Interaction of point sources and vortices for incompressible planar fluids

We consider a new system of differential equations which is at the same time gradient and locally Hamiltonian. It is obtained by just replacing a factor in the equations of interaction for N point vortices, and it is interpreted as an interaction of N point sources. Because of the local Hamiltonian structure and the symmetries it obeys, it does possess some of the first integrals that appear in the N vortex problem. We will show that binary collisions are easily blown up in this case since the equations of motion are of first order. This method may be easily generalized to the blow up of higher order collisions. We then generalize the model further to interactions of sources and vortices.Comment: 9 page

Vortex crystals

Vortex crystals is one name in use for the subject of vortex patterns that move without change of shape or size. Most of what is known pertains to the case of arrays of parallel line vortices moving so as to produce an essentially two-dimensional flow. The possible patterns of points indicating the intersections of these vortices with a plane perpendicular to them have been studied for almost 150 years. Analog experiments have been devised, and experiments with vortices in a variety of fluids have been performed. Some of the states observed are understood analytically. Others have been found computationally to high precision. Our degree of understanding of these patterns varies considerably. Surprising connections to the zeros of 'special functions' arising in classical mathematical physics have been revealed. Vortex motion on two-dimensional manifolds, such as the sphere, the cylinder (periodic strip) and torus (periodic parallelogram) has also been studied, because of the potential applications, and some results are available regarding the problem of vortex crystals in such geometries. Although a large amount of material is available for review, some results are reported here for the first time. The subject seems pregnant with possibilities for further development.published or submitted for publicationis peer reviewe

A Sawtooth Permanent Magnetic Lattice for Ultracold Atoms and BECs

We propose a new permanent magnetic lattice for creating periodic arrays of Ioffe-Pritchard permanent magnetic microtraps for holding and controlling ultracold atoms and Bose-Einstein condensates (BECs). Lattice can be designed on thin layer of magnetic films such as $Tb_6$$Gd_10$$Fe_{80}$$Co_4$. In details, we investigate single layer and two crossed layers of sawtooth magnetic patterns with thicknesses of 50 and 500nm respectively with a periodicity of 1$\mu$m. Trap depth and frequencies can be changed via an applied bias field to handle tunneling rates between lattice sites. We present analytical expressions and using numerical calculations show that this lattice has non-zero potential minima to avoid majorana spin flips. One advantage of this lattice over previous ones is that it is easier to manufacture.Comment: 8 pages, 6 figure

Viscous evolution of point vortex equilibria: The collinear state

When point vortex equilibria of the 2D Euler equations are used as initial conditions for the corre- sponding Navier-Stokes equations (viscous), typically an interesting dynamical process unfolds at short and intermediate time scales, before the long time single peaked, self-similar Oseen vortex state dom- inates. In this paper, we describe the viscous evolution of a collinear three vortex structure that cor- responds to an inviscid point vortex fixed equilibrium. Using a multi-Gaussian 'core-growth' type of model, we show that the system immediately begins to rotate unsteadily, a mechanism we attribute to a 'viscously induced' instability. We then examine in detail the qualitative and quantitative evolution of the system as it evolves toward the long-time asymptotic Lamb-Oseen state, showing the sequence of topological bifurcations that occur both in a fixed reference frame, and in an appropriately chosen rotating reference frame. The evolution of passive particles in this viscously evolving flow is shown and interpreted in relation to these evolving streamline patterns.Comment: 17 pages, 15 figure

Measles to the Rescue: A Review of Oncolytic Measles Virus

Oncolytic virotherapeutic agents are likely to become serious contenders in cancer treatment. The vaccine strain of measles virus is an agent with an impressive range of oncolytic activity in pre-clinical trials with increasing evidence of safety and efficacy in early clinical trials. This paramyxovirus vaccine has a proven safety record and is amenable to careful genetic modification in the laboratory. Overexpression of the measles virus (MV) receptor CD46 in many tumour cells may direct the virus to preferentially enter transformed cells and there is increasing awareness of the importance of nectin-4 and signaling lymphocytic activation molecule (SLAM) in oncolysis. Successful attempts to retarget MV by inserting genes for tumour-specific ligands to antigens such as carcinoembryonic antigen (CEA), CD20, CD38, and by engineering the virus to express synthetic microRNA targeting sequences, and "blinding" the virus to the natural viral receptors are exciting measures to increase viral specificity and enhance the oncolytic effect. Sodium iodine symporter (NIS) can also be expressed by MV, which enables in vivo tracking of MV infection. Radiovirotherapy using MV-NIS, chemo-virotherapy to convert prodrugs to their toxic metabolites, and immune-virotherapy including incorporating antibodies against immune checkpoint inhibitors can also increase the oncolytic potential. Anti-viral host immune responses are a recognized barrier to the success of MV, and approaches such as transporting MV to the tumour sites by carrier cells, are showing promise. MV Clinical trials are producing encouraging preliminary results in ovarian cancer, myeloma and cutaneous non-Hodgkin lymphoma, and the outcome of currently open trials in glioblastoma multiforme, mesothelioma and squamous cell carcinoma are eagerly anticipated