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A 36-item short-form (SF-36) was constructed to survey health status in the Medical Outcomes Study. The SF-36 was designed for use in clinical practice and research, health policy evaluations, and general population surveys. The SF-36 includes one multi-item scale that assesses eight health concepts: 1) limitations in physical activities because of health problems; 2) limitations in social activities because of physical or emotional problems; 3) limitations in usual role activities because of physical health problems; 4) bodily pain; 5) general mental health (psychological distress and well-being); 6) limitations in usual role activities because of emotional problems; 7) vitality (energy and fatigue); and 8) general health perceptions. The survey was constructed for self-administration by persons 14 years of age and older, and for administration by a trained interviewer in person or by telephone. The history of the development of the SF-36, the origin of specific items, and the logic underlying their selection are summarized. The content and features of the SF-36 are compared with the 20-item Medical Outcomes Study short-form.

The primary purpose of this article is to obtain from the general relativity form of the energy-momentum principle certain new consequences which are needed for later work that the author has in mind. In addition, it is the intention to give at the same time a somewhat comprehensive and coherent treatment of the principle and its consequences, which it is hoped will increase the confidence and facility of physicists in the use of this important part of the general theory of relativity. In carrying out the investigation, it has seemed desirable for English readers, to take Eddington's "Mathematical Theory of Relativity" as a starting point, and this has incidentally led to a new form of deduction for certain consequences of the energy-momentum principle that were already known.After presenting the energy-momentum principle in the form discovered by Einstein and showing its application to the case of the conservation of energy in an isolated system, an important expression is derived which gives the total densities of energy and momentum in the form of a divergence. This expression is equivalent to one previously obtained by Einstein but on account of the starting point adopted is derived and expressed in terms of the quantities ${\mathfrak{g}}^{\ensuremath{\mu}\ensuremath{\nu}}$ and ${\mathfrak{g}}_{\ensuremath{\alpha}}^{\ensuremath{\mu}\ensuremath{\nu}}$ instead of the ${g}^{\ensuremath{\mu}\ensuremath{\nu}}$ and ${g}_{\ensuremath{\alpha}}^{\ensuremath{\mu}\ensuremath{\nu}}$. Following this, the limiting values at large distances from an isolated material system are obtained for the quantities ${\mathfrak{g}}^{\ensuremath{\alpha}\ensuremath{\beta}}\frac{\ensuremath{\partial}\mathfrak{L}}{\ensuremath{\partial}{\mathfrak{g}}_{\ensuremath{\gamma}}^{\ensuremath{\alpha}\ensuremath{\beta}}}$ and ${\mathfrak{g}}^{\ensuremath{\alpha}4}\frac{\ensuremath{\partial}\mathfrak{L}}{\ensuremath{\partial}{\mathfrak{g}}_{\ensuremath{\gamma}}^{\ensuremath{\alpha}4}}$. These values, which have considerable use, have not previously received explicit expression. This is followed by a deduction from our present starting point of Einstein's famous relation $U=m$ between the energy and gravitational producing mass of an isolated system. An important expression is then obtained which gives the energy of a quasi-static isolated system in the form of an integral which has to be extended only over the portion of space actually occupied by matter or radiation. This expression has not previously received a satisfactory derivation. The result is used to obtain an expression for the energy of a spherical distribution of a perfect fluid, and it is then shown that this expression, in the case of a sphere of ordinary material, approaches in a sufficiently weak field to the classical expression for energy including the potential gravitational energy. This result is not only intrinsically useful, but also shows for a particular case that a higher order of approximation to the general relativity value for total energy is obtained by including the classical gravitational energy than by going at once to flat space-time as is often done. Finally, a general consideration is given to the problem of determining the conditions imposed on those changes from one static state to another which could occur in a non-isolated system forming part of a larger static system, without changing the distribution of matter and radiation outside the boundary and without contravening the energy-momentum principle as applied to the system as a whole.

The available potential energy of the atmosphere may be defined as the difference between the total potential energy and the minimum total potential energy which could result from any adiabatic redistribution of mass. It vanishes if the density stratification is horizontal and statically stable everywhere, and is positive otherwise. It is measured approximately by a weighted vertical average of the horizontal variance of temperature. In magnitude it is generally about ten times the total kinetic energy, but less than one per cent of the total potential energy. Under adiabatic flow the sum of the available potential energy and the kinetic energy is conserved, but large increases in available potential energy are usually accompanied by increases in kinetic energy, and therefore involve nonadiabatic effects. Available potential energy may be partitioned into zonal and eddy energy by an analysis of variance of the temperature field. The zonal form may be converted into the eddy form by an eddy-transport of sensible heat toward colder latitudes, while each form may be converted into the corresponding form of kinetic energy. The general circulation is characterized by a conversion of zonal available potential energy, which is generated by low-latitude heating and high-latitude cooling, to eddy available potential energy, to eddy kinetic energy, to zonal kinetic energy.

