ResearchPad - partial-differential-equations https://www.researchpad.co Default RSS Feed en-us © 2020 Newgen KnowledgeWorks <![CDATA[Agent-based and continuous models of hopper bands for the Australian plague locust: How resource consumption mediates pulse formation and geometry]]> https://www.researchpad.co/article/elastic_article_14654 Locusts aggregate in swarms that threaten agriculture worldwide. Initially these aggregations form as aligned groups, known as hopper bands, whose individuals alternate between marching and paused (associated with feeding) states. The Australian plague locust (for which there are excellent field studies) forms wide crescent-shaped bands with a high density at the front where locusts slow in uneaten vegetation. The density of locusts rapidly decreases behind the front where the majority of food has been consumed. Most models of collective behavior focus on social interactions as the key organizing principle. We demonstrate that the formation of locust bands may be driven by resource consumption. Our first model treats each locust as an individual agent with probabilistic rules governing motion and feeding. Our second model describes locust density with deterministic differential equations. We use biological observations of individual behavior and collective band shape to identify numerical values for the model parameters and conduct a sensitivity analysis of outcomes to parameter changes. Our models are capable of reproducing the characteristics observed in the field. Moreover, they provide insight into how resource availability influences collective locust behavior that may eventually aid in disrupting the formation of locust bands, mitigating agricultural losses.

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<![CDATA[Exact flow of particles using for state estimations in unmanned aerial systems` navigation]]> https://www.researchpad.co/article/Nb8d1b185-24ca-4749-9cc9-bbc7ade34d0a

The navigation is a substantial issue in the field of robotics. Simultaneous Localization and Mapping (SLAM) is a principle for many autonomous navigation applications, particularly in the Global Navigation Satellite System (GNSS) denied environments. Many SLAM methods made substantial contributions to improve its accuracy, cost, and efficiency. Still, it is a considerable challenge to manage robust SLAM, and there exist several attempts to find better estimation algorithms for it. In this research, we proposed a novel Bayesian filtering based Airborne SLAM structure for the first time in the literature. We also presented the mathematical background of the algorithm, and the SLAM model of an autonomous aerial vehicle. Simulation results emphasize that the new Airborne SLAM performance with the exact flow of particles using for recursive state estimations superior to other approaches emerged before, in terms of accuracy and speed of convergence. Nevertheless, its computational complexity may cause real-time application concerns, particularly in high-dimensional state spaces. However, in Airborne SLAM, it can be preferred in the measurement environments that use low uncertainty sensors because it gives more successful results by eliminating the problem of degeneration seen in the particle filter structure.

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<![CDATA[Forward Period Analysis Method of the Periodic Hamiltonian System]]> https://www.researchpad.co/article/5989dad3ab0ee8fa60bb7165

Using the forward period analysis (FPA), we obtain the period of a Morse oscillator and mathematical pendulum system, with the accuracy of 100 significant digits. From these results, the long-term [0, 1060] (time unit) solutions, ranging from the Planck time to the age of the universe, are computed reliably and quickly with a parallel multiple-precision Taylor series (PMT) scheme. The application of FPA to periodic systems can greatly reduce the computation time of long-term reliable simulations. This scheme provides an efficient way to generate reference solutions, against which long-term simulations using other schemes can be tested.

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<![CDATA[Analysis of Nonlinear Thermoelastic Dissipation in Euler-Bernoulli Beam Resonators]]> https://www.researchpad.co/article/5989daa2ab0ee8fa60ba6496

The linear theory of thermoelastic damping (TED) has been extensively developed over the past eight decades, but relatively little is known about the different types of nonlinearities that are associated with this fundamental mechanism of material damping. Here, we initiate the study of a dissipative nonlinearity (also called thermomechanical nonlinearity) whose origins reside at the heart of the thermomechanical coupling that gives rise to TED. The finite difference method is used to solve the nonlinear governing equation and estimate nonlinear TED in Euler-Bernoulli beams. The maximum difference between the nonlinear and linear estimates ranges from 0.06% for quartz and 0.3% for silicon to 7% for aluminum and 28% for zinc.

