Theoretical analysis of the thermal effects during in vivo tissue electroporation

Tissue electroporation is a technique that facilitates the introduction of molecules into cells by applying a series of short electric pulses to specific areas of the body. These pulses temporarily increase the permeability of the cell membrane to small drugs and macromolecules. The goal of this paper is to provide information on the thermal effects of these electric pulses for consideration when designing electroporation protocols. The parameters investigated include electrode geometry, blood flow, metabolic heat generation, pulse frequency, and heat dissipation through the electrodes. Basic finite-element models were created in order to gain insight and weigh the importance of each parameter. The results suggest that for plate electrodes, the energy from the pulse may be used to adequately estimate the heating in the tissue. However, for needle electrodes, the geometry, i.e. spacing and diameter, and pulse frequency are critical when determining the thermal distribution in the tissue.     

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schr?dinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.     

Soliton spiraling in optically induced rotating Bessel lattices

We address soliton spiraling in optical lattices induced by multiple coherent Bessel beams and show that the dynamic nature of such lattices makes it possible for them to drag different soliton structures, setting them into rotation. We can control the rotation rate by varying the topological charges of lattice-inducing Bessel beams.     

Three-dimensional light bullets in arrays of waveguides

We report the first experimental observation of three-dimensional light bullets, excited by femtosecond pulses in a system featuring quasi-instantaneous cubic nonlinearity and a periodic, transversally modulated refractive index. Stringent evidence of the excitation of light bullets is based on time-gated images and spectra which perfectly match our numerical simulations. Furthermore, we reveal a novel evolution mechanism forcing the light bullets to follow varying dispersion or diffraction conditions, until they leave their existence range and decay.     

Vortex revivals with trapped light

We predict that vortex dipoles nested in light beams trapped in graded-index media can undergo closed Berry trajectories, yielding periodic vortex annihilations and revivals along the light-propagation direction. The vortex revivals from vortex-free wave fronts are mediated by Freund stationary point bundles that carry the necessary Poincaré-Hopf indices. Vortex spiraling and spontaneous generation of circular-edge dislocations are also found to occur.     

Anderson cross-localization

We report Anderson localization in two-dimensional optical waveguide arrays with disorder in waveguide separation introduced along one axis of the array, in an uncorrelated fashion for each waveguide row. We show that the anisotropic nature of such disorder induces a strong localization along both array axes. The degree of localization in the cross-axis remains weaker than that in the direction in which disorder is introduced. This effect is illustrated both theoretically and experimentally.     

Robust control volume finite element methods for numerical wave tanks using extreme adaptive anisotropic meshes

Multiphase inertia-dominated flow simulations, and free surface flow models in particular, continue to this day to present many challenges in terms of accuracy and computational cost to industry and research communities. Numerical wave tanks and their use for studying wave-structure interactions are a good example. Finite element method (FEM) with anisotropic meshes combined with dynamic mesh algorithms has already shown the potential to significantly reduce the number of elements and simulation time with no accuracy loss. However, mesh anisotropy can lead to mesh quality-related instabilities. This article presents a very robust FEM approach based on a control volume discretization of the pressure field for inertia dominated flows, which can overcome the typically encountered mesh quality limitations associated with extremely anisotropic elements. Highly compressive methods for the water-air interface are used here. The combination of these methods is validated with multiphase free surface flow benchmark cases, showing very good agreement with experiments even for extremely anisotropic meshes, reducing by up to two orders of magnitude the required number of elements to obtain accurate solutions.     

Soliton dragging by dynamic optical lattices

We report on the phenomenon of controllable soliton dragging by dynamic optical lattices induced by three imbalanced interfering plane waves. Because of such an imbalance, the transverse momentum of the lattice does not vanish, and thus the dynamic lattice can cause soliton dragging. The dragging rate is shown to depend on the amplitude and on the angle of incidence of the third plane wave making the optical lattice.     

Vortex lattice solitons supported by localized gain

We show that localized gain supports the existence of dissipative vortex solitons in periodic Kerr media with strong two-photon absorption. Vortex solitons exist in both focusing and defocusing media, with their propagation constants emerging from semi-infinite or finite gaps in the lattice spectrum. Coincidence of the discrete rotational symmetries of the gain landscape and refractive index distribution is a necessary condition for exciting vortex solitons, which otherwise transform into stable dissipative multipoles.