Non-static Model Research Articles

Merging Alternate Remotely-Sensed Soil Moisture Retrievals Using a Non-Static Model Combination Approach

Soil moisture is an important variable in the coupled hydrologic and climate system. In recent years, microwave-based soil moisture products have been shown to be a viable alternative to in situ measurements. A popular way to measure the performance of soil moisture products is to calculate the temporal correlation coefficient (R) against in situ measurements or other appropriate reference datasets. In this study, an existing linear combination method improving R was modified to allow for a non-static or nonstationary model combination as the basis for improving remotely-sensed surface soil moisture. Previous research had noted that two soil moisture products retrieved using the Japan Aerospace Exploration Agency (JAXA) and Land Parameter Retrieval Model (LPRM) algorithms from the same Advanced Microwave Scanning Radiometer 2 (AMSR2) sensor are spatially complementary in terms of R against a suitable reference over a fixed period. Accordingly, a linear combination was proposed to maximize R using a set of spatially-varying, but temporally-fixed weights. Even though this approach showed promising results, there was room for further improvements, in particular using non-static or dynamic weights that take account of the time-varying nature of the combination algorithm being approximated. The dynamic weighting was achieved by using a moving window. A number of different window sizes was investigated. The optimal weighting factors were determined for the data lying within the moving window and then used to dynamically combine the two parent products. We show improved performance for the dynamically-combined product over the static linear combination. Generally, shorter time windows outperform the static approach, and a 60-day time window is suggested to be the optimum. Results were validated against in situ measurements collected from 124 stations over different continents. The mean R of the dynamically-combined products was found to be 0.57 and 0.62 for the cases using the European Centre for Medium-Range Weather Forecasts Reanalysis-Interim (ERA-Interim) and Modern-Era Retrospective Analysis for Research and Applications Land (MERRA-Land) reanalysis products as the reference, respectively, outperforming the statically-combined products (0.55 and 0.54).

Einstein Rosen Mesonic Perfect Fluid Cosmological Model with Time Dependent Λ-Term

Mesonic perfect fluid solutions are found in general relativity with the aid of Einstein’s Rosen cylindrically symmetric space time. A static vacuum model and a non-static cosmological model corresponding to perfect fluid are investigated. The cosmological term Λ is found to be a decreasing function of time which is supported by the result found from recent type Ia Supernovae observations. The various physical and geometrical features of the model are discussed.

EINSTEIN–ROSEN STRING COSMOLOGICAL MODEL IN BARBER'S SECOND SELF-CREATION THEORY

Field equations in the presence of cosmic string source are obtained in Barber's second self-creation theory of gravitation (Gen. Relativ. Gravit.14, 117 (1982)) with the aid of Einstein–Rosen cylindrically symmetric metric. A static vacuum model and a nonstatic exact string cosmological model are presented which represents Reddy string (Astrophys. Space Sci.286, 365 (2003)) in self-creation theory. Some physical and kinematical properties of the model are also discussed.

Evaluation of Cutting Efficiency of Orthograde Ultrasonic Tips by Using a Nonstatic Model

The purpose of this in vitro study was to evaluate the cutting efficiency of 4 orthograde ultrasonic tips and describe a nonstatic cutting model. Forty molars were extracted and decoronated. Each group contained 10 tips. The samples were fixed to a double pan balance that applied a constant vertical force of 40 g to the ultrasonic tips. The ultrasonic handpiece was mounted to a cyclic axial fatigue testing apparatus to generate a 3-mm horizontal movement of the ultrasonic tip during the cutting procedure. Three cutting cycles of 30 seconds were tested for each power setting of 3, 5, and 7. The weight of the samples was measured before and after the 3 cycles. The cutting efficiency was determined by the weight change caused by dentin removal. The Buc-1 ultrasonic tip had a significantly greater cutting efficiency than the other 3 tips at each of the 3 power settings ( P < .05).

Bianchi type-III non-static magnetized cosmological model for perfect fluid distribution in general relativity

We have investigated Bianchi type III non-static magnetized cosmological model for perfect fluid distribution in general relativity. We assume that F12 is the only non-vanishing component of Fij. Maxwell’s equation $$\frac{\partial}{\partial {x}^{j}}\bigl(F_{{ij}}\sqrt{-g}\bigr)=0$$ leads to $${F}_{12}=\mathrm{Ke}^{-\alpha {x}}$$ where K and α are constants.

