scholarly journals A simple mathematical model for Batesian mimicry

2005 ◽  
Vol 2005 (1) ◽  
pp. 87-92 ◽  
Author(s):  
Terence R. Blows ◽  
Barry J. Wimmer
Keyword(s):  
Mathematical Model ◽  
Full Range ◽  
Logistic Map ◽  
Period Doubling ◽  
Species Interaction ◽  
Batesian Mimicry ◽  
Simple Mathematical Model ◽  
Predator Prey ◽  
The Mathematical Model ◽  
Period Doubling Bifurcations

A simple mathematical model is presented for Batesian mimicry, which occurs when a harmless species (mimic) is morphologically similar to another species (model) that is noxious or distasteful to predators, thus gaining a measure of protection. Although mathematical models for species interaction, such as predator-prey or competition, are well known, there is no similar literature on mimicry. The mathematical model developed here is a one-dimensional iterated map which has the full range of dynamic behavior present in the logistic map, depending on the values of its parameters. The dynamics ranges from a stable fixed point and stable cycles through chaotic dynamics achieved through a sequence of period doubling bifurcations.

scholarly journals Hybrid Secondary Suspension Systems

2009 ◽  
Vol 16 (5) ◽  
pp. 467-480 ◽  
Author(s):  
Nader Vahdati ◽  
Mehdi Ahmadian
Keyword(s):  
Mathematical Model ◽  
Vibration Absorbers ◽  
Simple Mathematical Model ◽  
System Behavior ◽  
Engine Mounts ◽  
Suspension Systems ◽  
Tuned Vibration Absorbers ◽  
Simulation Results ◽  
Secondary Suspension ◽  
The Mathematical Model

Passive fluid mounts are used in the fixed wing applications as engine mounts. The passive fluid mount is placed in between the engine and the fuselage to reduce the cabin's structure- borne noise and vibration generated by the engine.To investigate the benefits of passive fluid mounts used in conjunction with tuned vibration absorbers (TVA), a simple mathematical model is developed. This mathematical model includes the mathematical model of a passive fluid mount, a TVA, and a spring representing the fuselage structure. The simulation results indicate that when passive fluid mounts are used in conjunction with TVAs, an active suspension system behavior is nearly created.

scholarly journals Mathematical Modeling of the Fracture Toughness of Phenol Formaldehyde Composites Reinforced with E-Spheres

2009 ◽  
Vol 79-82 ◽  
pp. 1165-1168
Author(s):  
H. Ku ◽  
W. Xiang ◽  
N. Pattarachaiyakoop
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Fracture Toughness ◽  
Tensile Strength ◽  
Polynomial Interpolation ◽  
Phenol Formaldehyde ◽  
Simple Mathematical Model ◽  
The Mathematical Model ◽  
Conventional Oven ◽  
Lagrange’S Method

The fracture toughness of SLG filled phenolic composites have been determined by short bar tests. It is expensive to prepare the samples for the tests. Therefore, it is necessary to develop a mathematical model that will predict the fracture toughness of particulate filled phenolic composites. Mathematical models for tensile strength, Young’s modulus are available but not for impact strength and fracture toughness. There is no sign that it can be built up from simple mathematical model; polynomial interpolation using Lagrange’s method was therefore employed to generate the fracture toughness model using the data obtained from experiments. From experiments, it was found that the trend of the fracture toughness of the samples cured conventionally was similar to that cured in microwaves; it is therefore possible to predict the fracture toughness of the samples cured in microwaves from shifting the mathematical model generated for fracture toughness of samples post-cured in conventional oven. The shifted model represented the fracture toughness of the samples cured in microwaves vey well.

