Finite, Dynamic Motions of Thin Rate-Dependent Sheets

1990 ◽  
Vol 57 (4) ◽  
pp. 821-827 ◽  
Author(s):  
J. A. Blume
Keyword(s):  
Transient Response ◽  
Power Law ◽  
Thin Sheet ◽  
Power Law Model ◽  
Axially Symmetric ◽  
Varying Thickness ◽  
Rate Dependent ◽  
Axially Symmetry ◽  
Constitutive Response

The transient response of a thin sheet comprised of a rate-dependent solid is determined. The material is assumed to be incompressible, and the constitutive response is governed by a nonlinearly viscous power-law model. The sheet has axially symmetry, but an otherwise arbitrarily varying thickness. Axially symmetric, finite, dynamic motions of the sheet are identified.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals Unsteady thermal Maxwell power law nanofluid flow subject to forced thermal Marangoni Convection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Jawad ◽  
Anwar Saeed ◽  
Taza Gul ◽  
Zahir Shah ◽  
Poom Kumam
Keyword(s):  
Relaxation Time ◽  
Power Law ◽  
Marangoni Convection ◽  
Power Law Model ◽  
Analysis Method ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Welan Gum ◽  
Homotopy Analysis ◽  
Power Law Nanofluid

AbstractIn the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered. The flow is also exposed to Joule heating and magnetic effects. The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model. For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations. This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM). It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time. It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid’s film.

scholarly journals X-ray Properties of 3C 111: Separation of Primary Nuclear Emission and Jet Continuum

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 219
Author(s):  
Elena Fedorova ◽  
B.I. Hnatyk ◽  
V.I. Zhdanov ◽  
A. Del Popolo
Keyword(s):  
Accretion Disk ◽  
Power Law ◽  
Line Emission ◽  
High Energy ◽  
Power Law Model ◽  
X Ray ◽  
Additional Information ◽  
Observational Dataset ◽  
Simple Power ◽  
Photon Index

3C111 is BLRG with signatures of both FSRQ and Sy1 in X-ray spectrum. The significant X-ray observational dataset was collected for it by INTEGRAL, XMM-Newton, SWIFT, Suzaku and others. The overall X-ray spectrum of 3C 111 shows signs of a peculiarity with the large value of the high-energy cut-off typical rather for RQ AGN, probably due to the jet contamination. Separating the jet counterpart in the X-ray spectrum of 3C 111 from the primary nuclear counterpart can answer the question is this nucleus truly peculiar or this is a fake “peculiarity” due to a significant jet contribution. In view of this question, our aim is to estimate separately the accretion disk/corona and non-thermal jet emission in the 3C 111 X-ray spectra within different observational periods. To separate the disk/corona and jet contributions in total continuum, we use the idea that radio and X-ray spectra of jet emission can be described by a simple power-law model with the same photon index. This additional information allows us to derive rather accurate values of these contributions. In order to test these results, we also consider relations between the nuclear continuum and the line emission.

Dynamics of Developing Laminar Non-Newtonian Falling Liquid Films With Free Surface

1978 ◽  
Vol 45 (1) ◽  
pp. 19-24 ◽  
Author(s):  
V. Narayanamurthy ◽  
P. K. Sarma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Mathematical Formulation ◽  
Liquid Films ◽  
Interfacial Shear ◽  
Newtonian Liquid ◽  
Power Law Model ◽  
Falling Liquid Film ◽  
Falling Liquid Films ◽  
Special Case

The dynamics of accelerating, laminar non-Newtonian falling liquid film is analytically solved taking into account the interfacial shear offered by the quiescent gas adjacent to the liquid film under adiabatic conditions of both the phases. The results indicate that the thickness of the liquid film for the assumed power law model of the shear deformation versus the shear stress is influenced by the index n, the modified form of (Fr/Re). The mathematical formulation of the present analysis enables to treat the problem as a general type from which the special case for Newtonian liquid films can be derived by equating the index in the power law to unity.

