Astrophysics Data System (ADS)

Pirozzi, K. L.; Long, C. J.; McAleer, C. W.; Smith, A. S. T.; Hickman, J. J.

2013-08-01

Rigorous analysis of muscle function in in vitro systems is needed for both acute and chronic biomedical applications. Forces generated by skeletal myotubes on bio-microelectromechanical cantilevers were calculated using a modified version of Stoney's thin-film equation and finite element analysis (FEA), then analyzed for regression to physical parameters. The Stoney's equation results closely matched the more intensive FEA and the force correlated to cross-sectional area (CSA). Normalizing force to measured CSA significantly improved the statistical sensitivity and now allows for close comparison of in vitro data to in vivo measurements for applications in exercise physiology, robotics, and modeling neuromuscular diseases.

An analysis of the extension of a ZnO piezoelectric semiconductor nanofiber under an axial force

NASA Astrophysics Data System (ADS)

Zhang, Chunli; Wang, Xiaoyuan; Chen, Weiqiu; Yang, Jiashi

2017-02-01

This paper presents a theoretical analysis on the axial extension of an n-type ZnO piezoelectric semiconductor nanofiber under an axial force. The phenomenological theory of piezoelectric semiconductors consisting of Newton’s second law of motion, the charge equation of electrostatics and the conservation of charge was used. The equations were linearized for small axial force and hence small electron concentration perturbation, and were reduced to one-dimensional equations for thin fibers. Simple and analytical expressions for the electromechanical fields and electron concentration in the fiber were obtained. The fields are either totally or partially described by hyperbolic functions relatively large near the ends of the fiber and change rapidly there. The behavior of the fields is sensitive to the initial electron concentration and the applied axial force. For higher initial electron concentrations the fields are larger near the ends and change more rapidly there.

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

Unseren, M.A.

A general framework for solving the dynamic load distribution when two manipulators hold a rigid object is proposed. The underspecified problem of solving for the contact forces and torques based on the object`s equations of motion is transformed into a well specified problem. This is accomplished by augmenting the object`s equations of motion with additional equations which relate a new vector variable quantifying the internal contact force and torque degrees of freedom (DOF) as a linear function of the contact forces and torques. The resulting augmented system yields a well specified solution for the contact forces and torques in whichmore » they are separated into their motion inducing and internal components. A particular solution is suggested which enables the designer to conveniently specify what portion of the payload`s mass each manipulator is to bear. It is also shown that the results of the previous work are just a special case of the general load distribution framework described here.« less

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

NASA Astrophysics Data System (ADS)

Wu, Kailiang; Tang, Huazhong

2018-06-01

The paper studies the physical-constraints-preserving (PCP) schemes for multi-dimensional special relativistic magnetohydrodynamics with a general equation of state (EOS) on more general meshes. It is an extension of the work (Wu and Tang in Math. Models Methods Appl. Sci. 27:1871-1928, 2017) which focuses on the ideal EOS and uniform Cartesian meshes. The general EOS without a special expression poses some additional difficulties in discussing the mathematical properties of admissible state set with the physical constraints on the fluid velocity, density and pressure. Rigorous analyses are provided for the PCP property of finite volume or discontinuous Galerkin schemes with the Lax-Friedrichs (LxF)-type flux on a general mesh with non-self-intersecting polytopes. Those are built on a more general form of generalized LxF splitting property and a different convex decomposition technique. It is shown in theory that the PCP property is closely connected with a discrete divergence-free condition, which is proposed on the general mesh and milder than that in Wu and Tang (2017).

Optimization of an auto-thermal ammonia synthesis reactor using cyclic coordinate method

NASA Astrophysics Data System (ADS)

A-N Nguyen, T.; Nguyen, T.-A.; Vu, T.-D.; Nguyen, K.-T.; K-T Dao, T.; P-H Huynh, K.

2017-06-01

The ammonia synthesis system is an important chemical process used in the manufacture of fertilizers, chemicals, explosives, fibers, plastics, refrigeration. In the literature, many works approaching the modeling, simulation and optimization of an auto-thermal ammonia synthesis reactor can be found. However, they just focus on the optimization of the reactor length while keeping the others parameters constant. In this study, the other parameters are also considered in the optimization problem such as the temperature of feed gas enters the catalyst zone, the initial nitrogen proportion. The optimal problem requires the maximization of an objective function which is multivariable function and subject to a number of equality constraints involving the solution of coupled differential equations and also inequality constraint. The cyclic coordinate search was applied to solve the multivariable-optimization problem. In each coordinate, the golden section method was applied to find the maximum value. The inequality constraints were treated using penalty method. The coupled differential equations system was solved using Runge-Kutta 4th order method. The results obtained from this study are also compared to the results from the literature.