Winding String Dynamics in a Time-Dependent Beta Deformed Background

We investigate string theory on the analytically continued β deformed background proposed in hep-th/0509036. This non-static model provides a solvable conformal field theory which describes time-dependent twisted string dynamics. We also study its low energy limit using the mini-superspace analysis. We examine winding string pair production via Bogoliubov coefficients and disk one-point correlators of D-branes. We find that these results are consistent with the CFT computations.

Nonexistence of Plane Symmetric String Cosmological Model in Brans-Dicke Theory of Gravitation

Field equations in Brans-Dicke scalar-tensor theory of gravitation are obtained with the aid a non-static plane symmetric metric in the presence of massive string source. It is shown that a non-static string model, in this theory, does not exist when the sum of the energy density and the tension density of the cosmic string vanishes.

Einstein-Rosen Universe in the Scale-Covariant Theory of Gravitation

Field equations in the presence of a perfect fluid distributionc for Einstein-Rosen cylindrically symmetric metric are obtained in the scale-covariant theory of gravitation proposed by Canuto et al. (1977a). A static vacuum model and a non-static cosmological model corresponding to perfect fluid are presented. Physical and Kinematical properties of the models are also discussed.

Non-static plane symmetric cosmological model in Wesson’s theory

The problem of non-static plane symmetric perfect fluid distribution in Wesson’s [1] scale invariant theory of gravitation with a time-dependent gauge function is investigated. The false vacuum model of the universe is constructed and some physical properties of the model are discussed.

Non-Static Plane Symmetric Cosmological Models in Bimetric Theory

The problems of non-static plane symmetric meson field and mesonic perfect fluid in Rosen's [Gen. Rel. Gray., Vol. 4 (1973) 435] bimetric theory of gravitation are considered. It is observed that plane symmetric non-static cosmological model exists in case of scalar meson field where the scalar field becomes constant. Further it is found that in case of mesonic perfect fluid, the bimetric theory does not admit perfect fluid but allows only mesonic scalar field with constant scalar field. In both the cases a cosmological model with constant scalar field is obtained.

Inelastic energy loss of light particles scattered by solid surfaces at low energy: influence of the `gap'

The energy spectra of particles scattered by solid surfaces are used to determine the inelastic energy loss at low energy. Assuming the binary collision approximation, a modified TRIM code provides length distributions which are converted to time-of-flight (TOF) spectra by using the friction coefficient as an adjustable parameter. Owing to the nonlinear effects occurring in this energy range, the theoretical value of the electronic stopping power is performed from electron-particle scattering cross-section using a screened potential and so, the phase shifts, obtained self-consistently in the framework of density functional theory (DFT). In the case of He/a:Si interaction at 4 keV, the standard model leads to a largely overestimated value. This fact has been attributed to the presence of the electron energy gap EG and to the structure of the valence band. We verify this assumption in a non-static model involving all electrons of the valence band with a threshold condition ve′2>vF2+2EG, where vF is the Fermi velocity and ve the electron velocity after scattering (non-static extended collisional model). The theoretical results agree very well with the experimental ones for He colliding three targets: a:Si, a:Ge and polycrystalline Ni at 4 keV. The calculations performed for the velocity range below 1 a.u. confirm the important role of the gap and the band structure in the lowering of stopping power at low velocity.

Nonstatic G�del-type cosmological model with perfect fluid and heat flow

We obtain some cosmological models that are exact solutions of Einstein field equations. The metric utilized is the nonstatic Godel-type cosmological model and the curvature source is a perfect fluid with heat flow. The solutions reported here are nonstatic generalizations of Godel's rotating cosmos.

Internal source of the vaidya solution

A nonstatic model of a radiating star is constructed with the energy-momentum tensor of a non-Pascal fluid and nonequilibrium radiation. The gravity equations are reduced to an equation which permits one to immediately generalize known analytic static solutions to nonstatic ones with radiation. The approximation of a homogeneous star is considered in detail, and an evaluation is performed which shows that for a Sun-like star physical parameters which follow from the model, lie between reasonable limits and agree with observations.

A plane-symmetric universe in the presence of zero-mass scalar fields

A non-static plane-symmetric cosmological model in the presence of zero-mass scalar fields is obtained when the source of the gravitational field is a perfect fluid with pressure equal to energy density. Some properties of the model are discussed.

