Motion of magnetotactic bacteria swarms in an external field

Magnetotactic bacteria moving on circular orbits form hydrodynamically bound states. When close to a surface and with the tilting of the field in a direction close to the perpendicular to this surface these swarms move perpendicularly to the tilting angle. We describe quantitatively this motion by a continuum model with couple stress arising from the torques produced by the rotary motors of the amphitrichous magnetotactic bacteria. The model not only correctly describes the change of direction of swarm motion while inverting the tangential field but also predicts reasonable value of the torque produced by the rotary motors

Gyromagnetic effects in dynamics of magnetic microparticles

We derive equations of motion for paramagnetic and ferromagnetic particles fully accounting for gyromagnetic effects. Considering the Einstein-de Haas effect for an ellipsoidal paramagnetic particle we find that starting from a quiescent non-magnetized state, after the field is switched on a rotation along the short axis is established. This is confirmed by the stability analysis of the fixed points of the corresponding ordinary differential equations. In the case of a ferromagnetic particle we integrate the equations of motion in the dissipationless case by finding the integrals of motion. We also reformulate the equations in a Hamiltonian framework in this case and find a period of small nutation oscillations.Comment: 24 pages, 15 figure

On the polynomial parity argument complexity of the combinatorial nullstellensatz

The complexity class PPA consists of NP-search problems which are reducible to the parity principle in undirected graphs. It contains a wide variety of interesting problems from graph theory, combinatorics, algebra and number theory, but only a few of these are known to be complete in the class. Before this work, the known complete problems were all discretizations or combinatorial analogues of topological fixed point theorems. Here we prove the PPA-completeness of two problems of radically different style. They are PPA-Circuit CNSS and PPA-Circuit Chevalley, related respectively to the Combinatorial Nullstellensatz and to the Chevalley-Warning Theorem over the two elements field GF(2). The input of these problems contain PPA-circuits which are arithmetic circuits with special symmetric properties that assure that the polynomials computed by them have always an even number of zeros. In the proof of the result we relate the multilinear degree of the polynomials to the parity of the maximal parse subcircuits that compute monomials with maximal multilinear degree, and we show that the maximal parse subcircuits of a PPA-circuit can be paired in polynomial time

Degenerate matrices methods by splines for boundary values problems of ordinary differential equations

A method for numerical solving of boundary values problems of ordinary differential equations based on the use of splines and differentiation matrices with nodes as zeroes of classical orthogonal polynomials is considered. Possibilities of the method are shown by means of different examples. The method essentially uses the results obtained by Degenerate Matrices methods and it is applied for solving initial values problems of ordinary differential equations. Darbe nagrinejamas paprastuju lygčiu su kraštinemis salygomis skaitinis sprendimo metodas. Šio metodo pagrinda sudaro nereguliariuju matricu bei splainu konstravimas klasikiniu ortogonaliuju polinomu pavidalu. Nagrinejamo straipsnyje metodo taikymo galimybes parodytos ivairiais pavyzdžiais. First Published Online: 14 Oct 201

Quantum Coupon Collector

We study how efficiently a k-element set S?[n] can be learned from a uniform superposition |S> of its elements. One can think of |S>=?_{i?S}|i>/?|S| as the quantum version of a uniformly random sample over S, as in the classical analysis of the "coupon collector problem." We show that if k is close to n, then we can learn S using asymptotically fewer quantum samples than random samples. In particular, if there are n-k=O(1) missing elements then O(k) copies of |S> suffice, in contrast to the ?(k log k) random samples needed by a classical coupon collector. On the other hand, if n-k=?(k), then ?(k log k) quantum samples are necessary. More generally, we give tight bounds on the number of quantum samples needed for every k and n, and we give efficient quantum learning algorithms. We also give tight bounds in the model where we can additionally reflect through |S>. Finally, we relate coupon collection to a known example separating proper and improper PAC learning that turns out to show no separation in the quantum case

Efficient Distributed Quantum Computing

We provide algorithms for efficiently addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the circuit model can be used by algorithm designers without worrying whether the underlying architecture supports the connectivity of the circuit. In addition, we apply our results to existing memory intensive quantum algorithms. We present a parallel quantum search algorithm and improve the time-space trade-off for the Element Distinctness and Collision problems.Comment: Some material rearranged and references adde

From SICs and MUBs to Eddington

This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.Comment: 12 pages; from the Festschrift for Tony Sudber

Practical implementation of a quantum backtracking algorithm

In previous work, Montanaro presented a method to obtain quantum speedups for backtracking algorithms, a general meta-algorithm to solve constraint satisfaction problems (CSPs). In this work, we derive a space efficient implementation of this method. Assume that we want to solve a CSP with $m$ constraints on $n$ variables and that the union of the domains in which these variables take their value is of cardinality $d$. Then, we show that the implementation of Montanaro's backtracking algorithm can be done by using $O(n \log d)$ data qubits. We detail an implementation of the predicate associated to the CSP with an additional register of $O(\log m)$ qubits. We explicit our implementation for graph coloring and SAT problems, and present simulation results. Finally, we discuss the impact of the usage of static and dynamic variable ordering heuristics in the quantum setting.Comment: 18 pages, 10 figure

Magnetic micro-swimmers propelling through bio-rheological liquid bounded within an active channel

The dynamics of a micro-organism swimming through a channel with undulating walls subject to constant transverse applied magnetic field is investigated. The micro-organism is modeled as self-propelling undulating sheet which is out of phase with the channel waves while the electrically conducting biofluid (through which micro-swimmers propel) is characterized by the non-Newtonian shear-rate dependent Carreau fluid model. Creeping flow is mobilized in the channel due to the self-propulsion of the micro-organism and the undulatory motion of narrow gapped walls. Under these conditions the conservation equations are formulated under the long wavelength and low Reynolds number assumptions. The speed of the self-propelling sheet and the rate of work done at higher values of rheological parameters are obtained by using a hybrid numerical technique (MATLAB routine bvp-4c combined with a modified Newton-Raphson method). The results are validated through an alternative hybrid numerical scheme (implicit finite difference method (FDM) in conjunction with a modified Newton-Raphson method). The assisting role of magnetic field and rheological effects of the surrounding biofluid on the swimming mode are shown graphically and interpreted at length. The global behavior of biofluid is also expounded via visualization of the streamlines in both regions (above and below the swimming sheet) for realistic micro-organism speeds. The computations reveal that optimal swimming conditions for the micro-organism (i.e., greater speed with lower energy losses) are achievable in magnetohydrodynamic (MHD) environments including magnetic field-assisted cervical treatments. Keywords: Micro-organism; peristaltic (active) channel; Carreau fluid; Swimming speed; biomagnetohydrodynamics (bioMHD); Rate of work done; Hybrid numerical method, Newton-Raphson method; Cervical magnetic therap