scholarly journals Closed form solution of the SIR model for the COVID-19 outbreak in Italy

2020 ◽  
Author(s):  
Riccardo Giubilei
Keyword(s):  
Experimental Data ◽  
Closed Form ◽  
Closed Form Solution ◽  
Sir Model ◽  
Form Solution ◽  
Model Equations

AbstractThe CODIV-19 outbreak in early 2020 generated a tremendous effort of epidemiologists and researchers to fit the experimental data with the solutions of the SIR model equations [1] or with more sophisticated models. In this paper we show that under same hypotheses, a closed form solution exists that reasonably fits the experimental data for Italy, and the results can be extended to any other area.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

Fractional Calculus Model of the Semilunar Heart Valve Vibrations

2003 ◽  
Author(s):  
Moustafa El-Shahed
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Numerical Methods ◽  
Fractional Calculus ◽  
Closed Form ◽  
Heart Valve ◽  
Laplace Transformation ◽  
Closed Form Solution ◽  
Equation Of Motion ◽  
Form Solution

The objective of this paper is to solve the equation of motion of semilunar heart valve vibrations. The vibrations of the closed semilunar valves were modeled with a Caputo hactional derivative of order α. With the help of Laplace transformation, closed-form solution is obtained for the equation of motion in terms of Mittag-Leffler function. An alternative Method for Semi-differential equation, when α = 0.5, is examined using MATHEMATICA. The simplicity of these solutions makes them ideal for testing the accuracy of numerical methods. This solution can be of some interest for a better fit of experimental data.

scholarly journals The Missing Link: A Closed Form Solution to the Kermack and McKendrick Model Equations

2021 ◽  
Author(s):  
Theodore G Duclos ◽  
Thomas A Reichert
Keyword(s):  
Closed Form ◽  
Complete Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Policy Makers ◽  
Mobility Data ◽  
Forward Limit ◽  
Containment Measures ◽  
Model Equations ◽  
Analytical Tools

Susceptible infectious recovered (SIR) models are widely used for estimating the dynamics of epidemics. Such models project that containment measures flatten the curve, i.e., reduce but delay the peak in daily infections, cause a longer epidemic, and increase the death toll. These projections have entered common understanding; individuals and governments often advocate lifting containment measures such as social distancing to shift the peak forward, limit societal and economic disruption, and reduce mortality. It was, then, an extraordinary surprise to discover that COVID-19 pandemic data exhibit phenomenology opposite to the projections of SIR models. With the knowledge that the commonly used SIR equations only approximate the original equations developed to describe epidemics, we identified a closed form solution to the original epidemic equations. Unlike the commonly used approximations, the closed form solution replicates the observed phenomenology and quantitates pandemic dynamics with simple analytical tools for policy makers. The complete solution is validated using independently measured mobility data and accurately predicts COVID19 case numbers in multiple countries.

scholarly journals An Identification Method for Orifice-Type Restrictors Based on the Closed-Form Solution of Reynolds Equation

Lubricants ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 55
Author(s):  
Federico Colombo ◽  
Luigi Lentini ◽  
Terenziano Raparelli ◽  
Andrea Trivella ◽  
Vladimir Viktorov
Keyword(s):  
Experimental Data ◽  
Closed Form ◽  
Analytical Model ◽  
Hybrid Method ◽  
Reynolds Equation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Aerostatic Bearing ◽  
Discharge Coefficients ◽  
Aerostatic Bearings

Even though the behavior of aerostatic bearings has for long been the topic of extensive research, there are still many aspects that require further investigation. Among these, the identification of the discharge coefficients is one the most crucial. This paper presents a hybrid method to identify the discharge coefficients of aerostatic bearing orifices. The method is termed as hybrid since it exploits experimental data and the equations of the analytical model of a circular and centrally fed aerostatic pad. The obtained results demonstrate the accuracy of the method. The proposed method further offers practical advantages compared to the conventional methods.

A Dishing Model for STI CMP Process

2005 ◽  
Vol 867 ◽  
Author(s):  
Shih-Hsiang Chang
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Closed Form ◽  
Contact Mechanics ◽  
Closed Form Solution ◽  
Form Solution ◽  
Experimental Results ◽  
Quantitative Prediction ◽  
Comparison With Experimental Data

AbstractIt is well known that oxide dishing occurring in STI CMP leads to considerable sidewall and edge-parasitic conduction. Thus, a closed-form solution for quantitative prediction of oxide dishing is needed. A contact-mechanics-based approach to describe the steady-state oxide dishing occurring in STI CMP process is presented. The theory is validated through comparison with experimental data in the literature. Once validated, the model is used to quantify the effect of pattern geometry on oxide dishing. It is shown that the predictions of the model agree reasonably well with the experimental results measured in overpolishing time.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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