Shape resonances in electron–molecule scattering. A proposed model in terms of S matrix poles and associated generalized quantum numbers

AbstractAs an extension of the recent atomic work of Krylstedt et al. [1, 2], we propose the synthesis of the static exchange plus polarization model within the multiple scattering Xα formalism and the exterior complex rotation method for the study of shape resonances occurring in molecular collisional systems. The bound state multiple scattering Xα method is reviewed with special attention to the form of the various wave functions for the different molecular regions. In connection with the inclusion of continuum electron exchange into the scattering model, we analyze a possible solution to the problem of asymptotical behavior caused by the local density‐based free electron gas approximation used in this case. We also propose a method to fix the cutoff parameter, inherent in the polarization potential, for symmetry‐related molecular participants in the scattering process, thereby obtaining a possible predictive power for the one‐parameter scattering model.Titchmarsh–Weyl's theory is used to formally connect the above formulation to scattering theory. The theoretical difficulties in obtaining a unique meromorphic continuation of the S matrix are investigated in connection with the requirements on the actual potential to be exterior dilation analytic. Furthermore, the occurrence of asymptotic quantum numbers is noted and discussed in conjunction with muffin tin‐like approximations and related exterior complex rotated schemes.It is found that the electron exchange part of the nonstatic one‐body potential exhibits a functional form that is not exterior dilation analytic, albeit the general electron and nuclear many‐body problem involving Coulomb forces are dilation analytic. Although the immediate consequences indicate a rotation angle (θ) dependence on the S matrix continuation, a uniquely defined assignment of the cutoff parameter r0 = r0(θ) makes the present nonstatic model “exterior dilation analytic” in the sense that it mimics the dilation analytic structure of the full many‐body problem at the same time obeying “asymptotic” spherical symmetry via the associated constant of evolution. However, in the static exchange approximation the above difficulties are shown to be circumvented via a certain reformulation, leading to a regular analytic asymptotic form for the interaction potential.

A plane symmetric cosmological model in Lyra manifold

A non-static plane-symmetric cosmological model in Lyra's manifold is obtained when the source of the gravitational field is a perfect fluid with pressure equal to energy density. Some properties of the model have also been discussed.

Self-gravitating fluids in cylindrically-symmetric non-static space-time

In this paper we have obtained a cylindrically symmetric non-static model of the perfect fluid distribution, satisfying one of the Petrov type D conditions. This turned out to be a FRW model.

Spherically symmetric conformally flat distributions of charged dust and zero-mass scalar fields

The problem of charged dust distribution in the presence of zero-mass scalar field for a spherically symmetric conformally flat metric has been investigated. Exact solutions are obtained in the comoving coordinate system for the static model as well as for the nonstatic model. It has been shown that in the nonstatic model the electromagnetic field and dust distribution cannot survive when the scalar field is taken to be a function of timet only. Physical interpretation of the solutions has been investigated.

Simple model of pion-nucleon elastic scattering

A nonstatic model for elastic pion-nucleon scattering is developed using knowledge of the analytic structure of the scattering amplitude and partial wave $\frac{N}{D}$ dispersion techniques. In $S$, $D$, and $F$ partial wave channels the model is equivalent to a separable potential model which includes the coupling to inelastic channels. In $P$-wave channels the nucleon pole which arises from absorption and emission of the pion is included. A more general model which incorporates both a nucleon pole term and a separable potential term is developed for the ${P}_{11}$ channel. This model is capable of reproducing the change of sign which is present in the ${P}_{11}$ phase shifts. The necessary information concerning the coupling of the inelastic scattering to the elastic scattering is taken from the experimentally determined phase shifts as input. If simple kinematic factors are included explicitly, quite simple analytic functions for the form factors in the model are able to reproduce the experimental phase shifts for pion laboratory kinetic energies up to 1.2 GeV. The model produces off-shell behavior which is different from previous models. In particular, the inclusion of the nucleon pole alters substantially the range of the interaction in all $P$-wave channels.NUCLEAR REACTIONS Pion-nucleon elastic scattering; separable potential and Chew-Low models extended; $S$-, $P$-, $D$-, and $F$-wave phase shifts for $E&lt;~1.2$ GeV.

A Cosmological Model of Class One in Lyra's Manifold

A study is presented of a spherically symmetric class-one cosmological model based on Lyra's geometry. The static universe is shown to be physically unrealistic. The nonstatic model parallels Lemaitre's in the Riemannian case but the law of mass-energy onservation does not hold.