Optimum acoustic design of free-running low speed propellers

NASA Technical Reports Server (NTRS)

Ormsbee, A. I.; Woan, C. J.

1977-01-01

A theoretical analysis is conducted concerning the effect of blade loading on the noise output of a free-running propeller in axial motion. The minimization of the mean square sound pressure at a point in space is considered, taking into account constraints on propeller thrust and torque. Attention is given to aerodynamic equations, acoustic equations, the expansion of the aerodynamic variables, and the nonlinear programming formulation.

Weak- and strong-turbulence regimes of the forced Hasegawa-Mima equation

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

Ottaviani, M.; Krommes, J.A.

1992-11-16

A Kolmogorov-type analysis of the energy- and enstrophy-cascading ranges of a forced Hasegawa-Mima equation allows one to derive a criterion for the threshold of the transition between the weak-turbulence and the strong-turbulence regimes. Contrary to general belief, it is found that due to the inverse energy cascade the large-scale portion of the inertial range is in the strong-turbulence regime in the limit of infinite Reynolds-like numbers for any finite amount of forcing.

A multilinear regression methodology to analyze the effect of atmospheric and surface forcing on Arctic clouds

NASA Astrophysics Data System (ADS)

Boeke, R.; Taylor, P. C.; Li, Y.

2017-12-01

Arctic cloud amount as simulated in CMIP5 models displays large intermodel spread- models disagree on the processes important for cloud formation as well as the radiative impact of clouds. The radiative response to cloud forcing can be better assessed when the drivers of Arctic cloud formation are known. Arctic cloud amount (CA) is a function of both atmospheric and surface conditions, and it is crucial to separate the influences of unique processes to understand why the models are different. This study uses a multilinear regression methodology to determine cloud changes using 3 variables as predictors: lower tropospheric stability (LTS), 500-hPa vertical velocity (ω500), and sea ice concentration (SIC). These three explanatory variables were chosen because their effects on clouds can be attributed to unique climate processes: LTS is a thermodynamic indicator of the relationship between clouds and atmospheric stability, SIC determines the interaction between clouds and the surface, and ω500 is a metric for dynamical change. Vertical, seasonal profiles of necessary variables are obtained from the Coupled Model Intercomparison Project 5 (CMIP5) historical simulation, an ocean-atmosphere couple model forced with the best-estimate natural and anthropogenic radiative forcing from 1850-2005, and statistical significance tests are used to confirm the regression equation. A unique heuristic model will be constructed for each climate model and for observations, and models will be tested by their ability to capture the observed cloud amount and behavior. Lastly, the intermodel spread in Arctic cloud amount will be attributed to individual processes, ranking the relative contributions of each factor to shed light on emergent constraints in the Arctic cloud radiative effect.

Effects of the oceans on polar motion: Extended investigations

NASA Technical Reports Server (NTRS)

Dickman, Steven R.

1986-01-01

A method was found for expressing the tide current velocities in terms of the tide height (with all variables expanded in spherical harmonics). All time equations were then combined into a single, nondifferential matrix equation involving only the unknown tide height. The pole tide was constrained so that no tidewater flows across continental boundaries. The constraint was derived for the case of turbulent oceans; with the tide velocities expressed in terms of the tide height. The two matrix equations were combined. Simple matrix inversion then yielded the constrained solution. Programs to construct and invert the matrix equations were written. Preliminary results were obtained and are discussed.

A homotopy algorithm for synthesizing robust controllers for flexible structures via the maximum entropy design equations

NASA Technical Reports Server (NTRS)

Collins, Emmanuel G., Jr.; Richter, Stephen

1990-01-01

One well known deficiency of LQG compensators is that they do not guarantee any measure of robustness. This deficiency is especially highlighted when considering control design for complex systems such as flexible structures. There has thus been a need to generalize LQG theory to incorporate robustness constraints. Here we describe the maximum entropy approach to robust control design for flexible structures, a generalization of LQG theory, pioneered by Hyland, which has proved useful in practice. The design equations consist of a set of coupled Riccati and Lyapunov equations. A homotopy algorithm that is used to solve these design equations is presented.