A free energy model for the inhomogeneous hard-sphere fluid mixture was derived recently [Phys. Rev. Lett. 63, 980 (1989)], which is based on the fundamental geometric measures of the particles. Along with an updated assessment of its accuracy, this model is first generalized for charged hard-sphere fluid mixtures, in which every particle carries a central Yukawa charge, and it is then extended to general fluid mixtures in external fields. The Yukawa-charged hard-sphere mixture provides a quite general reference system for many interesting physical systems including plasmas, molten salts, and colloidal dispersions, the screening parameter enabling to interpolate between the long range Coulomb forces and the short range hard cores. A special renormalization property of the Yukawa potential provides the means to derive the exact Onsager-type lower bound for the potential energy of the mixture, and its related asymptotic strong-coupling limit of the liquid pair correlation functions. These results are obtained analytically for the general homogeneous mixture with Yukawa interactions. They enable to extend the fundamental measure free energy model to inhomogeneous charged Yukawa mixtures, with the charge contributions given by a truncated second order expansion from the uniform (bulk) fluid limit. The resulting free energy model, which interpolates between the ideal-gas and ‘‘ideal-liquid’’ limits, then leads to a self-consistent method for calculating the density profiles for general fluid mixtures in external fields. This method is equivalent to an ansatz of ‘‘universality of the bridge functional.’’ The ‘‘bridge functional’’ consists of all the terms beyond the second order, in the expansion of the excess free energy functional around a reference uniform fluid. The self-consistency is imposed by applying the general method in the special case when the external potential is generated by a ‘‘test particle’’ at the origin of coordinates. In this limit, our general method for nonuniform fluids corresponds to an established and successful theory for the bulk uniform fluid pair structure, namely the thermodynamically consistent modified-hypernetted-chain theory, with the bridge functions now generated by an explicit and demonstratively accurate, ‘‘universal,’’ hard-sphere bridge functional. As a stringent test for the general model, the strongly coupled one-component plasma, in the bulk and near a hard wall, is considered in some detail.

In this paper we investigate possible ways to improve the energy efficiency of a general purpose microprocessor. We show that the energy of a processor depends on its performance, so we chose the energy-delay product to compare different processors. To improve the energy-delay product we explore methods of reducing energy consumption that do not lead to performance loss (i.e. wasted energy), and explore methods to reduce delay by exploiting instruction level parallelism. We found that careful design reduced the energy dissipation by almost 25%. Pipelining can give approximately a 2/spl times/ improvement in energy-delay product. Superscalar issue, however, does not improve the energy-delay product any further since the overhead required offsets the gains in performance. Further improvements will be hard to come by since a large fraction of the energy (50-80%) is dissipated in the clock network and the on-chip memories. Thus, the efficiency of processors will depend more on the technology being used and the algorithm chosen by the programmer than the micro-architecture.

The topic of energy is in the news a lot these days. Not only are we concerned about having enough energy for today's civilization and tomorrow's needs, but also energy is at the core of our understanding of the inner workings of the Sun, Earth, and life itself. Indeed, energy may well be the most common currency in all of natural science, helping us to appreciate where we came from and guiding us toward a sustainable society in the future. Energy plays a vital role in the origin and evolution of all complex systems in the universe, including galaxies, stars, planets, and life forms. Treating each of these systems as open thermodynamic structures that acquire, store, and express energy, it can be shown that over billions of years since the Big Bang, the energy rate densities (watts per kilogram) of these systems have risen with the cosmic march of time. General, coherent worldviews, based largely on the concept of energy, are now being developed by many researchers around the world. I certainly share many of my colleagues' enthusiasm for the fundamental function of energy in our world and for the need to study it more.

The problem of the dynamical structure and definition of energy for the classical general theory of relativity is considered on a formal level. As in a previous paper, the technique used is the Schwinger action principle. Starting with the full Einstein Lagrangian in first order Palatini form, an action integral is derived in which the algebraic constraint variables have been eliminated. This action possesses a "Hamiltonian" density which, however, vanishes due to the differential constraints. If the differential constraints are then substituted into the action, the true, nonvanishing Hamiltonian of the theory emerges. From an analysis of the equations of motion and the constraint equations, the two pairs of dynamical variables which represent the two independent degrees of freedom of the gravitational field are explicitly exhibited. Four other variables remain in theory; these may be arbitrarily specified, any such specification representing a choice of coordinate frame. It is shown that it is possible to obtain truly canonical pairs of variables in terms of the dynamical and arbitrary variables. Thus a statement of the dynamics is meaningful only after a set of coordinate conditions have been chosen. In general, the true Hamiltonian will be time dependent even for an isolated gravitational field. There thus arises the notion of a preferred coordinate frame, i.e., that frame in which the Hamiltonian is conserved. In this special frame, on physical grounds, the Hamiltonian may be taken to define the energy of the field. In these respects the situation in general relativity is analogous to the parametric form of Hamilton's principle in particle mechanics.

