scholarly journals Solving the problem of overdetermination of quasisymmetric equilibrium solutions by near-axis expansions. I. Generalized force balance

2021 ◽  
Vol 28 (1) ◽  
pp. 012508 ◽  
Author(s):  
E. Rodríguez ◽  
A. Bhattacharjee
Keyword(s):  
Force Balance ◽  
Equilibrium Solutions ◽  
Generalized Force

NUMERICAL AND STABILITY ANALYSIS OF THE TRANSMISSION DYNAMICS OF SVIR EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE

2019 ◽  
Vol 4 (2) ◽  
pp. 349 ◽  
Author(s):  
Oluwatayo Michael Ogunmiloro ◽  
Fatima Ohunene Abedo ◽  
Hammed Kareem
Keyword(s):  
Reproduction Number ◽  
Disease Spread ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Transform Method ◽  
Globally Asymptotically Stable ◽  
Differential Transform ◽  
Mathematical Techniques ◽  
Fourth Order Method ◽  
Theoretical Results

In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results. 

scholarly journals Decision and Coordination in a Dual-Channel Three-Layered Green Supply Chain

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 549 ◽  
Author(s):  
Zilong Song ◽  
Shiwei He ◽  
Baifeng An
Keyword(s):  
Sustainable Development ◽  
Supply Chain ◽  
Environmental Performance ◽  
Fresh Produce ◽  
Green Supply Chain ◽  
Market Demand ◽  
Equilibrium Solutions ◽  
Sustainable Performance ◽  
Dual Channel ◽  
Social And Environmental Performance

This paper investigated, for the first time, the game and coordination of a dual-channel, three-layered, green fresh produce supply chain, with regard to its economic, social, and environmental performance. Considering that the market demand is dual-channel priced and sensitive to the degree of greenness and the freshness-level, four game models, under different scenarios have been established. These included a centralized scenario, a decentralized scenario, and two contractual scenarios. The equilibrium solutions under the four scenarios were characterized. From the perspective of a sustainable development, the economic, social, and environmental performance of the supply chain was analyzed. To enhance the supply chain performance, two contract mechanisms were designed and the conditions for a multi-win outcome were obtained. Accordingly, many propositions and management implications were provided. The results showed that, (1) compared to the centralized supply chain case, the performance of the decentralized supply chain case is inferior; (2) in addition to increasing the concentration of the supply chain decisions, the two contracts proposed can effectively coordinate the green supply chain and improve its sustainable performance; and (3) the performance of the supply chain is positively driven by the consumers’ sensitivity to greenness degree and the freshness level of fresh produce. This paper fills a research gap and helps the participants of the channel recognize the operational decision principle of a complex green supply chain, in order to achieve a higher and a long-term sustainable-development performance.

A New Generation of Tools for the Design of Tall Buildings Subjected to Wind Loads

2008 ◽  
Author(s):  
Emil Simiu ◽  
Rene D. Gabbai
Keyword(s):  
Structural Engineering ◽  
Tall Buildings ◽  
Building Envelope ◽  
Force Balance ◽  
Wind Loads ◽  
Individual Member ◽  
Engineering Practice ◽  
Wind Effects ◽  
Uncertainty Estimates ◽  
Internal Forces

Current approaches to the estimation of wind-induced wind effects on tall buildings are based largely on 1970s and 1980s technology, and were shown to result in some cases in errors of up to 40%. Improvements are needed in: (i) the description of direction-dependent aerodynamics; (ii) the description of the direction-dependent extreme wind climate; (iii) the estimation of inertial wind effects induced by fluctuating aerodynamic forces acting on the entire building envelope; (iv) the estimation of uncertainties inherent in the wind effects; and (v) the use of applied wind forces, calculated inertial forces, and uncertainty estimates, to obtain via influence coefficients accurate and risk-consistent estimates of wind-induced internal forces or demand-to-capacity ratios for any individual structural member. Methods used in current wind engineering practice are especially deficient when the distribution of the wind loads over the building surface and their effects at levels other than the building base are not known, as is the case when measurements are obtained by the High-Frequency Force Balance method, particularly in the presence of aerodynamic interference effects due to neighboring buildings. The paper describes a procedure that makes it possible to estimate wind-induced internal forces and demand-to-capacity ratios in any individual member by: developing aerodynamic and wind climatological data sets, as well as aerodynamic/climatological directional interaction models; significantly improving the quality of the design via rigorous structural engineering methods made possible by modern computational resources; and properly accounting for knowledge uncertainties. The paper covers estimates of wind effects required for allowable stress design, wherein knowledge uncertainties pertaining to the parameters that determine the wind loading are not considered, as well as estimates required for strength design, in which these uncertainties need to be accounted for explicitly.

scholarly journals Location-Specific Adjustments in Population and Employment across Metropolitan America

Urban Science ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 24
Author(s):  
Gordon F. Mulligan ◽  
John I. Carruthers
Keyword(s):  
Labor Markets ◽  
Metropolitan Areas ◽  
Adjustment Process ◽  
Equilibrium Solutions ◽  
Natural Amenities ◽  
Long Run ◽  
Local Sustainability ◽  
Universal Solution ◽  
Standard Linear ◽  
Local Solutions

This paper examines the joint adjustment of population and employment numbers across America’s metropolitan areas during the period 1990–2015. Current levels of both are estimated, for 10 year periods, using their lagged (own and cross) levels and eight other lagged variables. Population is affected by both human and natural amenities and employment by wages, patents, and other attributes of the workforce. This paper questions the conventional interpretation of the adjustment process by using geographically weighted regression (GWR) instead of standard linear (OLS, 2GLS) regression. Here the various estimates are all local, so the long-run equilibrium solutions for the adjustment process vary over space. Convergence no longer indicates a stable universal solution but instead involves a mix of stable and unstable local solutions. Local sustainability becomes an issue when making projections because employment can quickly lead or lag population in some metropolitan labor markets.

scholarly journals Stationary Non-equilibrium Solutions for Coagulation Systems

2021 ◽  
Vol 240 (2) ◽  
pp. 809-875
Author(s):  
Marina A. Ferreira ◽  
Jani Lukkarinen ◽  
Alessia Nota ◽  
Juan J. L. Velázquez
Keyword(s):  
Power Law ◽  
Source Term ◽  
Continuous Model ◽  
Stationary Solutions ◽  
Weight Functions ◽  
Equilibrium Solutions ◽  
Coagulation Rate ◽  
Diffusion Limited Aggregation ◽  
Coagulation Equations ◽  
Non Equilibrium

AbstractWe study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of coagulation rate kernels, with the main restriction being boundedness from above and below by certain weight functions. The weight functions depend on two power law parameters, and the assumptions cover, in particular, the commonly used free molecular and diffusion limited aggregation coagulation kernels. Our main result shows that the two weight function parameters already determine whether there exists a stationary solution under the presence of a source term. In particular, we find that the diffusive kernel allows for the existence of stationary solutions while there cannot be any such solutions for the free molecular kernel. The argument to prove the non-existence of solutions relies on a novel power law lower bound, valid in the appropriate parameter regime, for the decay of stationary solutions with a constant flux. We obtain optimal lower and upper estimates of the solutions for large cluster sizes, and prove that the solutions of the discrete model behave asymptotically as solutions of the continuous model.

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