Properties of signature partner superdeformed bands in mercury nuclei

2015 ◽  
Vol 11 (1) ◽  
pp. 2918-2926 ◽  
Author(s):  
Mahmoud Abokilla ◽  
Hayam Yassin ◽  
Eman R. Abo Elyazeed
Keyword(s):  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Transition Energies ◽  
Fitting Procedure ◽  
Higher Order Terms ◽  
Fourth Derivative ◽  
The Difference ◽  
Experimental Transition ◽  
Search Program

The properties of superdeformed (SD) bands of five pairs signature partners in mercury nuclei have been systematically analyzed in framework of four parameters formula including higher order terms of Bohr-Mottelson collective rotational energies. The level spins and the model parameters are determined by fitting procedure using a computer simulated search program in order to obtain minimum root mean square deviations between the calculated and the experimental transition energies.The best fitted parameters have been used to calculate the transition energies Eγ, the rotational frequencies , the kinematic J(1) and dynamic J(2) moments of inertia. The calculated results agree excellently with the experimental data. J(2) is significantly larger than J(1) for all values of  . Also J(2) show a smooth increase with increasing . The appearance of ΔI = 1 and ΔI = 2 staggering in γ-ray transition energies have been examined by using the five-points formula representing the finite difference approximation to the fourth derivative of the γ-ray transition energies at a given spin. The signature partners in Hg nuclei show large amplitude staggering. Also to appear the ΔI = 1 staggering, the transition energies relative to a rigid rotor with a moment of inertia J = 128.219 are plotted against spins for each signature partner pairs. The difference in transition energies between transitions in the two SD bands 191Hg(SD3)and 193Hg(SD3) are small, therefore, these two bands have been considered as identical bands.

scholarly journals A Numerical Model of Temperate Glacier Flow Applied to the Quiescent Phase of a Surge-Type Glacier

1982 ◽  
Vol 28 (99) ◽  
pp. 239-265 ◽  
Author(s):  
Robert Bindschadler
Keyword(s):  
Shear Stress ◽  
Numerical Model ◽  
Stress Gradient ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Small Contribution ◽  
Base Shear ◽  
Quiescent Phase ◽  
Glacier Flow

AbstractA time-dependent numerical model of temperate glacier flow without sliding is developed and applied to the quiescent phase of surge-type Variegated Glacier, Alaska. The model is based on a one-dimensional continuity equation but the transverse channel shape is explicitly included allowing the complex geometries of real glaciers to be modelled. Velocities and volume fluxes are calculated from the glacier geometry. Transverse stress is taken into account by shape factors which are fitted to measurements of geometry and velocity and are chosen to be insensitive to changes in geometry. Longitudinal stress gradients are taken into account by use of a large-scale surface slope. A Crank-Nicholson finite-difference approximation is used and it is unconditionally stable when a small contribution from the local slope is added to the average slope.Model parameters are fitted to extensive data collected on Variegated Glacier in 1973 and 1974. Predictions of the model over a four year interval agree well with field measurements. Predictions of the current quiescent phase (1965–84) indicate depth increases in the upper glacier of more than 75 m with a twenty-fold increase in the volume flux. During this interval the base shear stress increases 40% in the upper glacier and decreases 20% in the lower glacier. During the mid to late quiescent phase, ice motion becomes more important than mass balance in the redistribution of mass over the central region of the glacier. If normal flow were to persist, the predicted steady-state profile would be an average of 100 m deeper and 41% more voluminous than in 1973.The predicted base shear-stress gradient is never negative enough to satisfy Robin and Weertman’s (1973) condition for blockage of subglacial water flow. The annual rate of water production by dissipation of mechanical straining at the bed remains two orders of magnitude below that produced by summer surface melt. The predicted fractional increase in base stress during the quiescent phase is a maximum in the region believed to be the trigger zone of the surges.

