scholarly journals Mathematical analysis of laboratory microbial experiments demonstrating deterministic chaotic dynamics

2021 ◽  
Author(s):  
Fred Molz ◽  
Boris Faybishenko
Keyword(s):  
Dilution Rate ◽  
Mathematical Analysis ◽  
Chaotic Dynamics ◽  
Minimum Energy ◽  
Living Systems ◽  
Microbial Populations ◽  
Classical Dynamics ◽  
Monod Kinetics ◽  
Model Simulations ◽  
Minimum Energy Dissipation

AbstractPresented is a system of four ordinary differential equations and a mathematical analysis of microbiological experiments in a four-component chemostat—nutrient n, rods r, cocci c, and predators p. The analysis is consistent with the conclusion that previous experiments produced features of deterministic chaotic and classical dynamics depending on dilution rate. The surrogate model incorporates as much experimental detail as possible, but necessarily contains unmeasured parameters. The objective is to understand better the differences between model simulations and experimental results in complex microbial populations. The key methodology for simulation of chaotic dynamics, consistent with the measured dilution rate and microbial volume averages, was to cause the preference of p for r vs. c to vary with the r and c concentrations, to make r more competitive for nutrient than c, and to recycle some dying p biomass, leading to a modified version of the Monod kinetics model. Our mathematical model demonstrated that the occurrence of chaotic dynamics requires a predator, p, preference for r versus c to increase significantly with increases in r and c populations. Also included is a discussion of several generalizations of the existing model and a possible involvement of the minimum energy dissipation principle. This principle appears fundamental to thermodynamic systems including living systems. Several new experiments are suggested.

On the Variational Principle and Lagrange Equations in Studies of Gasdynamic Lubrication

1964 ◽  
Vol 31 (1) ◽  
pp. 43-46 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Variational Formulation ◽  
Lagrangian Density ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Minimum Energy ◽  
Classical Dynamics ◽  
Lagrange Equations ◽  
Rayleigh Principle ◽  
Special Case ◽  
Minimum Energy Dissipation

The paper is concerned with the variational formulation in studies of gasdynamic lubrication. It is shown that Reynolds’ equation of lubrication is equivalent to a set of Lagrange equations similar to those in classical dynamics. The Lagrangian and the dissipation-production are defined. Furthermore, based on the Hamiltonian principle for the field of a continuum, the Lagrangian density and the dissipation-production density are established. This formulation includes the incompressible problem, which is obtainable from the Helmholtz-Rayleigh principle of minimum energy-dissipation, as a special case. Hence a unification of the variational methods for both gasdynamic and hydrodynamic lubrication is accomplished.

scholarly journals Which Is the Motion State of a Droplet on an Inclined Hydrophilic Rough Surface in Gravity: Pinned or Sliding?

2021 ◽  
Vol 11 (9) ◽  
pp. 3734
Author(s):  
Jian Dong ◽  
Youhai Guo ◽  
Long Jiao ◽  
Chao Si ◽  
Yinbo Bian ◽  
...  
Keyword(s):  
Rough Surface ◽  
Contact Angle Hysteresis ◽  
Minimum Energy ◽  
Contact Angles ◽  
Microfluidic Chips ◽  
Motion State ◽  
Receding Contact ◽  
Novel Design ◽  
Minimum Energy Dissipation ◽  
Good Agreement

The motion state of a droplet on an inclined, hydrophilic rough surface in gravity, pinned or sliding, is governed by the balance between the driving and the pinned forces. It can be judged by the droplet’s shape on the inclined hydrophilic rough surface and the droplet’s contact angle hysteresis. In this paper, we used the minimum energy theory, the minimum energy dissipation theory, and the nonlinear numerical optimization algorithm to establish Models 1–3 to calculate out the advancing/receding contact angles (θa/θr), the initial front/rear contact angles (θ1−0/θ2−0) and the dynamic front/rear contact angles (θ1−*/θ2−*) for a droplet on a rough surface. Also, we predicted the motion state of the droplet on an inclined hydrophilic rough surface in gravity by comparing θ1−0(θ2−0) and θ1−*(θ2−*) with θa(θr). Experiments were done to verify the predictions. They showed that the predictions were in good agreement with the experimental results. These models are promising as novel design approaches of hydrophilic functional rough surfaces, which are frequently applied to manipulate droplets in microfluidic chips.

