Designing a laser-cut panel for light collection for daylighting using a generalised mathematical model

2020 ◽  
pp. 147715352093262
Author(s):  
S Singh ◽  
DS Bisht ◽  
H Garg
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Flat Plate ◽  
Light Output ◽  
The Other ◽  
Light Collection ◽  
Light Pipe ◽  
Current Design ◽  
Complex Mechanisms ◽  
Flat Plate Collector

The current daylighting requirements require a system that can maintain a uniform light output throughout the day while enabling deep and controlled penetration of sunlight. If such a system is simple to manufacture, inexpensive and incorporates no moving parts and maintenance, it can easily fulfil all the daylighting needs. This paper focuses on the development of such a system using laser-cut panels. Mathematical models for determining the dimensions of a laser-cut panel and its efficiency were developed. A laser-cut panel collector was designed based on these models and simulated. The results showed enhanced light output at light pipe end by up to 47 times and 32 times as compared to a flat plate collector in the month of June and December, respectively and up to nine times for a dome collector for the designed range of sun altitudes. For this range, the ratio of pipe output to input was up to 4.5 times higher than the other collectors. The light at diffuser side was more distributed for the laser-cut panel collector. The current design, however, did not provide appropriate reduction in illuminance at peak hours in June. This approach can easily be used for light collection without involving any complex mechanisms.

The property market, property valuations and property performance measurement

1985 ◽  
Vol 112 (1) ◽  
pp. 19-60 ◽  
Author(s):  
David P. Hager ◽  
David J. Lord
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Performance Measurement ◽  
The Other ◽  
Property Market ◽  
Institutional Investment ◽  
Property Valuation ◽  
Valuation Method ◽  
Property Performance

1.1. The Institute has discussed papers on most aspects of institutional investment in recent years, with the notable exception of property. This is not due to the lack of importance of this investment sector to pension funds and life offices, but perhaps to the greater role of actuaries (rather than surveyors) in the other investment media and to the interest in mathematical models for gilts and equities.1.2. In this paper we have not tried to produce a mathematical model of the property market, a new valuation method for property or solutions to the extensive problems of property performance measurement and indices. We have, however, tried to pull together, in a single paper, the volumes of material on the property market and property valuation methods. We have also tried to set down some of the pitfalls of property performance measurement, which often tend to be overlooked in the relentless pursuit for more statistics in this important area.

Exploring Theories of Victimization Using a Mathematical Model of Burglary

2011 ◽  
Vol 48 (1) ◽  
pp. 83-109 ◽  
Author(s):  
Ashley B. Pitcher ◽  
Shane D. Johnson
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Qualitative Agreement ◽  
The Other ◽  
Residential Burglary ◽  
Foraging Activity ◽  
Good Qualitative Agreement ◽  
Agent Based ◽  
Stable Variation ◽  
Near Repeat

Research concerned with burglary indicates that it is clustered not only at places but also in time. Some homes are victimized repeatedly, and the risk to neighbors of victimized homes is temporarily elevated. The latter type of burglary is referred to as a near repeat. Two theories have been proposed to explain observed patterns. The boost hypothesis states that risk is elevated following an event reflecting offender foraging activity. The flag hypothesis, on the other hand, suggests that time-stable variation in risk provides an explanation where data for populations with different risks are analyzed in the aggregate. To examine this, the authors specify a series of discrete mathematical models of urban residential burglary and examine their outcomes using stochastic agent-based simulations. Results suggest that variation in risk alone cannot explain patterns of exact and near repeats, but that models which also include a boost component show good qualitative agreement with published findings.

scholarly journals Phenotypic Tolerance: Antibiotic Enrichment of Noninherited Resistance in Bacterial Populations

2005 ◽  
Vol 49 (4) ◽  
pp. 1483-1494 ◽  
Author(s):  
C. Wiuff ◽  
R. M. Zappala ◽  
R. R. Regoes ◽  
K. N. Garner ◽  
F. Baquero ◽  
...  
Keyword(s):  
Escherichia Coli ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Antibiotic Treatment ◽  
A Priori ◽  
The Other ◽  
Bacterial Populations ◽  
Microbiological Outcome