Multiple Scenarios of Transition to Chaos in the Alternative Splicing Model

2017 ◽  
Vol 27 (02) ◽  
pp. 1730006 ◽  
Author(s):  
Vladislav V. Kogai ◽  
Vitaly A. Likhoshvai ◽  
Stanislav I. Fadeev ◽  
Tamara M. Khlebodarova
Keyword(s):  
Alternative Splicing ◽  
Period Doubling ◽  
Genetic System ◽  
Protein Isoforms ◽  
Type I ◽  
Transition To Chaos ◽  
Delayed Arguments ◽  
The Mathematical Model ◽  
Period Doubling Bifurcations ◽  
Type Of Transition

We have investigated the scenarios of transition to chaos in the mathematical model of a genetic system constituted by a single transcription factor-encoding gene, the expression of which is self-regulated by a feedback loop that involves protein isoforms. Alternative splicing results in the synthesis of protein isoforms providing opposite regulatory outcomes — activation or repression. The model is represented by a differential equation with two delayed arguments. The possibility of transition to chaos dynamics via all classical scenarios: a cascade of period-doubling bifurcations, quasiperiodicity and type-I, type-II and type-III intermittencies, has been numerically demonstrated. The parametric features of each type of transition to chaos have been described.

scholarly journals Optimisation of a clam bunk skidder from the emission production point of view

2012 ◽  
Vol 58 (No. 4) ◽  
pp. 136-141
Author(s):  
A. Janeček ◽  
R. Adamovský
Keyword(s):  
Mathematical Model ◽  
Production System ◽  
Operating Performance ◽  
Point Of View ◽  
Optimal Rate ◽  
Simple Mathematical Model ◽  
Operation Performance ◽  
The Mathematical Model

This article presents a proposal of a simple mathematical model for minimisation of the production of extraneous substances as a function of the rate of operation performance of a production system. The model is then verified by operation tests of the Terri 2040 clam bunk skidder and by determining the system&rsquo;s optimal rate of performance from the point of view of production of SO<sub>2</sub>, HC and NO<sub>x </sub>emissions. The operation tests conducted to verify the mathematical model have confirmed that conditions can be determined for the production system at which it produces minimum emissions. Min. values of SO<sub>2</sub>, and HC were achieved at approximately the same rate of performance of the clam bunk skidder. Minimum values of NO<sub>x </sub>were achieved at significantly higher rate of performance of the equipment. At the calculated optimal rate of operating performance of the Terri 2040 clam bunk skidder, the values of the produced emissions were determined per m<sup>3</sup> of timber: SO<sub>2</sub> = 1.00035 g/m<sup>3</sup>, HC = 7.796 g/m<sup>3</sup> and NO<sub>x</sub> = 0.277 g/m<sup>3</sup>.

scholarly journals Application of a Semi-Empirical Dynamic Model to Forecast the Propagation of the COVID-19 Epidemics in Spain

Forecasting ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 452-469
Author(s):  
Juan Carlos Mora ◽  
Sandra Pérez ◽  
Alla Dvorzhak
Keyword(s):  
Mathematical Model ◽  
Intensive Care ◽  
Good Accuracy ◽  
Logistic Map ◽  
Semiempirical Model ◽  
The Third ◽  
Third Phase ◽  
Daily Rate ◽  
Semi Empirical ◽  
The Mathematical Model

A semiempirical model, based in the logistic map, was developed to forecast the different phases of the COVID-19 epidemic. This paper shows the mathematical model and a proposal for its calibration. Specific results are shown for Spain. Four phases were considered: non-controlled evolution; total lock-down; partial easing of the lock-down; and a phased lock-down easing. For no control the model predicted the infection of a 25% of the Spanish population, 1 million would need intensive care and 700,000 direct deaths. For total lock-down the model predicted 194,000 symptomatic infected, 85,700 hospitalized, 8600 patients needing an Intensive Care Unit (ICU) and 19,500 deaths. The peak was predicted between the 29 March/3 April. For the third phase, with a daily rate r=1.03, the model predicted 400,000 infections and 46,000±15,000 deaths. The real r was below 1%, and a revision with updated parameters provided a prediction of 250,000 infected and 29,000±15,000 deaths. The reported values by the end of May were 282,870 infected and 28,552 deaths. After easing of the lock-down the model predicted that the health system would not saturate if r was kept below 1.02. This model provided good accuracy during epidemics development.

