Effects of varying nonlocality on dynamics of two-component vector spatial solitons

The randomly and the periodically varying weak nonlocalities are investigated by the variational approach in the self-focusing nonlinear media, and their effects are analyzed on the propagation and interaction of the two-component spatial solitons. The results show that they lead to the soliton disintegration and enhance the interaction between the spatial solitons, and their effects depend on the fluctuation strength and the period length of the varying nonlocalities. Finally, the numerical results confirm the theoretical findings.     

Excess Molar Volumes and Thermal Expansivities of Aqueous Solutions of Dimethylsulfoxide,Tetrahydrofuran and 1,4-Dioxane

Densities, , of the systems water (W) + dimethylsulfoxide (DMSO), W + tetrahydrofuran (THF) and W + 1,4-dioxane (DO) have been determined in the temperature range 303.15-323.15 K. Excess molar volumes, $V_m^E $ , have been found to be negative and large in magnitude. Thermal expansivities, f , and excess thermal expansivities, f E , have been calculated. Densities, excess molar volumes, thermal expansivities and excess thermal expansivities have been plotted against mole fraction of solutes. All these properties have been expressed satisfactorily by appropriate polynomials. Attempt has been made to explain $V_m^E$ in terms of hydrophobic hydration and hydrophilic effect of the solutes.     

BSHM meetings

In a deliberately provocative first part to this paper, I argue that nineteenth-century British mathematicians had an unduly high opinion of themselves and a striking lack of appreciation for contemporary continental developments. I argue that this failure was rooted in the institutions that supported mathematics, and was only remedied towards the end of the century. In the more sober second half of the paper I ask if historians of mathematics have subscribed to this overestimate, and explore some related questions, among them what are historians doing when they write history: telling it as it was, or righting or defending the record? Historians of mathematics also need to consider British priorities for research in the nineteenth century, and a comparison with other minor players (such as Japan, Portugal, or Poland) might be illuminating.     

Electron acceleration considering pondermotive force effect in a plasma-filled rectangular waveguide by microwave radiation

The electron acceleration inside the plasma-filled rectangular waveguide is numerically investigated for the externally injected single-electron model considering the effects of density modification under a balance between the ponderomotive force and the pressure gradient force. Using Maxwell’s equations, we evaluate the field components of the fundamental mode in the plasma-filled rectangular waveguide, where the obtained equations are solved numerically using the fourth-order Runge–Kutta method for the electric field amplitude of the microwave. Besides, by solving the relativistic momentum and energy equations using the fourth-order Runge–Kutta method, the deflection angle and the total energy of the electron in the waveguide are obtained. Furthermore, it is shown that the electron energy gain can be controlled using superposing microwave fundamental modes. Effects of various parameters on the results are graphically presented.