scholarly journals BRANE UNIVERSES TESTED AGAINST ASTRONOMICAL DATA

2004 ◽  
Vol 13 (08) ◽  
pp. 1669-1702 ◽  
Author(s):  
MARIUSZ P. DABROWSKI ◽  
WŁODZIMIERZ GODŁOWSKI ◽  
MAREK SZYDŁOWSKI
Keyword(s):  
Cosmological Constant ◽  
Likelihood Method ◽  
Model Parameters ◽  
Density Parameter ◽  
Brane Model ◽  
Fitting Procedure ◽  
Type Ia ◽  
The Difference ◽  
Age Of The Universe ◽  
Phantom Matter

We discuss observational constrains coming from supernovae imposed on the behaviour of the Randall–Sundrum models. We test the models using the Perlmutter SNIa data as well as the new Knop and Tonry/Barris samples. The data indicates that, under the assumption that we admit zero pressure dust matter on the brane, the cosmological constant is still needed to explain current observations. We estimate the model parameters using the best-fitting procedure and the likelihood method. The observations from supernovae give a large value of the density parameter for brane matter Ωλ,0≃0.01 as the best fit. For high redshifts z>1.2, the difference between the brane model and the ΛCDM (Perlmutter) model becomes detectable observationally. From the maximum likelihood method we obtained the favored value of Ωλ,0=0.004±0.016 for Ωk,0=0 and Ω m ,0=0.3. This gives the limit Ωλ,0<0.02 at 1σ level. While the model with brane effects is preferred by the supernovae type Ia data, the model without brane fluid is still statistically admissible. We also discuss how fit depends on restrictions of the sample, especially with respect to redshift criteria. We also pointed out the property of sensitive dependence of results with respect to the choice of ℳ parameter. For comparison the limit on brane effects which comes from CMB anisotropies and BBN is also obtained. The uncertainty in the location of the first peak gives a stronger limit Ωλ,0<1.0×10-12, whereas from BBN we obtain that Ωλ,0<1.0×10-27. However, both very strict limits are obtained with the assumption that brane effects do not change the physics in the pre-recombination era, while the SNIa limit is model independent. We demonstrate that the fit to supernovae data can also be obtained if we admit the phantom matter p=-(4/3)ϱ on the brane, where this matter mimics the influence of the cosmological constant. We show that phantom matter enlarges the age of the universe on the brane which is demanded in cosmology. Finally, we propose to check for dark radiation and brane tension by the application of the angular diameter of galaxies minimum value test.

Nature of cross-talk transitions and ΔI = 1 energy staggering in signature partners of odd mass superdeformed nuclei

2017 ◽  
Vol 26 (04) ◽  
pp. 1750011
Author(s):  
A. M. Khalaf ◽  
M. Kotb ◽  
T. M. Awwad
Keyword(s):  
Cross Talk ◽  
Large Amplitude ◽  
Model Parameters ◽  
Kinematic Formula ◽  
Rotational Model ◽  
Moments Of Inertia ◽  
Transition Energies ◽  
Increasing Trend ◽  
Search Program

Two-way cross-talk transitions between pairs of signature partners superdeformed (SD) bands in [Formula: see text]Hg (SD2,SD3), [Formula: see text]Hg (SD3,SD4) and [Formula: see text]T1(SD1,SD2) built on the configurations [Formula: see text], respectively, are proposed. The [Formula: see text] energy staggering presented in these odd SD nuclei are investigated and parametrized by proposing two staggering functions depending on the dipole transitions linking the signature partners. These staggering functions differ from the conventional staggering functions employed in previous works which depend on the quadruple transitions within each band. For parametrization, we used the two-term formula of Bohr–Mottelson collective rotational model. The model parameters and the bandhead spins of the considered signature partners are determined by using a simulated fitting search program and the values of the adopted parameters are used to calculate transition energies [Formula: see text], rotational frequencies [Formula: see text], kinematic [Formula: see text] and dynamic [Formula: see text] moments of inertia. The calculated results agree very well with the experimental ones. The bands exhibit the usual increasing trend. Large amplitude staggering has been found in the considered three signature partner pairs in [Formula: see text]Hg and [Formula: see text]T1 nuclei.

scholarly journals Three-dimensional modeling of hydrodynamic problems taking into account elastic processes

