Static Buckling Analysis of a Quadratic-Cubic Model Structure Using the Phase Plane Method and Method of Asymptotics

The exact and asymptotic analyses of the buckling of a quadratic-cubic model structure subjected to static loading are discussed. The governing equation is first solved using the phase plane method and next, using the method of asymptotics. In the asymptotic method, we discuss the possibilities of using regular perturbation method in asymptotic expansions of the relevant variables to get an approximate analytical solution to the problem. Finally, the two results are compared using numerical results obtained with the aid of Q-Basic codes. In the two methods discussed in this work, it is clearly seen that the static buckling loads decrease as the imperfection parameters increase. It is also observed that the static buckling loads obtained using the exact method are higher than those obtained using the method of asymptotics.

On closed-form tight bounds and approximations for the median of a gamma distribution

The median of a gamma distribution, as a function of its shape parameter k, has no known representation in terms of elementary functions. In this work we use numerical simulations and asymptotic analyses to bound the median, finding bounds of the form 2−1/k(A + Bk), including an upper bound that is tight for low k and a lower bound that is tight for high k. These bounds have closed-form expressions for the constant parameters A and B, and are valid over the entire range of k > 0, staying between 48 and 55 percentile. Furthermore, an interpolation between these bounds yields closed-form expressions that more tightly bound the median, with absolute and relative margins to both upper and lower bounds approaching zero at both low and high values of k. These bound results are not supported with analytical proofs, and hence should be regarded as conjectures. Simple approximation expressions between the bounds are also found, including one in closed form that is exact at k = 1 and stays between 49.97 and 50.03 percentile.

Darboux transformation and soliton solutions of the (2+1)-dimensional Schwarz–Korteweg–de Vries equation

In this paper, we deduce the (2+1)-dimensional Schwarz–Korteweg–de Vries equation from two (1+1)-dimensional equations. Based on the resulting Lax pairs, we present its [Formula: see text]-fold Darboux transformation. From a trivial solution, we get [Formula: see text]-soliton and [Formula: see text]-soliton solutions of the (2+1)-dimensional Schwarz–Korteweg–de Vries equation. The asymptotic analyses of the [Formula: see text]-soliton, [Formula: see text]-soliton and [Formula: see text]-soliton solutions are presented theoretically and graphically.

Finite-Energy Dressed String-Inspired Dirac-Like Monopoles

On extending the Standard Model (SM) Lagrangian, through a non-linear Born–Infeld (BI) hypercharge term with a parameter β (of dimensions of [mass] 2 ), a finite energy monopole solution was claimed by Arunasalam and Kobakhidze. We report on a new class of solutions within this framework that was missed in the earlier analysis. This new class was discovered on performing consistent analytic asymptotic analyses of the nonlinear differential equations describing the model; the shooting method used in numerical solutions to boundary value problems for ordinary differential equations is replaced in our approach by a method that uses diagonal Padé approximants. Our work uses the ansatz proposed by Cho and Maison to generate a static and spherically-symmetric monopole with finite energy and differs from that used in the solution of Arunasalam and Kobakhidze. Estimates of the total energy of the monopole are given, and detection prospects at colliders are briefly discussed.