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High-harmonic generation is one of the most extreme nonlinear-optical processes observed to date. By focusing an intense laser pulse into a gas, the light-atom interaction that occurs during the process of ionising the atoms results in the generation of harmonics of the driving laser frequency, that extend up to order ~300 (corresponding to photon energies from 4 to >500eV). Because this technique is simple to implement and generates coherent, laser-like, soft-x-ray beams, it is currently being developed for applications in science and technology including probing of dynamics in chemical and materials systems and for imaging. In this work we demonstrate that by carefully controlling the shape of intense light pulses of 6-8 optical cycles, we can control the interaction of light with an atom as it is being ionised, in a way that improves the efficiency of x-ray generation by an order of magnitude. Furthermore, we demonstrate that it is possible to control the spectral characteristics of the emitted radiation and to channel the interaction between different-order nonlinear processes. The result is an increased utility of harmonic generation as a light source, as well as the first demonstration of optical pulse-shaping techniques to control high-order nonlinear processes., Comment: 16 pages, 3 figures

Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. To solve such problems, we first derive a complete set of odd and even orthonormal eigenfunctions -- resembling trigonometric sines and cosines, as well as the so-called ``beam'' functions. These functions intrinsically satisfy boundary conditions (BCs) of relevance to thin-film flows, since they are the solutions of a self-adjoint sixth-order Sturm--Liouville BVP with the same BCs. Next, we propose a Galerkin spectral approach for sixth-order problems; namely the sought function as well as all its derivatives and terms appearing in the differential equation are expanded into an infinite series with respect to the derived complete orthonormal (CON) set of eigenfunctions. The unknown coefficients in the series expansion are determined by solving the algebraic system derived by taking successive inner products with each member of the CON set of eigenfunctions. The proposed method and its convergence are demonstrated by solving two model sixth-order BVPs., Comment: 18 pages, 5 figures, IoP jpconf style; v2: correct minor typos, to appear in the proceedings of the Fifteenth Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'23)

Acoustic shock and acceleration waves in inhomogeneous fluids are investigated using both analytical and numerical methods. In the context of start-up signaling problems, and based on linear acoustics theory, we study the propagation of such waveforms in the atmosphere and in fluids that possess a periodic ambient density profile. It is shown that vertically-running shock and acceleration waves in the atmosphere suffer amplitude growth. In contrast, those in the periodic-density fluid have bounded amplitudes that exhibit periodic, but non-trivial, oscillations; this is illustrated via a series of numerically-generated profile-evolution plots, which were computed using the PyClaw software package., Comment: 9 pages, 4 figures, elsarticle class; accepted for publication in Mechanics Research Communications for the special issue in memoriam G. A. Maguin; v2 corrects minor typographical errors

We explore a variant of the $\phi^6$ model originally proposed in Phys.\ Rev.\ D {\bf 12}, 1606 (1975) as a prototypical, so-called, "bag" model in which domain walls play the role of quarks within hadrons. We examine the steady state of the model, namely an apparent bound state of two kink structures. We explore its linearization, and we find that, as a function of a parameter controlling the curvature of the potential, an {\it effectively arbitrary} number of internal modes may arise in the point spectrum of the linearization about the domain wall profile. We explore some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, and how they depend on the principal parameter of the model. We find that the critical velocity exhibits a non-monotonic dependence on the parameter controlling the curvature of the potential. For the multi-bounce windows, we find that their range and complexity decrease as the relevant parameter decreases (and as the number of internal modes in the model increases). We use a modified collective coordinates method [in the spirit of recent works such as {Phys.\ Rev.\ D} {\bf 94}, 085008 (2016)] in order to capture the relevant phenomenology in a semi-analytical manner., Comment: 23 pages, 11 figures, jheppub class; v2 minor revisions

We study one-dimensional (1D) and two-dimensional (2D) Helium atoms using a new time-dependent quantum Monte Carlo (TDQMC) method. The TDQMC method employs random walkers, with a separate guiding wave attached to each walker. The ground state is calculated by a self-consistent solution of complex-time Schroedinger equations for the guiding waves and of equations for the velocity fields of the walkers. Our results show that the many-body wavefunction and the ground state energy of the model atoms are very close to those predicted by the standard diffusion quantum Monte Carlo method. The obtained ground state can further be used to examine correlated time-dependent processes which include, for example, interaction of atoms and molecules with external electromagnetic fields., Comment: 9 pages, 5 figures