2021 ◽  
pp. 1-15
Author(s):  
Yuri Andreevich Poveschenko ◽  
Alexander Yur’evich Krukovskiy ◽  
Dmitri Sergeevich Boykov ◽  
Victoria Olegovna Podryga ◽  
Parvin Ilgar gizi Rahimly
Keyword(s):  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Difference Schemes ◽  
Finite Difference Approximation ◽  
Vector Analysis ◽  
Difference Approximation ◽  
Sound Waves ◽  
Displacement Vectors ◽  
The Difference ◽  
Elastic Processes

A finite-difference approximation of elastic forces on spaced Lagrangian grids is constructed, based on the method of support operators. For displacement vectors on irregular grids, on the topological and geometric structure of which minimal reasonable restrictions are imposed, the approximations of vector analysis operations are constructed in relation to difference schemes for problems of elasticity theory. Taking into account the energy balance of the medium, the constructed families of integrally consistent approximations of vector analysis operations are sufficient for discrete modeling of these processes. The schemes are considered, both using the stress tensor in an explicit form, and dividing it into spherical and shear components (pressure and deviator). The latter is used to construct homogeneous algorithms applicable to both the solid and the vaporized phase. The linear theory of elasticity is used for constructing approximations. The resulting forces in spatial geometry are obtained explicitly. Calculations of the sound waves propagation in a three-dimensional orthogonal aluminum plate due to end impact are presented. These calculations confirm the good quality of the difference schemes constructed in work.

scholarly journals Bed Topography and Mass-Balance Distribution of Columbia Glacier, Alaska, U.S.A., Determined from Sequential Aerial Photography

1988 ◽  
Vol 34 (117) ◽  
pp. 208-216 ◽  
Author(s):  
L. A. Rasmussen
Keyword(s):  
Mass Balance ◽  
Aerial Photography ◽  
Continuity Equation ◽  
The Other ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Bed Topography ◽  
Displacement Vectors ◽  
Grid Nodes

AbstractAn internally consistent data set of geometry and flow variables for the lower part of Columbia Glacier, south-central Alaska, is derived entirely from vertical aerial photography. The principle of mass conservation is imposed on the data in the form of a centered finite-difference approximation of the continuity equation. It is applied on a 120-node section of a square grid covering the 15 km long, high-velocity stretch ending at the grounded, heavily calving terminus of this large glacier.Photography was obtained 22 times between June 1977 and September 1981. Surface altitudes on the dates of the flights and the displacement vectors between pairs of flights were determined photogrammetrically. Natural features on the glacier surface were sufficiently prominent and enduring to be followed from the date of one flight to the next.Because both the altitude points and displacement vectors were irregularly positioned spatially, interpolation was necessary to get values on the grid nodes. The points had already been subjected to the method of optimum interpolation to get surface altitudes on the grid nodes. The displacement vectors are subjected here to a constrained–interpolation method to get velocity vectors at the grid nodes that are consistent, through the continuity equation, with the other variables.The other variables needed to achieve closure of the variable set are bed topography and mass-balance distribution. The latter was taken to be a separate linear function of altitude for each time interval. Values for bed altitudes at 120 nodes and two coefficients of each 21 balance functions were inferred as the 162 model parameters in a non-linear minimization problem having 4305 observed velocity components as its data.

Efficient inversion of 2.5D electrical resistivity data using the discrete adjoint method

Geophysics ◽  
2021 ◽  
pp. 1-54
Author(s):  
Diego Domenzain ◽  
John Bradford ◽  
Jodi Mead
Keyword(s):  
Electrical Resistivity ◽  
Gradient Descent ◽  
Adjoint Method ◽  
Sparse Matrices ◽  
Joint Inversion ◽  
Geophysical Data ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Inversion Algorithm

