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It is shown that under very general conditions, any inhomogeneous cosmological model with a positive cosmological constant that can be described in a synchronous reference system will tend asymptotically in time towards the de Sitter solution. This renders the problem of initial conditions less severe.
Kalman-Bucy filtering for estimating initial conditions and smoothing problems in linear dynamic systems, applicable to rectilinear motion of randomly accelerated spacecraft
Kalman-Bucy filtering technique for estimation of initial conditions and smoothing in linear dynamic systems, noting rectilinear motion of randomly accelerated spacecraft
A constitutive law by which structural damping is modeled as a relationship between stress, strain, and strain rate in a material is used in conjunction with the finite element method to develop general integral expressions for viscous and nonviscous damping matrices. To solve the set of nonlinear equations resulting from the presence of nonviscous damping, a solution technique is developed by modifying the Newmark method to accommodate an iterative solution and treat the nonviscous damping as a pseudo-force. The technique is then checked for accuracy and convergence in single- and multi-degree-of-freedom problems, and is found to be accurate and efficient for initial-condition problems with small nonviscous damping.
Large climate feedback uncertainties limit the prediction accuracy of the Earth s future climate with an increased CO2 atmosphere. One potential to reduce the feedback uncertainties using satellite observations of top-of-atmosphere (TOA) radiative energy imbalance is explored. Instead of solving the initial condition problem in previous energy balance analysis, current study focuses on the boundary condition problem with further considerations on climate system memory and deep ocean heat transport, which is more applicable for the climate. Along with surface temperature measurements of the present climate, the climate feedbacks are obtained based on the constraints of the TOA radiation imbalance. Comparing to the feedback factor of 3.3 W/sq m/K of the neutral climate system, the estimated feedback factor for the current climate system ranges from -1.3 to -1.0 W/sq m/K with an uncertainty of +/-0.26 W/sq m/K. That is, a positive climate feedback is found because of the measured TOA net radiative heating (0.85 W/sq m) to the climate system. The uncertainty is caused by the uncertainties in the climate memory length. The estimated time constant of the climate is large (70 to approx. 120 years), implying that the climate is not in an equilibrium state under the increasing CO2 forcing in the last century.
Statistical formulation of estimation and combined identification and control problems of nonlinear dynamical systems
Sufficient conditions for a weak relative minimum of a form of the Bolza problem of variational calculus are derived. The variational problem considered includes arbitrary numbers of constraints on the initial and terminal points, but assumes no control constraints or interior point constraints. Testing of the second-order conditions requires the backward integration of fewer matrix elements than in the case of previously published sets of conditions. The derivation, though lengthy, is felt to be simpler in concept than previous derivations. The application of these conditions is demonstrated in the context of a simple geometric problem.
Petschek's 're-connection' model, aspiring to be universal, treated as a boundary problem meets unresolvable difficulties connected with impossibility to specify correctly boundary and initial conditions. This problem was incorrectly formulated. Hence, ineradicable logarithmic singularities occurred on the boundary surfaces. Attempts to eliminate them by incorporating the finite electrical conductivity are incorrect. This should lead to the change in the equation type, boundary condition type and in consequence to the change in solutions. Besides, the slow mode shocks cannot be driven by small internal source. As an alternative a new plasma concept is suggested. The state of fully ionized plasma in space depends completely on the entropy of the plasma heating source and on the process in which plasma is involved. The presumptive source of the solar wind creation - the induction electric field of the solar origin - has very low entropy. The state of plasma should be very far from the thermodynamic equilibrium. Debye's screening is not complete. The excitation of the powerful resonant self-consistent electric fields in plasma provides low electric conductivity. The MHD problems should be treated in frameworks of dissipative theories.
In the proposal, the following three objectives are stated: (1) A p-version of the discontinuous Galerkin method for a one dimensional parabolic problem will be established. It should be recalled that the h-version in space was used for the discontinuous Galerkin method. An a priori error estimate as well as a posteriori estimate of this p-finite element discontinuous Galerkin method will be given. (2) The parameter alpha that describes the behavior double vertical line u(sub t)(t) double vertical line 2 was computed exactly. This was made feasible because of the explicitly specified initial condition. For practical heat transfer problems, the initial condition may have to be approximated. Also, if the parabolic problem is proposed on a multi-dimensional region, the parameter alpha, for most cases, would be difficult to compute exactly even in the case that the initial condition is known exactly. The second objective of this proposed research is to establish a method to estimate this parameter. This will be done by computing two discontinuous Galerkin approximate solutions at two different time steps starting from the initial time and use them to derive alpha. (3) The third objective is to consider the heat transfer problem over a two dimensional thin plate. The technique developed by Vogelius and Babuska will be used to establish a discontinuous Galerkin method in which the p-element will be used for through thickness approximation. This h-p finite element approach, that results in a dimensional reduction method, was used for elliptic problems, but the application appears new for the parabolic problem. The dimension reduction method will be discussed together with the time discretization method.
