Search results for "Stationary solutions"

showing 2 items of 2 documents

Steady‐state solutions of the aerotaxis problem

2022

We study the steady-state system of aerotaxis equations in higher dimensions.It is shown that the existence and multiplicity of solutions depend on the totalmass of the colony of bacteria, the energy function, and the boundary conditions.

aerotaxis equationsGeneral MathematicsGeneral Engineeringstationary solutionsnonlocal elliptic problemsMathematical Methods in the Applied Sciences
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Steady states and nonlinear buckling of cable-suspended beam systems

2018

This paper deals with the equilibria of an elastically-coupled cable-suspended beam system, where the beam is assumed to be extensible and subject to a compressive axial load. When no vertical load is applied, necessary and sufficient conditions in order to have nontrivial solutions are established, and their explicit closed-form expressions are found. In particular, the stationary solutions are shown to exhibit at most two non-vanishing Fourier modes and the critical values of the axial-load parameter which produce their pitchfork bifurcation (buckling) are established. Depending on two dimensionless parameters, the complete set of resonant modes is devised. As expected, breakdown of the p…

Perturbation (astronomy)010103 numerical & computational mathematicsBiparametric resonance; Cable-suspended beam; Nonlinear oscillations; Pitchfork bifurcation; Stationary solutions; Suspension bridgeCable-suspended beam01 natural sciencesBiparametric resonanceNonlinear oscillationssymbols.namesakeStationary solutions0101 mathematicsNonlinear bucklingNonlinear OscillationsPhysicsMechanical EngineeringPitchfork bifurcationMechanicsCondensed Matter PhysicsSuspension bridge010101 applied mathematicsPitchfork bifurcationFourier transformBucklingMechanics of MaterialssymbolsAxial loadDimensionless quantity
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