We present a memory and operation-count efficient 2.5D inversion algorithm of electrical resistivity (ER) data that can handle fine discretization domains imposed by other geophysical (e.g, ground penetrating radar or seismic) data. Due to numerical stability criteria and available computational memory, joint inversion of different types of geophysical data can impose different grid discretization constraints on the model parameters. Our algorithm enables the ER data sensitivities to be directly joined with other geophysical data without the need of interpolating or coarsening the discretization. We employ the adjoint method directly in the discretized Maxwell's steady state equation in order to compute the data sensitivity to the conductivity. In doing so, we make no finite difference approximation on the Jacobian of the data and avoid the need to store large and dense matrices. Rather, we exploit matrix-vector multiplication of sparse matrices and find successful convergence using gradient descent for our inversion routine without having to resort to the Hessian of the objective function. By assuming a 2.5D subsurface, we are able to linearly reduce memory requirements when compared to a 3D gradient descent inversion, and by a power of two when compared to storing a 2D Hessian. Moreover, our method linearly outperforms operation counts when compared to 3D Gauss-Newton conjugate-gradient schemes, which scales cubically in our favor with respect to the thickness of the 3D domain. We physically appraise the domain of the recovered conductivity using a cut-off of the electric current density present in our survey. We present two case studies in order to assess the validity of our algorithm. First, on a 2.5D synthetic example, and then on field data acquired in a controlled alluvial aquifer, where we were able match the recovered conductivity to borehole observations.

scholarly journals A Numerical Model of Temperate Glacier Flow Applied to the Quiescent Phase of a Surge-Type Glacier

1982 ◽  
Vol 28 (99) ◽  
pp. 239-265 ◽  
Author(s):  
Robert Bindschadler
Keyword(s):  
Shear Stress ◽  
Numerical Model ◽  
Stress Gradient ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Small Contribution ◽  
Base Shear ◽  
Quiescent Phase ◽  
Glacier Flow

AbstractA time-dependent numerical model of temperate glacier flow without sliding is developed and applied to the quiescent phase of surge-type Variegated Glacier, Alaska. The model is based on a one-dimensional continuity equation but the transverse channel shape is explicitly included allowing the complex geometries of real glaciers to be modelled. Velocities and volume fluxes are calculated from the glacier geometry. Transverse stress is taken into account by shape factors which are fitted to measurements of geometry and velocity and are chosen to be insensitive to changes in geometry. Longitudinal stress gradients are taken into account by use of a large-scale surface slope. A Crank-Nicholson finite-difference approximation is used and it is unconditionally stable when a small contribution from the local slope is added to the average slope.Model parameters are fitted to extensive data collected on Variegated Glacier in 1973 and 1974. Predictions of the model over a four year interval agree well with field measurements. Predictions of the current quiescent phase (1965–84) indicate depth increases in the upper glacier of more than 75 m with a twenty-fold increase in the volume flux. During this interval the base shear stress increases 40% in the upper glacier and decreases 20% in the lower glacier. During the mid to late quiescent phase, ice motion becomes more important than mass balance in the redistribution of mass over the central region of the glacier. If normal flow were to persist, the predicted steady-state profile would be an average of 100 m deeper and 41% more voluminous than in 1973.The predicted base shear-stress gradient is never negative enough to satisfy Robin and Weertman’s (1973) condition for blockage of subglacial water flow. The annual rate of water production by dissipation of mechanical straining at the bed remains two orders of magnitude below that produced by summer surface melt. The predicted fractional increase in base stress during the quiescent phase is a maximum in the region believed to be the trigger zone of the surges.

Band head spin assignment of superdeformed bands in 133Pr using two-parameter formulae

2018 ◽  
Vol 33 (09) ◽  
pp. 1850048 ◽  
Author(s):  
Honey Sharma ◽  
H. M. Mittal
Keyword(s):  
Power Index ◽  
Band Head ◽  
Least Square ◽  
Index Formula ◽  
Mean Deviation ◽  
Model Parameters ◽  
Transition Energies ◽  
Rotational Bands ◽  
Experimental Transition ◽  
Two Parameter

The two-parameter formulae viz. the power index formula, the nuclear softness formula and the VMI model are adopted to accredit the band head spin [Formula: see text] of four superdeformed rotational bands in [Formula: see text]. The technique of least square fitting is used to accredit the band head spin for four superdeformed rotational bands in [Formula: see text]. The root mean deviation among the computed transition energies and well-known experimental transition energies are attained by extracting the model parameters from the two-parameter formulae. The determined transition energies are in excellent agreement with the experimental transition energies, whenever exact spins are accredited. The power index formula coincides well with the experimental data and provides minimum root mean deviation. So, the power index formula is more efficient tool than the nuclear softness formula and the VMI model. The deviation of dynamic moment of inertia [Formula: see text] against the rotational frequency is also examined.

