Solusi Persamaan Burgers Inviscid dengan Metode Pemisahan Variabel

Penelitian ini mengkaji tentang solusi persamaan Burgers Inviscid dengan metode pemisahan variabel. Tujuan dari penelitian ini adalah untuk mengetahui penyederhanaan sistem persamaan Navier-Stokes menjadi persamaan Burgers Inviscid, menemukan solusi persamaan Burgers Inviscid dengan metode pemisahan variabel, dan melakukan simulasi solusi persamaan dengan menggunakan software Maple18. Persamaan Burgers muncul sebagai penyederhanaan model yang rumit dari sistem persamaan Navier-Stokes. Persamaan Burgers adalah persamaan diferensial parsial hukum konservasi dan merupakan masalah hiperbolik, yaitu representasi nonlinier paling sederhana dari persamaan Navier-Stokes. Metode pemisahan variabel merupakan salah satu metode klasik yang efektif digunakan dalam menyelesaikan persamaan diferensial parsial dengan mengasumsikan untuk mendapatkan komponen x dan t. Kemudian akan dilakukan subtitusi pada persamaan diferensial, sehingga dengan cara ini akan didapatkan solusi persamaan diferensial parsial.Kata Kunci: Persamaan Burgers Inviscid, metode pemisahan variabel, persamaan Navier-StokesThis study examines the solution of Burgers Inviscid equation with variable separation method. The purpose of this study was to find out the simplification of the Navier-Stokes equation system into the Burgers Inviscid equation, find a solution to the Burgers Inviscid equation with the variable separation method, and simulate equation solutions using Maple18 software. The Burgers equation emerged as a complicated simplification of the Navier-Stokes equation system. The Burgers equation is a partial differential equation of conservation law and is a hyperbolic problem, i.e. the simplest nonlinear representation of the Navier-Stokes equation. The variable separation method is one of the classic methods that is effectively used in solving partial differential equations assuming to obtain the x and t components. Then there will be substitutions to differential equations, so that in this way there will be a partial differential equation solution.Keywords: Burgers Inviscid Equation, variable separation method, Navier-Stokes equations.

Twisting to freedom: The evolution of copulation termination techniques across 48 species of sepsids (Diptera, Sepsidae)

Studies of insect mating behaviour usually focus on what happens before and during copulation. Few pay close attention to the actions needed to end copulation. However, genital separation after copulation is likely to be an important cause of mechanical stress and injuries because it often involves the withdrawal of heavily armoured male intromittent organs from membranous female reproductive tracts. Difficult and/or slow separations can also reduce male and female fitness by increasing their exposure to predation. We here report the results of a comparative study of separation behaviour in 48 species of Sepsidae (Diptera) and one outgroup. We find a surprising amount of qualitative and quantitative behavioural variability within and between species. We characterize and reconstruct three types of behaviours: 1) The sepsid ancestor likely used `back-off; a gentle separation technique that does not involve any pulling or twisting (https://youtu.be/EbkJvOaubZ0). 2) This potentially gave rise to the most common `pull' technique where the male turns 180 degrees and pulls in an opposite direction from the female (https://youtu.be/oLf4xGpkk1s). This separation can be quick and straightforward, but in some species the `pull' is slow and protracted and we routinely find dead males and/or females attached to their living partners in the latter (difficult: https://youtu.be/MbYPbXN6jr0; failure: https://youtu.be/leTiXefFzCc). 3) Finally, several species use `twist', a new technique where the male rotates >360 degrees from the initial mounting position (https://youtu.be/WMUXbIPyLbk). We document that species capable of using `twist' have shorter and less variable separation times than those using "pull". However, many species capable of `twist' also retain the ability to use `pull' (`back-off'/'pull'= 8%; `pull' only= 41%; `twist'/ `pull'= 24%; `twist' only = 27%). Overall, our study suggests that separation behaviour can vary among closely related species and highlights the significance of studying variable behavioural traits in a phylogenetic context.

Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker-Planck equation

Based on the idea of variable separation, the time-fractional Fokker-Planck equation with external force field is studied by using the property of Mittag-Leffler function and some special algorithm skills. In the cases of various external potential functions such as linear potential, harmonic potential, logarithmic potential, exponential potential, and quartic potential, exact solutions and dynamical properties of the above mentioned equation is investigated. The some interesting dynamical behaviors and phenomena are discovered. The profiles of some representative exact solutions are illustrated by 3D-graphs.

Novel Soliton Molecules and Wave Interactions for A (3+1)-Dimensional Nonlinear Evolutionary Equation

New wave excitations are revealed for a (3+1)-dimensional nonlinear evolution equation to enrich nonlinear wave patterns in nonlinear systems. Based on a new variable separation solution with two arbitrary variable separated functions obtained by means of the multilinear variable separation approach, localized excitations of N dromions, N x M lump lattice and N x M ring soliton lattice are explored. Interestingly, it is observed that soliton molecules can be composed of diverse "atoms" such as the dromions, lumps and ring solitons, respectively. Elastic interactions between solitons and soliton molecules are graphically demonstrated.