Validation of a Power Law Model in Upper Extremity Vessels: Potential Application in Ultrasound Bleed Detection

2012 ◽  
Vol 38 (4) ◽  
pp. 692-701 ◽  
Author(s):  
Aaron S. Wang ◽  
David H. Liang ◽  
Fritz Bech ◽  
Jason T. Lee ◽  
Christopher K. Zarins ◽  
...  
Keyword(s):  
Upper Extremity ◽  
Power Law ◽  
Potential Application ◽  
Power Law Model

Applicability of power law for describing the rheology of soils of different origins and characteristics

2009 ◽  
Vol 46 (9) ◽  
pp. 1011-1023 ◽  
Author(s):  
Sueng Won Jeong ◽  
Serge Leroueil ◽  
Jacques Locat
Keyword(s):  
Strain Rate ◽  
Power Law ◽  
Debris Flows ◽  
Rheological Behaviour ◽  
Strain Rate Range ◽  
Rate Dependent ◽  
Different Origins ◽  
Power Law Index ◽  
Soil Behaviour ◽  
Low Activity

The rate-dependent rheological behaviour of soils of different origins and characteristics was studied and the applicability of the power law model was examined. The studied soils were divided into three groups: (i) low-activity soils, (ii) high-activity soils, and (iii) silt-rich soils. The results show that the power law applies to all these soils and is representative of soil behaviour in a strain rate range corresponding to debris flows, which is generally not the case with the Bingham model. For low-activity clays, the power law index, n, is typically equal to 0.12 and seems to increase with the plasticity index; it is larger (i.e., in the range of 0.2–0.6) for silt-rich soils. Comparison of n values for tests performed on intact and remoulded low-activity clay specimens indicates that the power law index is possibly strain-rate dependent.

Risk transfer in project finance loans for toll road using credit default swaps

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wei Yang ◽  
Afshin Firouzi ◽  
Chun-Qing Li
Keyword(s):  
Power Law ◽  
Credit Default Swaps ◽  
Free Cash Flow ◽  
Project Finance ◽  
Cost Of Debt ◽  
Power Law Model ◽  
Data Set ◽  
Content Type ◽  
Toll Road ◽  
Credit Default

Purpose The purpose of this paper is to demonstrate the applicability of the Credit Default Swaps (CDS), as a financial instrument, for transferring of risk in project finance loans. Also, an equation has been derived for pricing of CDS spreads. Design/methodology/approach The debt service cover ratio (DSCR) is modeled as a Brownian Motion (BM) with a power-law model fitted to the mean and half-variance of the existing data set of DSCRs. The survival probability of DSCR is calculated during the operational phase of the project finance deal, using a closed-form analytical method, and the results are verified by Monte Carlo simulation (MCS). Findings It is found that using the power-law model yields higher CDS premiums. This in turn confirms the necessity of conducting rigorous statistical analysis in fitting the best performing model as uninformed reliance on constant time-invariant drift and diffusion model can erroneously result in smaller CDS spreads. A sensitivity analysis also shows that the results are very sensitive to the recovery rate and cost of debt values. Originality/value Insufficiency of free cash flow is a major risk in the toll road project finance and hence there is a need to develop innovative financial instruments for risk management. In this paper, a novel valuation method of CDS is proposed assuming that DSCR follows the BM stochastic process.

Optimal COVID-19 Vaccination Strategies with Limited Vaccine and Delivery Capabilities

2021 ◽  
Vol 2 (4) ◽  
pp. 1-16
Author(s):  
Simone Santini
Keyword(s):  
General Population ◽  
Power Law ◽  
Social Relations ◽  
Optimal Strategies ◽  
Power Law Model ◽  
Vulnerable Group ◽  
Vaccination Strategies ◽  
The Social ◽  
Short Time ◽  
Maximal Reduction

We develop a model of infection spread that takes into account the existence of a vulnerable group as well as the variability of the social relations of individuals. We develop a compartmentalized power-law model, with power-law connections between the vulnerable and the general population, considering these connections as well as the connections among the vulnerable as parameters that we vary in our tests. We use the model to study a number of vaccination strategies under two hypotheses: first, we assume a limited availability of vaccine but an infinite vaccination capacity, so all the available doses can be administered in a short time (negligible with respect to the evolution of the epidemic). Then, we assume a limited vaccination capacity, so the doses are administered in a time non-negligible with respect to the evolution of the epidemic. We develop optimal strategies for the various social parameters, where a strategy consists of (1) the fraction of vaccine that is administered to the vulnerable population and (2) the criterion that is used to administer it to the general population. In the case of a limited vaccination capacity, the fraction (1) is a function of time, and we study how to optimize it to obtain a maximal reduction in the number of fatalities.

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