Steady dark solitary flexural gravity waves

The nonlinear Schrödinger (NLS) equation describes the modulational limit of many surface water wave problems. Dark solitary waves of the NLS equation asymptote to a constant in the far field and have a localized decrease to zero amplitude at the origin, corresponding to water wave solutions that asymptote to a uniform periodic Stokes wave in the far field and decreasing oscillations near the origin. It is natural to ask whether these dark solitary waves can be found in the irrotational Euler equations. In this paper, we find such solutions in the context of flexural-gravity waves, which are often used as a model for waves in ice-covered water. This is a situation in which the NLS equation predicts steadily travelling dark solitons. The solution branches of dark solitons are continued, and one branch leads to fully localized solutions at large amplitudes

Non-wetting impact of a sphere onto a bath and its application to bouncing droplets

We present a fully predictive model for the impact of a smooth, convex and perfectly hydrophobic solid onto the free surface of an incompressible fluid bath of infinite depth in a regime where surface tension is important. During impact, we impose natural kinematic constraints along the portion of the fluid interface that is pressed by the solid. This provides a mechanism for the generation of linear surface waves and simultaneously yields the pressure applied on the impacting masses. The model compares remarkably well with data of the impact of spheres and bouncing droplet experiments, and is completely free of any of impact parametrisation

Computation of three-dimensional flexural-gravity solitary waves in arbitrary depth

Fully-localised solitary waves propagating on the surface of a three-dimensional ideal fluid of arbitrary depth, and bounded above by an elastic sheet that resists flexing, are computed. The cases of shallow and deep water are distinct. In shallow water, weakly nonlinear modulational analysis (see Milewski & Wang 6) predicts waves of arbitrarily small amplitude and these are found numer- ically. In deep water, the same analysis rules out the existence of solitary waves bifurcating from linear waves, but, nevertheless, we find them at finite amplitude. This is accomplished using a continuation method following the branch from the shallow regime. All solutions are computed via a fifth-order Hamiltonian truncation of the full ideal free-boundary fluid equations. We show that this truncation is quantitatively accurate by comparisons with full potential flow in two-dimensions

Two-dimensional flexural-gravity waves of finite amplitude in deep water

Steady periodic and solitary waves propagating in a 2D fluid bounded above by a flexible sheet—which may be viewed as modelling an ice sheet—are considered in deep water. The non-linear elastic model is based on the special Cosserat theory of hyperelastic shells proposed by Toland (2008, Steady periodic hydroelastic waves. Arch. Ration. Mech. Anal., 189, 325–362) for this problem. Numerical solutions are computed via conformal mapping and a pseudo-spectral method. New solitary waves are found by using a continuation method to follow the branch of elevation waves. The results extend Guyenne and Părău's findings (2012, Computations of fully non-linear hydroelastic solitary wave on deep water. J. Fluid Mech., 713, 307–329). It is shown that, for periodic waves, far along the branches the profiles become overhanging and ultimately approach configurations with a trapped bubble at their troughs

Numerical study of interfacial solitary waves propagating under an ice sheet

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field

Dynamics of fully nonlinear capillary–gravity solitary waves under normal electric fields

Two-dimensional capillary–gravity waves travelling under the effect of a vertical electric field are considered. The fluid is assumed to be a dielectric of infinite depth. It is bounded above by another fluid which is hydrodynamically passive and perfectly conducting. The problem is solved numerically by time-dependent conformal mapping methods. Fully nonlinear waves are presented, and their stability and dynamics are studied

Self-focusing dynamics of patches of ripples

The dynamics of focussing of extended patches of nonlinear capillary gravity waves within the primitive fluid dynamic equations is presented. It is found that, when the envelope has certain properties, the patch focusses initially in accordance to predictions from nonlinear Schrodinger equation, and focussing can concentrate energy to the vicinity of a point or a curve on the fluid surface. After initial focussing, other effects dominate and the patch breaks up into a complex set of localised structures lumps and breathers - plus dispersive radiation. We perform simulations both in the inviscid regime and for small viscosities. Lastly we discuss throughout the similarities and differences between the dynamics of ripple patches and self-focussing light beams. (C) 2016 The Authors. Published by Elsevier B.V