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<![CDATA[Flow and Heat Transfer in Sisko Fluid with Convective Boundary Condition]]> https://www.researchpad.co/article/5989da08ab0ee8fa60b76836

In this article, we have studied the flow and heat transfer in Sisko fluid with convective boundary condition over a non-isothermal stretching sheet. The flow is influenced by non-linearly stretching sheet in the presence of a uniform transverse magnetic field. The partial differential equations governing the problem have been reduced by similarity transformations into the ordinary differential equations. The transformed coupled ordinary differential equations are then solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting method. Effects of different parameters like power-law index , magnetic parameter , stretching parameter , generalized Prandtl number Pr and generalized Biot number are presented graphically. It is found that temperature profile increases with the increasing value of and whereas it decreases for . Numerical values of the skin-friction coefficient and local Nusselt number are tabulated at various physical situations. In addition, a comparison between the HAM and exact solutions is also made as a special case and excellent agreement between results enhance a confidence in the HAM results.

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<![CDATA[IOPA: I/O-aware parallelism adaption for parallel programs]]> https://www.researchpad.co/article/5989db52ab0ee8fa60bdc5ad

With the development of multi-/many-core processors, applications need to be written as parallel programs to improve execution efficiency. For data-intensive applications that use multiple threads to read/write files simultaneously, an I/O sub-system can easily become a bottleneck when too many of these types of threads exist; on the contrary, too few threads will cause insufficient resource utilization and hurt performance. Therefore, programmers must pay much attention to parallelism control to find the appropriate number of I/O threads for an application. This paper proposes a parallelism control mechanism named IOPA that can adjust the parallelism of applications to adapt to the I/O capability of a system and balance computing resources and I/O bandwidth. The programming interface of IOPA is also provided to programmers to simplify parallel programming. IOPA is evaluated using multiple applications with both solid state and hard disk drives. The results show that the parallel applications using IOPA can achieve higher efficiency than those with a fixed number of threads.

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<![CDATA[Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary]]> https://www.researchpad.co/article/5989da41ab0ee8fa60b8a288

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

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<![CDATA[The Dynamics of Disease Progression in Cystic Fibrosis]]> https://www.researchpad.co/article/5989db43ab0ee8fa60bd7709

In cystic fibrosis, statistical models have been more successful in predicting mortality than the time course of clinical status. We develop a system of partial differential equations that simultaneously track mortality and patient status, with all model parameters estimated from the extensive and carefully maintained database from the Cystic Fibrosis Foundation. Cystic fibrosis is an autosomal recessive disease that leads to loss of lung function, most commonly assessed using the Forced Expiratory Volume in 1 second (FEV1%). This loss results from inflammation secondary to chronic bacterial infections, particularly Pseudomonas aeruginosa, methicillin-sensitive Staphylococcus aureus (MSSA) and members of the virulent Burkholderia complex. The model tracks FEV1% and carriage of these three bacteria over the course of a patient’s life. Analysis of patient state changes from year to year reveals four feedback loops: a damaging positive feedback loop between P. aeruginosa carriage and lower FEV1%, negative feedback loops between P. aeruginosa and MSSA and between P. aeruginosa and Burkholderia, and a protective positive feedback loop between MSSA carriage and higher FEV1%. The partial differential equations built from this data analysis accurately capture the life-long progression of the disease, quantify the key role of high annual FEV1% variability in reducing survivorship, the relative unimportance of short-term bacterial interactions for long-term survival, and the potential benefits of eradicating the most harmful bacteria.

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<![CDATA[Heat and Mass Transfer in Unsteady Rotating Fluid Flow with Binary Chemical Reaction and Activation Energy]]> https://www.researchpad.co/article/5989da40ab0ee8fa60b899c2

In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations.

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<![CDATA[Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition]]> https://www.researchpad.co/article/5989da65ab0ee8fa60b91ad3

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables.

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