A general variational method for efficiently calculating energy bands and charge densities in solids is presented; the method can be viewed as a weighted local-energy procedure or alternately as a numerical integration scheme. This rapidly convergent procedure circumvents many of the difficulties associated with the evaluation of matrix elements of the Hamiltonian in an arbitrary basis and treats the general nonspherical potential with no more complication than the usual "muffin-tin" approximation. Thus the band structure of ionic and covalent materials can be calculated with realistic crystal potentials. As an example, the method is applied to the one-electron model Hamiltonian with a nonspherical local potential, using a linear combination of atomic orbitals basis. Matrix elements of the Hamiltonian are evaluated directly without decomposition into atomic basis integrals; no "tight-binding" approximations are made. Detailed calculations are presented for the band structure and charge density of bcc lithium which demonstrate the feasibility of our method, and reveal the sensitivity of the energy bands to nonspherical and exchange components of the crystal potential. Various prescriptions for the construction of crystal potentials are considered, and convenient least-squares expansions are described. The extension of these methods to nonlocal potentials such as are encountered in the Hartree-Fock self-consistent-field procedure is discussed.

A generalization of the single soil layer variable infiltration capacity (VIC) land surface hydrological model previously implemented in the Geophysical Fluid Dynamics Laboratory general circulation model (GCM) is described. The new model is comprised of a two‐layer characterization of the soil column, and uses an aerodynamic representation of the latent and sensible heat fluxes at the land surface. The infiltration algorithm for the upper layer is essentially the same as for the single layer VIC model, while the lower layer drainage formulation is of the form previously implemented in the Max‐Planck‐Institut GCM. The model partitions the area of interest (e.g., grid cell) into multiple land surface cover types; for each land cover type the fraction of roots in the upper and lower zone is specified. Evapotranspiration consists of three components: canopy evaporation, evaporation from bare soils, and transpiration, which is represented using a canopy and architectural resistance formulation. Once the latent heat flux has been computed, the surface energy balance is iterated to solve for the land surface temperature at each time step. The model was tested using long‐term hydrologic and climatological data for Kings Creek, Kansas to estimate and validate the hydrological parameters, and surface flux data from three First International Satellite Land Surface Climatology Project Field Experiment intensive field campaigns in the summer‐fall of 1987 to validate the surface energy fluxes.

The invariance of various definitions proposed for the energy and momentum of the gravitational field is examined. We use the boundary conditions that ${g}_{\ensuremath{\mu}\ensuremath{\nu}}$ approaches the Lorentz metric as $\frac{1}{r}$, but allow ${g}_{\ensuremath{\mu}\ensuremath{\nu},\ensuremath{\alpha}}$ to vanish as slowly as $\frac{1}{r}$. This permits "coordinate waves." It is found that none of the expressions giving the energy as a two-dimensional surface integral are invariant within this class of frames. In a frame containing coordinate waves they are ambiguous, since their value depends on the location of the surface at infinity (unlike the case where ${g}_{\ensuremath{\mu}\ensuremath{\nu},\ensuremath{\alpha}}$ vanishes faster than $\frac{1}{r}$). If one introduces the prescription of space-time averaging of the integrals, one finds that the definitions of Landau-Lifshitz and Papapetrou-Gupta yield (equal) coordinate-invariant results. However, the definitions of Einstein, M\o{}ller, and Dirac become unambiguous, but not invariant.The averaged Landau-Lifshitz and Papapetrou-Gupta expressions are then shown to give the correct physical energy-momentum as determined by the canonical formulations Hamiltonian involving only the two degrees of freedom of the field. It is shown that this latter definition yields that inertial energy for a gravitational system which would be measured by a nongravitational apparatus interacting with it. The canonical formalism's definition also agrees with measurements of gravitational mass by Newtonian means at spacial infinity. It is further shown that the energy-momentum may be invariantly calculated from the asymptotic form of the metric field at a fixed time.