Development and validation of mathematical model of hydrotropic-reactive extraction of lignin

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Indah Hartati ◽  
Wahyudi Budi Sediawan ◽  
Hary Sulistyo ◽  
Muhammad Mufti Azis ◽  
Moh Fahrurrozi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Effective Diffusivity ◽  
Reaction Rate Constant ◽  
Reactive Extraction ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Explicit Finite Difference ◽  
The Mathematical Model

AbstractHydrotropes have been largely explored as reactive extraction agent for lignin separation. In this paper, a mathematical model of hydrotropic-reactive extraction of sugarcane bagasse lignin was proposed and validated by experimental data from literature. The mathematical model was developed by assuming the particle is in slab shape, and by considering simultaneous processes of hydrotrope intra particle diffusion, second order reaction of lignin-hydrotrope, and intra-particle soluble delignification product diffusion. The proposed model results in a set of partial differential equations which were then solved by explicit finite difference approximation method. The mathematical model parameters were determined by fitting the model to the hydrotropic reactive extraction experimental data reported by Ansari and Gaikar (2014). Simulations show that the mathematical model of the hydrotropic-reactive extraction were well fitted to the experimental data with the obtained hydrotrope effective diffusivity (DeA) of 5.0 × 10−11 m2/s, effective diffusivity of soluble lignin product (DeC) of 9.0 × 10−12 m2/s and reaction rate constant (kr) of 1.78 × 10−10 m3/(g.s). It was also observed that the reaction was first order to the hydrotrope (n = 1), and one half order to the lignin (m = 0.5). Meanwhile the pseudo-stoichiometric mass ratio of hydrotrope to lignin was 6.4 g hydrotrope/g lignin.

scholarly journals Bed Topography and Mass-Balance Distribution of Columbia Glacier, Alaska, U.S.A., Determined from Sequential Aerial Photography

1988 ◽  
Vol 34 (117) ◽  
pp. 208-216 ◽  
Author(s):  
L. A. Rasmussen
Keyword(s):  
Mass Balance ◽  
Aerial Photography ◽  
Continuity Equation ◽  
The Other ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Bed Topography ◽  
Displacement Vectors ◽  
Grid Nodes

Abstract An internally consistent data set of geometry and flow variables for the lower part of Columbia Glacier, south-central Alaska, is derived entirely from vertical aerial photography. The principle of mass conservation is imposed on the data in the form of a centered finite-difference approximation of the continuity equation. It is applied on a 120-node section of a square grid covering the 15 km long, high-velocity stretch ending at the grounded, heavily calving terminus of this large glacier. Photography was obtained 22 times between June 1977 and September 1981. Surface altitudes on the dates of the flights and the displacement vectors between pairs of flights were determined photogrammetrically. Natural features on the glacier surface were sufficiently prominent and enduring to be followed from the date of one flight to the next. Because both the altitude points and displacement vectors were irregularly positioned spatially, interpolation was necessary to get values on the grid nodes. The points had already been subjected to the method of optimum interpolation to get surface altitudes on the grid nodes. The displacement vectors are subjected here to a constrained–interpolation method to get velocity vectors at the grid nodes that are consistent, through the continuity equation, with the other variables. The other variables needed to achieve closure of the variable set are bed topography and mass-balance distribution. The latter was taken to be a separate linear function of altitude for each time interval. Values for bed altitudes at 120 nodes and two coefficients of each 21 balance functions were inferred as the 162 model parameters in a non-linear minimization problem having 4305 observed velocity components as its data.

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