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.

SETS. Set Equation Transformation System

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

Worrell, R.B.

1992-01-13

SETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access throughmore » nullification of sensors in its protection system.« less

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

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

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

A method for paraplegic upper-body posture estimation during standing: a pilot study for rehabilitation purposes.

PubMed

Pages, Gaël; Ramdani, Nacim; Fraisse, Philippe; Guiraud, David

2009-06-01

This paper presents a contribution for restoring standing in paraplegia while using functional electrical stimulation (FES). Movement generation induced by FES remains mostly open looped and stimulus intensities are tuned empirically. To design an efficient closed-loop control, a preliminary study has been carried out to investigate the relationship between body posture and voluntary upper body movements. A methodology is proposed to estimate body posture in the sagittal plane using force measurements exerted on supporting handles during standing. This is done by setting up constraints related to the geometric equations of a two-dimensional closed chain model and the hand-handle interactions. All measured quantities are subject to an uncertainty assumed unknown but bounded. The set membership estimation problem is solved via interval analysis. Guaranteed uncertainty bounds are computed for the estimated postures. In order to test the feasibility of our methodology, experiments were carried out with complete spinal cord injured patients.

Study of flutter related computational procedures for minimum weight structural sizing of advanced aircraft

NASA Technical Reports Server (NTRS)

Oconnell, R. F.; Hassig, H. J.; Radovcich, N. A.

1976-01-01

Results of a study of the development of flutter modules applicable to automated structural design of advanced aircraft configurations, such as a supersonic transport, are presented. Automated structural design is restricted to automated sizing of the elements of a given structural model. It includes a flutter optimization procedure; i.e., a procedure for arriving at a structure with minimum mass for satisfying flutter constraints. Methods of solving the flutter equation and computing the generalized aerodynamic force coefficients in the repetitive analysis environment of a flutter optimization procedure are studied, and recommended approaches are presented. Five approaches to flutter optimization are explained in detail and compared. An approach to flutter optimization incorporating some of the methods discussed is presented. Problems related to flutter optimization in a realistic design environment are discussed and an integrated approach to the entire flutter task is presented. Recommendations for further investigations are made. Results of numerical evaluations, applying the five methods of flutter optimization to the same design task, are presented.

Viscous damping and spring force in periodic perforated planar microstructures when the Reynolds’ equation cannot be applied

PubMed Central

Homentcovschi, Dorel; Miles, Ronald N.

2010-01-01

A model of squeeze-film behavior is developed based on Stokes’ equations for viscous, compressible isothermal flows. The flow domain is an axisymmetrical, unit cell approximation of a planar, periodic, perforated microstructure. The model is developed for cases when the lubrication approximation cannot be applied. The complex force generated by vibrations of the diaphragm driving the flow has two components: the damping force and the spring force. While for large frequencies the spring force dominates, at low (acoustical) frequencies the damping force is the most important part. The analytical approach developed here yields an explicit formula for both forces. In addition, using a finite element software package, the damping force is also obtained numerically. A comparison is made between the analytic result, numerical solution, and some experimental data found in the literature, which validates the analytic formula and provides compelling arguments about its value in designing microelectomechanical devices. PMID:20329828

Computer Solution of the Two-Dimensional Tether Ball: Problem to Illustrate Newton's Second Law.

ERIC Educational Resources Information Center

Zimmerman, W. Bruce

Force diagrams involving angular velocity, linear velocity, centripetal force, work, and kinetic energy are given with related equations of motion expressed in polar coordinates. The computer is used to solve differential equations, thus reducing the mathematical requirements of the students. An experiment is conducted using an air table to check…

Measurements of Aerodynamic Damping in the MIT Transonic Rotor

NASA Technical Reports Server (NTRS)

Crawley, E. F.

1981-01-01

A method was developed and demonstrated for the direct measurement of aerodynamic forcing and aerodynamic damping of a transonic compressor. The method is based on the inverse solution of the structural dynamic equations of motion of the blade disk system in order to determine the forces acting on the system. The disturbing and damping forces acting on a given blade are determined if the equations of motion are expressed in individual blade coordinates. If the structural dynamic equations are transformed to multiblade coordinates, the damping can be measured for blade disk modes, and related to a reduced frequency and interblade phase angle. In order to measure the aerodynamic damping in this way, the free response to a known excitation is studied.

Using neutral models to identify constraints on low-severity fire regimes.