From bore-soliton-splash to a new wave-to-wire wave-energy model

We explore extreme nonlinear water-wave amplification in a contraction or, analogously, wave amplification in crossing seas. The latter case can lead to extreme or rogue-wave formation at sea. First, amplification of a solitary-water-wave compound running into a contraction is disseminated experimentally in a wave tank. Maximum amplification in our bore–soliton–splash observed is circa tenfold. Subsequently, we summarise some nonlinear and numerical modelling approaches, validated for amplifying, contracting waves. These amplification phenomena observed have led us to develop a novel wave-energy device with wave amplification in a contraction used to enhance wave-activated buoy motion and magnetically induced energy generation. An experimental proof-of-principle shows that our wave-energy device works. Most importantly, we develop a novel wave-to-wire mathematical model of the combined wave hydrodynamics, wave-activated buoy motion and electric power generation by magnetic induction, from first principles, satisfying one grand variational principle in its conservative limit. Wave and buoy dynamics are coupled via a Lagrange multiplier, which boundary value at the waterline is in a subtle way solved explicitly by imposing incompressibility in a weak sense. Dissipative features, such as electrical wire resistance and nonlinear LED loads, are added a posteriori. New is also the intricate and compatible finite-element space–time discretisation of the linearised dynamics, guaranteeing numerical stability and the correct energy transfer between the three subsystems. Preliminary simulations of our simplified and linearised wave-energy model are encouraging and involve a first study of the resonant behaviour and parameter dependence of the device

Microneedle Array Design Determines the Induction of Protective Memory CD8+ T Cell Responses Induced by a Recombinant Live Malaria Vaccine in Mice

BACKGROUND: Vaccine delivery into the skin has received renewed interest due to ease of access to the immune system and microvasculature, however the stratum corneum (SC), must be breached for successful vaccination. This has been achieved by removing the SC by abrasion or scarification or by delivering the vaccine intradermally (ID) with traditional needle-and-syringes or with long microneedle devices. Microneedle patch-based transdermal vaccine studies have predominantly focused on antibody induction by inactivated or subunit vaccines. Here, our principal aim is to determine if the design of a microneedle patch affects the CD8(+) T cell responses to a malaria antigen induced by a live vaccine. METHODOLOGY AND FINDINGS: Recombinant modified vaccinia virus Ankara (MVA) expressing a malaria antigen was percutaneously administered to mice using a range of silicon microneedle patches, termed ImmuPatch, that differed in microneedle height, density, patch area and total pore volume. We demonstrate that microneedle arrays that have small total pore volumes induce a significantly greater proportion of central memory T cells that vigorously expand to secondary immunization. Microneedle-mediated vaccine priming induced significantly greater T cell immunity post-boost and equivalent protection against malaria challenge compared to ID vaccination. Notably, unlike ID administration, ImmuPatch-mediated vaccination did not induce inflammatory responses at the site of immunization or in draining lymph nodes. CONCLUSIONS/SIGNIFICANCE: This study demonstrates that the design of microneedle patches significantly influences the magnitude and memory of vaccine-induced CD8(+) T cell responses and can be optimised for the induction of desired immune responses. Furthermore, ImmuPatch-mediated delivery may be of benefit to reducing unwanted vaccine reactogenicity. In addition to the advantages of low cost and lack of pain, the development of optimised microneedle array designs for the induction of T cell responses by live vaccines aids the development of solutions to current obstacles of immunization programmes

Mouse Transgenesis Identifies Conserved Functional Enhancers and cis-Regulatory Motif in the Vertebrate LIM Homeobox Gene Lhx2 Locus

The vertebrate Lhx2 is a member of the LIM homeobox family of transcription factors. It is essential for the normal development of the forebrain, eye, olfactory system and liver as well for the differentiation of lymphoid cells. However, despite the highly restricted spatio-temporal expression pattern of Lhx2, nothing is known about its transcriptional regulation. In mammals and chicken, Crb2, Dennd1a and Lhx2 constitute a conserved linkage block, while the intervening Dennd1a is lost in the fugu Lhx2 locus. To identify functional enhancers of Lhx2, we predicted conserved noncoding elements (CNEs) in the human, mouse and fugu Crb2-Lhx2 loci and assayed their function in transgenic mouse at E11.5. Four of the eight CNE constructs tested functioned as tissue-specific enhancers in specific regions of the central nervous system and the dorsal root ganglia (DRG), recapitulating partial and overlapping expression patterns of Lhx2 and Crb2 genes. There was considerable overlap in the expression domains of the CNEs, which suggests that the CNEs are either redundant enhancers or regulating different genes in the locus. Using a large set of CNEs (810 CNEs) associated with transcription factor-encoding genes that express predominantly in the central nervous system, we predicted four over-represented 8-mer motifs that are likely to be associated with expression in the central nervous system. Mutation of one of them in a CNE that drove reporter expression in the neural tube and DRG abolished expression in both domains indicating that this motif is essential for expression in these domains. The failure of the four functional enhancers to recapitulate the complete expression pattern of Lhx2 at E11.5 indicates that there must be other Lhx2 enhancers that are either located outside the region investigated or divergent in mammals and fishes. Other approaches such as sequence comparison between multiple mammals are required to identify and characterize such enhancers