ABSTRACT When growing bacteria are exposed to bactericidal concentrations of antibiotics, the sensitivity of the bacteria to the antibiotic commonly decreases with time, and substantial fractions of the bacteria survive. Using Escherichia coli CAB1 and antibiotics of five different classes (ampicillin, ciprofloxacin, rifampin, streptomycin, and tetracycline), we examine the details of this phenomenon and, with the aid of mathematical models, develop and explore the properties and predictions of three hypotheses that can account for this phenomenon: (i) antibiotic decay, (ii) inherited resistance, and (iii) phenotypic tolerance. Our experiments cause us to reject the first two hypotheses and provide evidence that this phenomenon can be accounted for by the antibiotic-mediated enrichment of subpopulations physiologically tolerant to but genetically susceptible to these antibiotics, phenotypic tolerance. We demonstrate that tolerant subpopulations generated by exposure to one concentration of an antibiotic are also tolerant to higher concentrations of the same antibiotic and can be tolerant to antibiotics of the other four types. Using a mathematical model, we explore the effects of phenotypic tolerance to the microbiological outcome of antibiotic treatment and demonstrate, a priori, that it can have a profound effect on the rate of clearance of the bacteria and under some conditions can prevent clearance that would be achieved in the absence of tolerance.

scholarly journals Improved Mathematical Model of Polluted Insulators nonlinear behaviour Under AC Voltage Based on Experimental Tests

2018 ◽  
Author(s):  
MousalrezaFaramarzi Palangar ◽  
Mohammad Mirzaie
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Experimental Tests ◽  
The Other ◽  
Critical Voltage ◽  
Nonlinear Behaviour ◽  
New Model ◽  
The Relationship ◽  
Good Agreement

Abstract—In this paper, an improved mathematical model for flashover behavior of polluted insulators is proposed based on experimental tests. In order to determine the flashover model of polluted insulators, the relationship between conductivity and salinity of solution pollution layer of the insulator is measured. Then, the leakage of current amplitude of four common insulators versus axial, thermal conductivity and arc constants temperature was determined. The experimental tests show that top leakage distance (TLd) to bottom leakage distance (BLd) ratio of insulators has a significant effect on critical voltage and current. Therefore, critical voltage and current were modeled by TLd to BLd ratio Index (M). Also, salinity of solution pollution layer of the insulators has been applied to this model by resistance pollution parameter. On the other hand, arc constants of each insulator in new model have been identified based on experimental results. Finally, a mathematical model is intended for critical voltage against salinity of solution pollution layer of different insulators. This model depends on insulator profile. There is a good agreement between the experimental tests of pollution insulators obtained in the laboratory and values calculated from the mathematical models developed in the present study.

scholarly journals Improved Mathematical Model of Polluted Insulators nonlinear behaviour Under AC Voltage Based on Experimental Tests

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
MousalrezaFaramarzi Palangar ◽  
Mohammad Mirzaie
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Experimental Tests ◽  
The Other ◽  
Critical Voltage ◽  
Nonlinear Behaviour ◽  
New Model ◽  
The Relationship ◽  
Good Agreement

In this paper, an improved mathematical model for flashover behavior of polluted insulators is proposed based on experimental tests. In order to determine the flashover model of polluted insulators, the relationship between conductivity and salinity of solution pollution layer of the insulator is measured. Then, the leakage of current amplitude of four common insulators versus axial, thermal conductivity and arc constants temperature was determined. The experimental tests show that top leakage distance (TLd) to bottom leakage distance (BLd) ratio of insulators has a significant effect on critical voltage and current. Therefore, critical voltage and current were modeled by TLd to BLd ratio Index (M). Also, salinity of solution pollution layer of the insulators has been applied to this model by resistance pollution parameter. On the other hand, arc constants of each insulator in new model have been identified based on experimental results. Finally, a mathematical model is intended for critical voltage against salinity of solution pollution layer of different insulators. This model depends on insulator profile. There is a good agreement between the experimental tests of pollution insulators obtained in the laboratory and values calculated from the mathematical models developed in the present study.