Treesearch

Donald McKenzie; Amy E. Hessl; Lara-Karena B. Kellogg

2006-01-01

Climate, topography, fuel loadings, and human activities all affect spatial and temporal patterns of fire occurrence. Because fire is modeled as a stochastic process, for which each fire history is only one realization, a simulation approach is necessary to understand baseline variability, thereby identifying constraints, or forcing functions, that affect fire regimes...

"Starting from Ground Zero:" Constraints and Experiences of Adult Women Returning to College

ERIC Educational Resources Information Center

Deutsch, Nancy L.; Schmertz, Barbara

2011-01-01

Women adult students face particular constraints when pursuing degrees. This paper uses focus group data to explore the educational pathways, barriers, and supports of women students. Women's educations are shaped by personal and structural gendered forces, including family, economic, and workplace issues. Women report conflict over short-term…

Analytical results for post-buckling behaviour of plates in compression and in shear

NASA Technical Reports Server (NTRS)

Stein, M.

1985-01-01

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

NASA Astrophysics Data System (ADS)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

Free energy from molecular dynamics with multiple constraints

NASA Astrophysics Data System (ADS)

den Otter, W. K.; Briels, W. J.

In molecular dynamics simulations of reacting systems, the key step to determining the equilibrium constant and the reaction rate is the calculation of the free energy as a function of the reaction coordinate. Intuitively the derivative of the free energy is equal to the average force needed to constrain the reaction coordinate to a constant value, but the metric tensor effect of the constraint on the sampled phase space distribution complicates this relation. The appropriately corrected expression for the potential of mean constraint force method (PMCF) for systems in which only the reaction coordinate is constrained was published recently. Here we will consider the general case of a system with multiple constraints. This situation arises when both the reaction coordinate and the 'hard' coordinates are constrained, and also in systems with several reaction coordinates. The obvious advantage of this method over the established thermodynamic integration and free energy perturbation methods is that it avoids the cumbersome introduction of a full set of generalized coordinates complementing the constrained coordinates. Simulations of n -butane and n -pentane in vacuum illustrate the method.

Light weakly coupled axial forces: models, constraints, and projections

DOE PAGES

Kahn, Yonatan; Krnjaic, Gordan; Mishra-Sharma, Siddharth; ...

2017-05-01

Here, we investigate the landscape of constraints on MeV-GeV scale, hidden U(1) forces with nonzero axial-vector couplings to Standard Model fermions. While the purely vector-coupled dark photon, which may arise from kinetic mixing, is a well-motivated scenario, several MeV-scale anomalies motivate a theory with axial couplings which can be UV-completed consistent with Standard Model gauge invariance. Moreover, existing constraints on dark photons depend on products of various combinations of axial and vector couplings, making it difficult to isolate the e ects of axial couplings for particular flavors of SM fermions. We present a representative renormalizable, UV-complete model of a darkmore » photon with adjustable axial and vector couplings, discuss its general features, and show how some UV constraints may be relaxed in a model with nonrenormalizable Yukawa couplings at the expense of fine-tuning. We survey the existing parameter space and the projected reach of planned experiments, brie y commenting on the relevance of the allowed parameter space to low-energy anomalies in π 0 and 8Be* decay.« less

Light weakly coupled axial forces: models, constraints, and projections

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

Kahn, Yonatan; Krnjaic, Gordan; Mishra-Sharma, Siddharth

Here, we investigate the landscape of constraints on MeV-GeV scale, hidden U(1) forces with nonzero axial-vector couplings to Standard Model fermions. While the purely vector-coupled dark photon, which may arise from kinetic mixing, is a well-motivated scenario, several MeV-scale anomalies motivate a theory with axial couplings which can be UV-completed consistent with Standard Model gauge invariance. Moreover, existing constraints on dark photons depend on products of various combinations of axial and vector couplings, making it difficult to isolate the e ects of axial couplings for particular flavors of SM fermions. We present a representative renormalizable, UV-complete model of a darkmore » photon with adjustable axial and vector couplings, discuss its general features, and show how some UV constraints may be relaxed in a model with nonrenormalizable Yukawa couplings at the expense of fine-tuning. We survey the existing parameter space and the projected reach of planned experiments, brie y commenting on the relevance of the allowed parameter space to low-energy anomalies in π 0 and 8Be* decay.« less

The ΩDE-ΩM Plane in Dark Energy Cosmology

NASA Astrophysics Data System (ADS)

Qiang, Yuan; Zhang, Tong-Jie

The dark energy cosmology with the equation of state w=const. is considered in this paper. The ΩDE-ΩM plane has been used to study the present state and expansion history of the universe. Through the mathematical analysis, we give the theoretical constraint of cosmological parameters. Together with some observations such as the transition redshift from deceleration to acceleration, more precise constraint on cosmological parameters can be acquired.

