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    Potential Scenario
    148

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    45

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    1999-Leonid_Hanin-Which tank empties first
    Suppose that water towers like those shown in the opening are initially filled with water and have the same volume, height, and cross-sectional outlet area. Which one empties first?
    tankTorricelli's Lawspherical tankemptyfrustrum of conecylinder
    Modeling Scenario
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    1-029-ConeToCubeFlow-ModelingScenario
    An inverted right circular cone with a hole at the bottom is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we model water flow from cone to cube and out the bottom of the...
    waterflowTorricelli's Lawconecube
    Modeling Scenario
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    283

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    1-055-WaterFallingInCone-ModelingScenario
    We offer an opportunity to model the height of a falling body of water in a right circular cone (funnel) and to estimate an appropriate parameter based on data collected from a video of the experiment found on YouTube.
    Torricelli's Lawdischarge coefficientconecontraction coefficient
    Modeling Scenario
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    1-140-LeakyBucket-ModelingScenario
    We seek to model the height of water in a cylindrical tank (bucket) in which water flows out the bottom of the tank through a small bore hole while we are pouring water into the tank at the top of the tank at a constant (or varying) rate.
    flowTorricelli's Lawleaky bucket
    Potential Scenario
    142

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    43

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    2008-Chernyshov-EtAl-The Problem of Modelling of Economic Dynamics in Differential Form
    The authors have tried to analyze procedures of the construction of differential equations that are employed for modeling of macroeconomic processes. The results prove to be rather unexpected.
    Fredholm integral equation ofLeontief’s modelmacroeconomic processes
    Potential Scenario
    154

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    62

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    2007-Mogen_Steffensen-Differential Equations in Finance and Life Insurance
    The mathematics of finance and the mathematics of life insurance were always intersecting. Life insurance contracts specify an exchange of streams of payments between the insurance company and the contract holder.
    financedisabilitylife insurancemortalityinsuraneThiele’s equationBlack-Scholes equation
    Potential Scenario
    211

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    26

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    2014-John_Cain-Chemical Reaction Kinetics Mathematical Underpinnings
    The usual way of deriving kinetic equations involves application of the principle of conservation of mass in conjunction with the law of mass action. Here, examples of kinetic models for several basic processes are discussed.
    kineticsbiochemical reactionreactantsproducts
    Potential Scenario
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    2016-Erno_Keszei-Chemical Kinetics for Beginners
    The most important goal of kinetic research is the identification and characterisation of elementary molecular events which make possible the transformation of reactants into products.
    kineticszeroth order reactionfirst order reactionsecond order reactionreaction ratesthird order reaction
    Article or Presentation
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    2011-Carl_Leinbach-Beyond_Newton_law_of_cooling_estimation_of_time_since_death
    The estimate of the time since death. Thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner’s cases, especially those that involve criminal or insurance...
    Newton's Law of Coolingtime of deathdouble exponentialcoroner
    Potential Scenario
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    60

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    1989-EY_Rodin-K_Egan-Mathematics modelling of the rate of chemical reactions
    The development of improved designs for chemical reactors as well as the prediction of optimal operating conditions in chemical production are based on an understanding of the rates at which chemical processes occur.
    kineticsfirst orderreactionsecond orderzeroth order
    Potential Scenario
    191

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    43

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    2000-Dwayne-Anderson-Estimates of the future membership of the Church of Jesus Christ of Latter-Day Saints
    Thus, the purpose of this paper is to model the membership of the Church of the Latter Day Saints from the available data on membership from 1844 to 2000.
    population dynamicslogisticLatter-Day Saints
    Article or Presentation
    174

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    40

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    2008-Keith_Landry-Brian_Winkel-Peak_Frequency_Responses_and_Tuned_Mass_Dampers
    We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and (1) peak frequency responses with stabilization of the structure by means of a (2) Tuned Mass Damper (TMD).
    vibrationresonancetuned mass damperpeak frequency responseexcitation
    Article or Presentation
    158

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    66

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    1981-Nielsen_Francois-Rachel_Rosenfeld-Substantive_Interpretations_of_Differential_Equation_Models
    The interpretation of parameters of dynamic models is illustrated with reference to research on two substantive topics: political mobilization and intragenerational mobility.
    differential equationsdynamical systemsFirst order linearintragenerational mobilitypolitical mobilizationmobility
    Potential Scenario
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    40

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    2012-José_Sérgio_Domingues-Gompertz Model - Resolution and Analysis for Tumors
    The main objective of this paper is to use the Gompertz equation in order to study the development of blood irrigated solid tumors, using parameters defined in some important bibliographic references about the mathematical modelling of tumors.
    tumorGompertz equationgrowth tumor
    Potential Scenario
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    2000-Erdman-Morelock-A Study of Kinetics The Estimation and Simulation of Systems of First-Order Differential Equations
    This paper introduces new and old features of the SAS System for the estimation and simulation of systems of first-order differential equations with emphasis on examples in kinetics.
    kineticsSAScompartmentpharmacokinetics
    Potential Scenario
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    96

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    2001-Smith-Moore-The SIR Model for Spread of Disease
    A multiple part tour of SIR Models freely available with Maple, Mathematics, and MatLab support files at MAA site.
    epidemicSIR modelEuler's methodherd immunityHong Kong flu
    Potential Scenario
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    1988-Michael Intriligator-Dagobert Brito-A Predator-Prey Model of Guerrilla Warfare
    The authors present a three variable: numbers of guerrillas, numbers of regular (government) soldiers, and size of population controlled by the guerrillas, at time t), nonlinear system of three differential equations.
    combat modelguerrilla warfaregovernment
    Modeling Scenario
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    1-051-OneTankSaltModel-ModelingScenario
    A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon. The incoming water is mixed in with the contents of the tank...
    compartmentsalttankmixingflow
    Modeling Scenario
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    1-064-TorricelliBox-ModelingScenario
    The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.
    groundwater flowcolumn of waterTorricelli's Lawwater displacementsubmerged box
    Article or Presentation
    140

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    50

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    2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne
    This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
    resistanceprojectile motionprojectilefluidMersenne