Demonstrations to run with Mathematica® or Wolfram CDF Player®

This page contains links to 154 free demonstrations downloadable from the Wolfram Demonstrations Project web site. Demonstrations contain active controls and run in Mathematica or right in your web browser after installation of the free Wolfram CDF Player application. For more information on Mathematica visit the Wolfram Research web site at:

For more information on the models see: Peleg, M. 2006. Advanced quantitative microbiology for food and biosystems: Models for predicting growth and inactivation. CRC Press, Boca Raton FL. (Click to download a 452K PDF file containing contents description.)

Heat Transfer

Estimating the Thermal Properties of Foods from their Moisture Contents
Heat Transfer in a Heat Exchanger
Logarithmic Mean Temperature of a Heat Exchanger
Steady State Heat Transfer Through an Insulated Wall
Stefan-Boltzmann Law

Kinetics: Microbial, Chemical and Biochemical

Dynamic Germination of Seeds and Microbial Spores
Extending the Square Root Growth Rate Model to Lethal Low Temperatures
Generalized Logistic (Verhulst) Isothermal Microbial Growth on Linear and Logarithmic Coordinates
Growth Curves for a Mixture of Two Subpopulations
Isothermal Germination of Seeds and Microbial Spores
Lag Time in Microbial Growth
Modified Logistic Isothermal Microbial Growth Ratio (Linear and Logarithmic) vs. Time
Ratio-Based Modified Logistic Isothermal Microbial Growth on Linear and Logarithmic Coordinates
Ratkowski's Square Root Growth Rate Model for High Temperatures
Square Root Model for Rates of Microbial Growth or Inactivation
Uncertainties in Isothermal Microbial Growth

Microbial Inactivation and Chemical Degradation
Degradation Parameters from Concentration Ratios
Degrees of Microbial Injury and Survival
Determining Shelf Life by Two Criteria
Endpoints Method for Predicting Chemical Degradation in Frozen Foods
Equivalent Isothermal Time at a Reference Temperature as a Function of Time
Extracting Fixed-Order Degradation Kinetics by the Endpoints Method
Extracting Microbial Inactivation Parameters from Final Isothermal Survival Ratios
Extracting Microbial Inactivation Parameters from Final Survival Ratios
Fit of First-Order Kinetic Model in Degradation Processes
Growth Inhibition and Retardation by Antimicrobials
Idealized Conventional and Pressure-Assisted Thermal Preservation Processes
Injury in Microbial Inactivation
Kinetic Order of Degradation Reactions
Log Survival Ratio as a Function of Time
Microbial Survival Curves with Asymptotic Residual[NEW icon]
Microbial Survival Curves with Definite Thermal Death Time[NEW icon]
Microbial Survival with Dissipating Disinfectant
Nonisothermal Degradation Kinetics
Prediction of Isothermal Degradation by the Endpoints Method
Primary and Secondary Shelf Life
Probabilistic Model for Microbial Mortality
Probabilistic Model Showing Sigmoid Semilogarithmic Survival
Rate Constant Calculation from Four Temperature and Moisture Combinations
Reaction Rate Dependence on Temperature and Moisture During Storage
Sigmoid Microbial Survival Curves
Simulating Ascorbic Acid Degradation
Simulating Temperature versus Time Relationships in the Thermal Preservation of Foods
Stochastic Model of Microbial Injury and Mortality
Stochastic Model of Seed and Spore Germination
Successive Three Point Method for Weibullian Chemical Degradation
Survival Curves of Bacilli Spores with an Activation Shoulder
Thermal Degradation of Three Nutrients in Foods
Three-Endpoints Method for Isothermal Weibullian Chemical Degradation
Uncertainties in Isothermal Microbial Inactivation
Vitamin C Loss in Foods During Heat Processing and Storage
Volatiles Formation Kinetics in Stored Fish
Weibullian Chemical Degradation
Weibullian Inactivation Rate as a Function of Temperature
Weibullian Inactivation Rate as a Function of Time
Weibullian versus Log-Linear Microbial Survival Models

Mixed Kinetics
Biphasic Exponential Decay And Growth
De Novo Growth Processes With Competing Mechanisms
Effects of Temperature Fluctuations on Oscillating Biological Systems
Food Preservation Hurdle Technology
Incipient Growth Processes With Competing Mechanisms
Microbial Population Growth, Mortality and Transitions Between Them
Synergism and Antagonism