The Mathematical Model of Online Quenching for Extruding Bar of 6061 Aluminum Alloy

2011 ◽  
Vol 117-119 ◽  
pp. 1798-1801
Author(s):  
Yi Lin ◽  
De Zhi Li ◽  
Jian Min Zeng ◽  
Ping Chen ◽  
Li Hua Liang
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Aluminum Alloy ◽  
Simple Mathematical Model ◽  
Extrusion Speed ◽  
6061 Aluminum Alloy ◽  
Different Temperatures ◽  
Set Up ◽  
The Mathematical Model ◽  
Quenching Apparatus

A simple mathematical model that correlates the temperature and extrusion speed of a 6061 aluminum bar extruded from the die has been established based on the principle of heat transfer in this paper. The 6061 alloy bar is extruded from the die orifice and is cooled through heat exchanged between the bar and ambient. The temperature of the bar decreases as the distance increases away from the die orifice. The more rapidly the temperature drops, the slower the extrusion speed is. A flexible online quenching apparatus has been set up before the critical quenching position to guarantee good supersaturation of alloying elements. The calculations have shown that at the extrusion speeds of 10m/min, 15 m/min and 20 m/min, the critical quenching positions are 0.44m, 0.88m and 1.30m from the die orifice, respectively for the temperature of 520°C; and for the different temperatures, the critical quenching positions from the die orifice are 0.66m, 1.31m, 1.95m at 530°C and 0.88m, 1.75m, 2.6m at 540°C, respectively.

Dynamic analysis of the mathematical model of COVID-19 with demographic effects

2020 ◽  
Vol 75 (11-12) ◽  
pp. 389-396 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
E. F. Doungmo Goufo ◽  
Amna Anjum ◽  
Ali Anjum
Keyword(s):  
Mathematical Model ◽  
Perturbation Method ◽  
Effective Treatment ◽  
Homotopy Perturbation Method ◽  
Simple Mathematical Model ◽  
Safety Measures ◽  
Seir Model ◽  
Homotopy Perturbation ◽  
The Mathematical Model ◽  
Demographic Effects

AbstractThe coronavirus is currently extremely contagious for humankind, which is a zoonotic tropical disease. The pandemic is the largest in history, affecting almost the whole world. What makes the condition the worst of all is no specific effective treatment available. In this article, we present an extended and modified form of SIR and SEIR model, respectively. We begin by investigating a simple mathematical model that describes the pandemic. Then we apply different safety measures to control the pandemic situation. The mathematical model with and without control is solved by using homotopy perturbation method. Obtained solutions have been presented graphically. Finally, we develop another mathematical model, including quarantine and hospitalization.

Modeling the Flexural Properties of SLG Reinforced Phenol Formaldehyde Composites Using Langrage’s Method

2011 ◽  
Vol 410 ◽  
pp. 305-308
Author(s):  
Harry Ku ◽  
Hong Zhou ◽  
Peter Wong ◽  
Gang Su ◽  
Jayant Vadher
Keyword(s):  
Mathematical Model ◽  
Fracture Toughness ◽  
Tensile Strength ◽  
Polynomial Interpolation ◽  
Phenol Formaldehyde ◽  
Flexural Properties ◽  
Simple Mathematical Model ◽  
The Mathematical Model ◽  
Conventional Oven ◽  
Lagrange’S Method

The flexural properties of SLG filled phenolic composites have been determined in previous study. It is time consuming to prepare the samples for the tests. In addition, it is even more time consuming to carry out the tests and analyze the results. It is therefore necessary to develop a mathematical model that will predict the flexural properties of particulate filled phenolic composites. Mathematical models for tensile strength, Young’s modulus are available but not for impact strength, flexural strength and fracture toughness. There is no sign that it can be built up from simple mathematical model; polynomial interpolation using Lagrange’s method was therefore employed to generate the flexural properties model using the data obtained from experiments. From experiments, it was found that the trend of the flexural properties of the samples post-cured conventionally was similar to that post-cured in microwaves; it is therefore possible to predict the flexural properties of the samples post-cured in microwaves from the mathematical model generated for flexural properties of samples post-cured in a conventional oven. The workload is therefore halved as the process of generating the mathematical was much faster and simpler.

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