scholarly journals A Mathematical Model of Universal Basic Income and Its Numerical Simulations

Algorithms ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 331
Author(s):  
Maria Letizia Bertotti
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Real World ◽  
Poverty Alleviation ◽  
The Other ◽  
Nonlinear Ordinary Differential Equations ◽  
Basic Income ◽  
Market Society ◽  
Number Of Individuals

In this paper, an elementary mathematical model describing the introduction of a universal basic income in a closed market society is constructed. The model is formulated in terms of a system of nonlinear ordinary differential equations, each of which gives account of how the number of individuals in a certain income class changes in time. Societies ruled by different fiscal systems (with no taxes, with taxation and redistribution, with a welfare system) are considered and the effect of the presence of a basic income in the various cases is analysed by means of numerical simulations. The main findings are that basic income effectively acts as a tool of poverty alleviation: indeed, in its presence the portion of individuals in the poorest classes and economic inequality diminish. Of course, the issue of a universal basic income in the real world is more complex and involves a variety of aspects. The goal here is simply to show how mathematical models can help in forecasting scenarios resulting from one or the other policy.

scholarly journals Mathematical Modeling to Perform an Analysis of Social Isolation Periods in the Dissemination of COVID-19

2021 ◽  
Vol 22 (4) ◽  
pp. 595-608
Author(s):  
A. Molter ◽  
R. S. Quadros ◽  
M. Rafikov ◽  
D. Buske ◽  
G. A. Gonçalves
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Social Isolation ◽  
Computer Simulations ◽  
The Other ◽  
Stable Level ◽  
The Social ◽  
The World ◽  
Second Peak

The outbreak of COVID-19 has made scientists from all over the world do not measureefforts to understand the dynamics of the disease caused by this coronavirus. Several mathematical models have been proposed to describe the dynamics and make predictions. This work proposes a mathematical model that includes social isolation of susceptible individuals as a strategy of suppression and mitigation of the disease. The Susceptible-Infectious-Isolated-Recovered-Dead (SIQRD) model is proposed to analyze three important issues about the dynamics of the disease taking into account social isolation: when the isolation should begin? How long to keep the isolation? How to get out of this isolation? To get answers, computer simulations are provided and their results discussed. The results obtained show that beginning social isolation on the 10th or 15th days, after confirmation of the 50th case, and with 70% of the population in isolation, seems to be promising, since the infected curve does not grow much until it enters the isolation and remains at a stable level during the isolation. On the other hand an abrupt release of the social isolation will imply a second peak of infected individuals above the first one, which is not desired. Therefore, the release from social isolation should be gradual.

scholarly journals Nanofluids for Solar Thermal Collection and Energy Conversion

2020 ◽  
Author(s):  
Mohammed Abdullah Hussain ◽  
Sumith Yesudasan ◽  
Sibi Chacko
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Solar Energy ◽  
Flat Plate ◽  
Volume Concentration ◽  
Particle Diameter ◽  
Fluid Medium ◽  
Efficiency Increase ◽  
Flat Plate Collector ◽  
Optimum Volume

This paper investigates the improvement in solar energy collection and conversion using Al2O3-Water nanofluids in a solar flat plate collector (SFPC). The efficiency of a solar flat plate collector using water as the fluid medium is analyzed experimentally and theoretically. For theoretical analysis, a mathematical model in MATLAB is used to simulate and is validated by the experimental results. To enhance the solar energy collection and conversion efficiency of the SFPC, Al2O3-Water nanofluid was selected as the fluid medium. The nanofluid properties like density, specific heat capacity, thermal conductivity and viscosity are analyzed and compared for several models of Al2O3-Water nanofluids and the best model was selected to modify the simulation. Effect of particle diameter in the nanofluid was found to be marginal on the nanofluid properties. The optimum volume concentration of the nanofluid was found to be 4% giving an efficiency increase of 7.78% in the SFPC over the use of water. This reduces the area of the SFPC by 10.5%.