Constraints on backreaction in dust universes

NASA Astrophysics Data System (ADS)

Räsänen, Syksy

2006-03-01

We study backreaction in dust universes using exact equations which do not rely on perturbation theory, concentrating on theoretical and observational constraints. In particular, we discuss the recent suggestion (Kolb et al 2005 Preprint hep-th/0503117) that superhorizon perturbations could explain present-day accelerated expansion as a useful example which can be ruled out. We note that a backreaction explanation of late-time acceleration will have to involve spatial curvature and subhorizon perturbations.

Application of singular value decomposition to structural dynamics systems with constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Pinson, L. D.

1985-01-01

Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.

Gravitational Harmonics from Shallow Resonant Orbits. [GEOS 2 satellite - orbit calculation

NASA Technical Reports Server (NTRS)

Wagner, C. A.; Klosko, S. M.

1975-01-01

Five gravitational constraints were derived for the GEOS 2 orbit (order 13, to 30th degree) whose principal resonant period is 6 days. The constraints explain the sinusoidal variation with argument of perigee of a lumped harmonic found from 41 6-day arcs of optical and laser data. The condition equations, derived from elementary perturbation theory are shown to account for almost all of the resonant information in the tracking data.

Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to Robin boundary condition

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

Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.

2014-02-15

Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to variousmore » forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.« less

A compendium of chameleon constraints

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

Burrage, Clare; Sakstein, Jeremy, E-mail: clare.burrage@nottingham.ac.uk, E-mail: jeremy.sakstein@port.ac.uk

2016-11-01

The chameleon model is a scalar field theory with a screening mechanism that explains how a cosmologically relevant light scalar can avoid the constraints of intra-solar-system searches for fifth-forces. The chameleon is a popular dark energy candidate and also arises in f ( R ) theories of gravity. Whilst the chameleon is designed to avoid historical searches for fifth-forces it is not unobservable and much effort has gone into identifying the best observables and experiments to detect it. These results are not always presented for the same models or in the same language, a particular problem when comparing astrophysical andmore » laboratory searches making it difficult to understand what regions of parameter space remain. Here we present combined constraints on the chameleon model from astrophysical and laboratory searches for the first time and identify the remaining windows of parameter space. We discuss the implications for cosmological chameleon searches and future small-scale probes.« less

Analysis of three different equations for predicting quadriceps femoris muscle strength in patients with COPD *

PubMed Central

Nellessen, Aline Gonçalves; Donária, Leila; Hernandes, Nidia Aparecida; Pitta, Fabio

2015-01-01

Abstract Objective: To compare equations for predicting peak quadriceps femoris (QF) muscle force; to determine the agreement among the equations in identifying QF muscle weakness in COPD patients; and to assess the differences in characteristics among the groups of patients classified as having or not having QF muscle weakness by each equation. Methods: Fifty-six COPD patients underwent assessment of peak QF muscle force by dynamometry (maximal voluntary isometric contraction of knee extension). Predicted values were calculated with three equations: an age-height-weight-gender equation (Eq-AHWG); an age-weight-gender equation (Eq-AWG); and an age-fat-free mass-gender equation (Eq-AFFMG). Results: Comparison of the percentage of predicted values obtained with the three equations showed that the Eq-AHWG gave higher values than did the Eq-AWG and Eq-AFFMG, with no difference between the last two. The Eq-AHWG showed moderate agreement with the Eq-AWG and Eq-AFFMG, whereas the last two also showed moderate, albeit lower, agreement with each other. In the sample as a whole, QF muscle weakness (< 80% of predicted) was identified by the Eq-AHWG, Eq-AWG, and Eq-AFFMG in 59%, 68%, and 70% of the patients, respectively (p > 0.05). Age, fat-free mass, and body mass index are characteristics that differentiate between patients with and without QF muscle weakness. Conclusions: The three equations were statistically equivalent in classifying COPD patients as having or not having QF muscle weakness. However, the Eq-AHWG gave higher peak force values than did the Eq-AWG and the Eq-AFFMG, as well as showing greater agreement with the other equations. PMID:26398750