We examine the AdS-CFT correspondence when gauge theory is considered on a compactified space with supersymmetry-breaking boundary conditions. We find that the corresponding supergravity solution has a negative energy, in agreement with the expected negative Casimir energy in the field theory. The stability of the gauge theory would imply that this supergravity solution has minimum energy among all solutions with the same boundary conditions. Hence we are led to conjecture a new positive energy theorem for asymptotically locally anti--de Sitter spacetimes. We show that the candidate minimum energy solution is stable against all quadratic fluctuations of the metric.

The mass-energy of spherically symmetric distributions of material is studied according to general relativity. An arbitrary orthogonal coordinate system is used whenever invariant properties are discussed. The Bianchi identity is shown to imply that the Misner-Sharp-Hernandez mass function is an integral of two combinations of Einstein's equations for any energy-momentum tensor and that mass-energy flow is conservative. The two mass equations thus found and the mass function provide a technique for casting Einstein's field equations into alternative forms. This mass-function technique is applied to the general problem of the motion of a perfect fluid and especially to the examination of negative-mass shells and their relation to singular behavior. The technique is then specialized to the study of a known class of solutions of Einstein's equations for a perfect fluid and to a brief treatment of uniform model universes and the charged point-mass solution.

The Hamiltonian for general relativity obtained in a previous paper furnishes a definition of energy whose physical interpretation is direct, and which fulfills the conditions required of the energy in other physical systems. The energy can be expressed as a surface integral at spacial infinity in terms of the spacial components of the covariant metric tensor at any given time. Thus, the energy depends only on the minimal initial Cauchy data and may be evaluated in any coordinate system, provided this system can be made asymptotically rectangular. These statements remain valid when particles are coupled to the gravitational field. The criteria for existence of gravitational radiation are formulated in terms of the canonical variables and the stress-tensor. These criteria are identical to those used in electromagnetic theory. Some applications are discussed.

A general equation of mechanical equilibrium of fluid membranes subject to bending elasticity [reported in Phys. Rev. Lett. 59, 2486 (1987)] is derived in detail. The second variation of the shape energy, also obtained for arbitrary shapes, is used to analyze stability with respect to deformational modes for spherical and cylindrical vesicles. The former analysis is well known, while the latter is presented here for the first time. The theoretical results are shown to agree very well with previous numerical calculations. In addition, they provide the energies controlling the shape fluctuations and show that spontaneous curvature may transform cylinders into tapes or strings of beads. The study of the energy of infinitesimal deformations is finally extended to include the third variation. Applying the general result to the sphere, we obtain the critical value of spontaneous curvature below which oblate ellipsoids of a deformed sphere are more stable than prolate ones. It is shown to be the same regardless of whether volume or pressure is kept constant.

The multiconfigurational time-dependent Hartree (MCTDH) approach facilitates multidimensional quantum dynamics calculations by representing the wavepacket in an optimal set of time-dependent basis functions, called single-particle functions. Choosing these single-particle functions to be themselves multidimensional wavefunctions which are represented using a MCTDH representation, a multilayer MCTDH scheme has been constructed and used for quantum dynamics calculations treating up to 1000 degrees of freedom rigorously [Wang and Thoss, J. Chem. Phys. 199, 1289 (2003)]. The present work gives a practical scheme which facilitates the application of the multilayer MCTDH approach, which previously has only been employed to study systems described by model-type Hamiltonians, to molecular systems described by more complicated Hamiltonians and general potential energy surfaces. A multilayer extension of the correlation discrete variable representation (CDVR) scheme employed in MCTDH calculations studying quantum dynamics on general potential energy surfaces is developed and tested in a simple numerical application. The resulting multilayer MCTDH/CDVR approach might offer a perspective to rigorously describe the quantum dynamics of larger polyatomic systems.

The energy flux in a finite-depth gravity-wave spectrum resulting from weak non-linear couplings between the spectral components is evaluated by means of a perturbation method. The fifth-order analysis yields a fourth-order effect comparable in magnitude to the generating and dissipating processes in wind-generated seas. The energy flux favours equidistribution of energy and vanishes in the limiting case of a white, isotropic spectrum. The influence on the equilibrium structure of fully developed wave spectra and on other phenomena in random seas is discussed briefly.

Abstract We describe a computer program we have been developing to build models of molecules and calculate their interactions using empirical energy approaches. The program is sufficiently flexible and general to allow modeling of small molecules, as well as polymers. As an illustration, we present applications of the program to study the conformation of actinomycin D. In particular, we study the rotational isomerism about the D ‐Val‐, L ‐Pro, and L ‐Pro‐Sar amide bonds as well as comparing the energy and structure of the Sobell model and the x‐ray structure of actinomycin D.