The design of an optimal dynamic compensator for a multivariable discrete time system is studied. Also the design of compensators to achieve minimum variance control strategies for single input single output systems is analyzed. In the first problem the initial conditions of the plant are random variables with known first and second order moments, and the cost is the expected value of the standard cost, quadratic in the states and controls. The compensator is based on the minimum order Luenberger observer and it is found optimally by minimizing a performance index. Necessary and sufficient conditions for optimality of the compensator are derived. The second problem is solved in three different ways; two of them working directly in the frequency domain and one working in the time domain. The first and second order moments of the initial conditions are irrelevant to the solution. Necessary and sufficient conditions are derived for the compensator to minimize the variance of the output.
Initial conditions estimation problem for nonlinear system asymptotic stability and satisfaction of output constraints on state variables
Time-dependent solutions of a one-fluid model of the interplanetary medium are investigated. This set of unsteady hydrodynamic equations has been written in conservation form in order to apply the Lax-Wendroff method for the solution of this problem. The initial condition is specified by a pulse at 1 solar radius. The equilibrium condition is chosen to be the steady solution of a quiet solar wind. The specified solar disturbances in this calculation are allowed to be both sub- and supersonic by the present theoretical formulation. The results are presented in terms of density, velocity, and temperature profiles of the interplanetary gas flow at heliocentric distances up to about 10 AU at any particular time. The trajectories of disturbances for various initial pulses are shown. Some 1972 solar-flare observational data are compared with these theoretical calculations. From these calculations, the effects on the interplanetary environment, due to the propagation of solar disturbances, can be determined.
The relationship between the dynamics of the interstellar gas and the thermal and chemical effects associated with interstellar molecules and dust is investigated. The evolution of a rather massive isolated initially diffuse cloud under self-gravity is studied, using the equations of hydrodynamics; only radial motions are considered, and the heat, chemical, and radiative-transfer equations are solved simultaneously with the hydrodynamic equations. The relevant chemistry is described along with the thermal model, the radiative-transfer process, and the numerical methods employed. Results for a contracting cloud are discussed in terms of the problem of initial conditions, the dynamical evolution of the cloud, its chemical and thermal evolution, time scales, and column densities. It is shown that the chemical evolution of a massive contracting diffuse cloud is sensitive to such physical properties as temperature and ion abundances, that warm and cool versions of a typical cloud evolve differently, and that the physical origin of this effect is the level of heating due to H2 formation on interstellar dust grains.
The effects of increasing the softening parameter, epsilon, in the two body-forces are investigated in order to ascertain the relative importance for this instability of close encounters and the bulk mean field. Consideration is given to both the mean e-folding times for individual particle perturbations and the e-folding times for the total 3N-dimensional configuration space perturbation, which continues to grow exponentially until the typical perturbation of an individual particle becomes comparable to the size of the system. Close encounters and the bulk mean field are both important and apparently reinforce each other: the relatively smooth, systematic tidal force associated with the mean field tends to amplify divergences associated with 'kicks' induced by shorter range effects, which remain important even for large N.
Numerical experiments have been performed using different ENO schemes and different time discretizations, in order to assess accuracy-degeneracy phenomena of the type described by Rogerson and Meiburg (1990). A modified ENO scheme recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives results comparable to the original ENO schemes for discontinuous problems. It is concluded that ENO schemes may lose the full high-order accuracy predicted by local truncation-error analysis for scalar linear conservation laws with smooth initial conditions. A modified ENO scheme can overcome this accuracy-degeneracy problem for the test problems without increasing the computational cost.
Spacecraft trajectory initial conditions expressions as parameters dependent functions, applying results to Mars lander mission
Further numerical experiments are made assessing an accuracy degeneracy phenomena. A modified essentially non-oscillatory (ENO) scheme is proposed, which recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives comparable results with the original ENO schemes for discontinuous problems.
The buffet response of the flexible twin-tail/delta wing configuration, a multidisciplinary problem, is solved using three sets of equations on a multi-block grid structure. The first set is the unsteady, compressible, full Navier-Stokes equations which are used for obtaining the flow-field vector and the aerodynamic loads on the twin tails. The second set is the coupled aeroelastic equations which are used for obtaining the bending and torsional deflections of the twin tails. The third set is the grid-displacement equations which are used for updating the grid coordinates due to the tail deflections. The computational model is similar to the one used by Washburn et. al. which consists of a delta wing of aspect ratio one and twin tails with taper ratios of 0.23. The vortex of the twin tails are located at the wing trailing edge. The configuration is pitched at 30 deg angle of attack, and the freestream Mach number and Reynolds number are 0.3 and 1.25 million, respectively. With the twin tails fixed as rigid surfaces, the problem is solved for the initial flow conditions. Next, the problem is solved for the twin tail response for uncoupled bending and torsional vibrations due to the unsteady loads produced by the vortex breakdown flow of the leading-edge vortex cores. The configuration is investigated for three spanwise positions of the twin tails; inboard, midspan and outboard locations. The computational results are validated and are in very good agreement with the experimental data of Washburn, et. al.