Mass Balance, Heat Balance, Pressure Balance and Flow

Compressive Stress-Strain Relationships of Layered Solid Foams
Dehydration by a Desiccant
Dynamic Water Absorption by Foods
Equivalent Length of a Pipe with Fittings and Valves
Estimating Processing Times in a Row of Storage Tanks
Flow Curves of a Herschel-Bulkley Fluid
Flow from a Tank at Constant Height
Food Calories
Force to Overcome Vacuum Pull
Frictional Pressure Drop in a Pipe
Heat Balance in Freezing and Thawing Food
Kjeldahl Method for Determining Percent Protein from Percent Nitrogen
Lubricated and Frictional Squeezing Flow
Mass Balance in a Single Stage Evaporator
Mass Balance of Binary Mixtures
Milk Centrifugation To Cream and Skim
Operation of an Ideal Belt Conveyor
Refrigeration Cycle Coefficient of Performance
Three Component Food Mixtures
Titration of Common Food Acids

Mathematical Functions and Miscellaneous

2D and 3D Packard-Takens Autocorrelation Plots of Sinusoidal Functions
A Contact Element in Rheological Models
A Sliding Element in Rheological Models
Arrhenius Equations for Reaction Rate and Viscosity
Arrhenius versus Exponential Model for Chemical Reactions
Arrhenius Versus Eyring-Polanyi Model
Beta Distributions for a Given Mean, Median or Mode [NEW icon]
Bimodal Normal Distribution Mixtures
Brix Corrections for Citric Acid and Temperature
Central Limit Theorem Applied to Samples of Different Sizes and Ranges
Characteristic Times in Accumulation and Decay
Choosing Initial Parameter Values for Nonlinear Regression
Comparing Measures of Line Jaggedness
Comparison of Six Sigmoid Growth Curve Models
Creep and Stress Relaxation for Four Element Viscoelastic Solids and Liquids
Distribution of the Means of Samples Having Random Sizes
Effect of Outliers on Fit of Growth Models
Ehrenfest's Double-Urn Game
Expanded Magnitude Estimation Method
Exponential Model For Arrhenius Activation Energy
Eyring-Polanyi versus Exponential Model for Chemical Reactions
Five Definitions of Strain for Large Deformations
Food Color Comparisons
Fourier Power Spectrum as a Measure of Line Jaggedness
Fracture Element in Rheological Models
Gordon-Taylor and Fox Equations for Glass Transition Temperature
Hysteresis in the Flow Curves of Pseudoplastic Semiliquid Foods
Laplace Distribution in Fluctuating Stock Index Records
Line Jaggedness Visualization with the Mandelbrot-Weierstrass Function
Mechanical Sensitivity of Soft Testing Machines
Monte Carlo Estimation of Area
Noise Retrieval from Averaged Sequences
Parameterizing Temperature-Viscosity Relations
Probability of Being Strange According to Paulos
Relaxation of a Discrete Maxwell Model
Relaxation of a Maxwell Element
Simulated Jagged Force-Displacement Curves
Three Element Viscoelastic Models
Viscosity in Glass Transitions [NEW icon]
Williams, Landel, and Ferry Equation Compared with Actual and "Universal" Constants


Bimodal Size Distributions in Grinding and Attrition
Comparison of Food Moisture Sorption Isotherm Equations
Container Filled with Particulates
Equilibrium Water Activity of Binary Dry Mixtures
Erosion Index For Particulates
Estimating Cohesion and Tensile Strength of Compacted Powders
Estimating Equilibrium Moisture Content [NEW icon]
Isotherms For Expedited Moisture Sorption [NEW icon]
Principal Stresses in Compacted Cohesive Powders
Structure of Dilute Suspensions
Surface Area Increase by Size Reduction
The Ratio of Surface Area to Volume for a Cube and a Sphere
Volume and Mass of a Spoonful of Powder
Wet and Dry Basis Moisture Content

Risk Assessment

A Probabilistic Model for Population Extinction
Additive and Multiplicative Risks
Assessing the Risk of Food Poisoning
Assessing Total Risk from Interacting Factors
Effect of Immunity and Susceptibility on Sickness or Mortality Risk
Estimation of Time to Excessive Microbial Count
Estimating the Time between Mishaps from Quality Control Data
Expanded Fermi Solution for Estimating a Complaint's Probability
Expanded Fermi Solution for Risk Assessment
Expanded Fermi Solutions in Pathogens' Dose-Response Curves
Expanded Fermi Solution to Retrodict the Initial from the Final Number in a Stochastic Process
Failure Probabilities from Quality Control Charts
Hidden Periodicity in Quality Control Records
Pathogen Dose-Response Curves with the Beta Poisson and Lognormal Models
Risk Guesstimation from Factor Ranges
Simulating Microbial Count Records with an Expanded Fermi Solution Model
Ticketing Options

[Return to ] Prof. Micha Peleg

Links to ten additional Wolfram Demonstrations are available here --> [Return to ] Mark D. Normand

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Content last updated: December 10, 2021