Computational Evolution of Optimal Iceform Shapes Over a Flat Plate

1991 ◽  
Author(s):  
Ronald S. LaFleur
Keyword(s):  
Energy Dissipation ◽  
Flat Plate ◽  
Thermal Field ◽  
Fluid Dynamic ◽  
Minimum Energy ◽  
Thermal Parameter ◽  
Thermal Constraints ◽  
Ice Water ◽  
Nonlinear Geometric ◽  
Minimum Energy Dissipation

Abstract This paper presents the computational evolution of minimum energy dissipation iceform contours. The ice/water interface is shaped according to fluid dynamic and heat transfer characteristics of the flow field near the interface. A Couette iceform design model is used to approximate flow and thermal field behavior near the interface. The theory used to calculate the interface shape is based on a wedge model of the ice contour over a cold flat plate. The steady state ice profile is calculated when Reynolds number and the thermal parameter are selected. The generation function, designation function and energy dissipation are related to the nonlinear geometric development. An optimal preprocess criterion is prescribed as zero evolution length. The result is optimal geometries that are adapted to the flow and thermal constraints.

scholarly journals Entropy Density Acceleration and Minimum Dissipation Principle: Correlation with Heat and Matter Transfer in Glucose Catabolism

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 929 ◽  
Author(s):  
Roberto Zivieri ◽  
Nicola Pacini
Keyword(s):  
Stem Cells ◽  
Metabolic Pathway ◽  
Cell Biology ◽  
Minimum Energy ◽  
Time Derivative ◽  
Entropy Density ◽  
Living Systems ◽  
Irreversible Processes ◽  
Glucose Catabolism ◽  
Matter Transfer

The heat and matter transfer during glucose catabolism in living systems and their relation with entropy production are a challenging subject of the classical thermodynamics applied to biology. In this respect, an analogy between mechanics and thermodynamics has been performed via the definition of the entropy density acceleration expressed by the time derivative of the rate of entropy density and related to heat and matter transfer in minimum living systems. Cells are regarded as open thermodynamic systems that exchange heat and matter resulting from irreversible processes with the intercellular environment. Prigogine’s minimum energy dissipation principle is reformulated using the notion of entropy density acceleration applied to glucose catabolism. It is shown that, for out-of-equilibrium states, the calculated entropy density acceleration for a single cell is finite and negative and approaches as a function of time a zero value at global thermodynamic equilibrium for heat and matter transfer independently of the cell type and the metabolic pathway. These results could be important for a deeper understanding of entropy generation and its correlation with heat transfer in cell biology with special regard to glucose catabolism representing the prototype of irreversible reactions and a crucial metabolic pathway in stem cells and cancer stem cells.

scholarly journals On using the minimum energy dissipation to estimate the steady-state of a flow network and discussion about the resulting power-law:application to tree-shaped networks in HVAC systems

Energy ◽  
2019 ◽  
Vol 172 ◽  
pp. 181-195 ◽  
Author(s):  
Víctor-Manuel Soto-Francés ◽  
José-Manuel Pinazo-Ojer ◽  
Emilio-José Sarabia-Escrivá ◽  
Pedro-Juan Martínez-Beltrán
Keyword(s):  
Steady State ◽  
Energy Dissipation ◽  
Minimum Energy ◽  
Hvac Systems ◽  
Flow Network ◽  
Minimum Energy Dissipation

Study On the Damage Evolution Equation of Rockburst

2008 ◽  
Vol 33-37 ◽  
pp. 663-668
Author(s):  
Quan Sheng Liu ◽  
Bin Liu ◽  
Wei Gao
Keyword(s):  
Energy Dissipation ◽  
Evolution Equation ◽  
Damage Evolution ◽  
Minimum Energy ◽  
Strength Criterion ◽  
Internal Variable ◽  
Total Strength ◽  
Damage Evolution Equation ◽  
Traditional Research ◽  
Minimum Energy Dissipation

This paper introduces the principle of minimum energy dissipation and its general procedures to establish development equation of internal variable. With the accepted viewpoint that the damage is only mechanics of energy dissipation during the rockburst and utilizing the total strength criterion based on released strain energy, the general damage evolution equation is deduced. Compared with the traditional research method of damage evolution equation, this method has universal and objective characteristics.

Micromagnetic study of minimum-energy dissipation during Landauer erasure of either isolated or coupled nanomagnetic switches

2014 ◽  
Vol 90 (10) ◽  
Author(s):  
M. Madami ◽  
M. d’Aquino ◽  
G. Gubbiotti ◽  
S. Tacchi ◽  
C. Serpico ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Minimum Energy ◽  
Minimum Energy Dissipation
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