Analysis of Selective Absorber Coatings on Thermal Performance of the Solar Flat-Plate Collector

2013 ◽  
Vol 690-693 ◽  
pp. 2093-2097
Author(s):  
Xiao Dong Han ◽  
Shi Wei Zhang ◽  
Chuan Chen ◽  
Yong Tang
Keyword(s):  
Flat Plate ◽  
Thermal Performance ◽  
Test System ◽  
Chromium Coating ◽  
Experimental Results ◽  
The Other ◽  
Thermal Loss ◽  
Anodic Coating ◽  
Relative Absorption ◽  
Flat Plate Collector

In this work, a solar flat-plate collector test system is developed. The solar flat-plate collectors with anodic coating, chromium coating and blue core coating are tested. The experimental results indicate that the relative absorption ration α/ε of blue core coating is up to 19. The efficiency of collector with blue core coating is 78.66%, which is 5% higher than collectors with the other two types of coatings. In addition, collector with blue core coating has smaller total thermal loss coefficient. The blue core coating can effectively improve the performance of solar flat-plate collectors.

Validation: What, Why and How

2016 ◽  
Author(s):  
Luís Eça ◽  
Guilherme Vaz ◽  
Arjen Koop ◽  
Filipe Pereira ◽  
Hugo Abreu
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Flat Plate ◽  
Parameter Uncertainty ◽  
Physical Reality ◽  
Physical Models ◽  
The Mathematical Model ◽  
Modelling Error ◽  
Quantities Of Interest

Offshore and Naval engineering have relied on physical models, i.e. experimental fluid dynamics (EFD), for several decades. Although the role of experiments in engineering is still unquestionable, some of the limitations of physical models, as for example domain size (blockage and scale effects), can be addressed using mathematical models, i.e. computational fluid dynamics (CFD). However, to gain confidence in the use of CFD it is fundamental to determine the modelling accuracy, i.e. to determine the difference between the “physical reality” and the selected mathematical model. The quantification of the modelling error is the goal of Validation. It must be emphasized that Validation applies to the mathematical model (and not the code) and is performed for selected flow quantities (the so-called quantities of interest). Ideally, Validation would be performed comparing an exact measurement of the “physical reality” with the exact solution of the selected mathematical model. However, exact measurements do not exist and mathematical models for turbulent flows do not have analytical solutions. Therefore, procedures must be developed to take into account experimental and numerical uncertainties. Furthermore, the exact values of the flow parameters as for example Reynolds number, fluid viscosity or inlet turbulence quantities are often unknown, which leads to the so-called parameter uncertainty that also has to be dealt within the assessment of the modelling error. The main goal of this paper is to demonstrate that the very popular designation of “code X is validated” is meaningless without saying what is the mathematical model embedded in the code, what are the quantities of interest for the specific application and what is the Validation uncertainty imposed by the experimental, numerical and parameter uncertainties. Furthermore, we also illustrate that Validation is not a pass or fail exercise. A modelling error of 10% may be acceptable for a given application, whereas 1% may not be enough for a different one. To this end, we present the application of the ASME V&V 20 Validation procedure for local set points and the metric for multiple set points to several practical test cases: prediction of transition from laminar to turbulent regime for the flow over a flat plate; flow around a circular cylinder; flow around the KVLCC2 tanker and current loads in shallow water for a LNG carrier. In most of these exercises, parameter uncertainty is assumed to be zero, which is an assumption often required for the so-called practical calculations due to the computational effort required to address it. Nonetheless, as an illustration of its application, the flow over the flat plate includes parameter uncertainty for the specification of the inlet turbulence quantities.

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