Bulk and surface localized modes on a magnetic nonlinear impurity

We study localized modes on a single magnetic impurity positioned in the bulk or at the surface of a one-dimensional chain, in the presence of a magnetic field B acting at the impurity site. The strong on-site nonlinear interaction U between two electrons of opposite spin at the impurity site, modelled here as a nonlinear local term, and the presence of the external field induce a strong correlation between parallel and antiparallel spin bound states. We find that, for an impurity in the bulk, a localized vector mode (with up and down spin components) is always possible for any given value of U and B, while for a surface impurity, a minimum value of both, U and B is needed to create a vector mode. In this case, up to two localized modes are possible, but only one of them is stable. The presence of the surface seems to destabilize the bulk mode in the parameter region U∼B, creating a “forbidden strip” region in parameter space, bounded by U=B+V and U=B−V, approximately.     

Transition De Phase Metamagnetique Du Bromure Ferreux

In a magnetic field parallel to the magnetization axis of an antiferromagnetic Fe Br₂ single crystal, a caracteristic metamagnetic behaviour is observed. The transition from an antiferromagnetic phase to a paramagnetic phase is studied by help of magnetization measurements in a steady field (H < 60 kOe). The measurement precision has allowed a detailed study of the magnetization isotherms, caracteristic of a first order magnetization phase transition (T < T_c = 4, 7 K) and of a second order phase transition (T_c < T < T_N = 14, 2 K).We have observed an original phase diagram. In a certain temperature and field range, the ordered phase is stable on the high temperature side of the transition point. Some theoretical studies in an Ising model, or in the hypothesis of a strong magnetoelastic coupling forecast the existence of such a magnetic phase diagram.At present, we proceed to a theoretical study, in a molecular field approximation, of the magnetic phase diagram of compounds similar to Fe Br₂ where we take into account the relative values of parameters J₁, J₂ and D associated with ferromagnetic and antiferromagnetic interactions and crystalline anisotropy.     

Overlapping branes in M-theory

We construct new supersymmetric solutions of D = 11 supergravity describing n orthogonally “overlapping” membranes and fivebranes for n = 2,…,8. Overlapping branes arise after separating intersecting branes in a direction transverse to all of the branes. The solutions, which generalize known intersecting brane solutions, preserve at least 2⁻ⁿ of the supersymmetry. Each pairwise overlap involves a membrane overlapping a membrane in a 0-brane, a fivebrane overlapping a fivebrane in a 3-brane or a membrane overlapping a fivebrane in a string. After reducing n overlapping membranes to obtain n overlapping D-2-branes in D = 10, T-duality generates new overlapping D-brane solutions in type IIA and type IIB string theory. Uplifting certain type IIA solutions leads to the D = 11 solutions. Some of the new solutions reduce to dilaton black holes in D = 4. Additionally, we present a D = 10 solution that describes two D-5-branes overlapping in a string. T-duality then generates further D = 10 solutions and uplifting one of the type IIA solutions gives a new D = 11 solution describing two fivebranes overlapping in a string.     

Larc: A State Reduction Theory of Quantum Measurement

This proposes a new theory of Quantum measurement; a state reduction theory in which reduction is to the elements of the number operator basis of a system, triggered by the occurrence of annihilation or creation (or lowering or raising) operators in the time evolution of a system. It is from these operator types that the acronym ‘LARC’ is derived. Reduction does not occur immediately after the trigger event; it occurs at some later time with probability P _t per unit time, where P _t is very small. Localisation of macroscopic objects occurs in the natural way: photons from an illumination field are reflected off a body and later absorbed by another body. Each possible absorption of a photon by a molecule in the second body generates annihilation and raising operators, which in turn trigger a probability per unit time P _t of a state reduction into the number operator basis for the photon field and the number operator basis of the electron orbitals of the molecule. Since all photons in the illumination field have come from the location of the first body, wherever that is, a single reduction leads to a reduction of the position state of the first body relative to the second, with a total probability of mP _t , where m is the number of photon absorption events. Unusually for a reduction theory, the larc theory is naturally relativistic.     

Searching for a near neighbor particle in DSMC cells using pseudo-subcells

LeBeau et al. (2003) [4] introduced the ‘virtual-subcell’ (VSC) method of finding a collision partner for a given DSMC particle in a cell; all potential collision partners in the cell are examined to find the nearest neighbor, which becomes the collision partner. Here I propose a modification of the VSC method, the ‘pseudo-subcell’ (PSC) method, whereby the search for a collision partner stops whenever a ‘near-enough’ particle is found, i.e. whenever another particle is found within the ‘pseudo-subcell’ of radius δ centered on the first particle. The radius of the pseudo-subcell is given by δ = Fd_n, where d_n is the expected distance to the nearest neighbor and F is a constant which can be adjusted to give a desired trade-off between CPU time and accuracy as measured by a small mean collision separation (MCS). For 3D orthogonal cells, of various aspect ratios, d_n/L ≈ 0.746/N^0.383 where N is the number of particles in the cell and L is the cube root of the cell volume. There is a good chance that a particle will be found in the pseudo-subcell and there is a good chance that such a particle is in fact the nearest neighbor. If no particle is found within the pseudo-subcell the closest particle becomes the collision partner.     

Monte Carlo simulations of magnetic particle suspensions with a simple assessment method for the particle overlap between magnetic spheroids

We have developed a simple assessment method for the overlap between spheroidal particles, which neither requires the complex manipulation of vectors and matrices that is indispensable in the ordinary methods, nor is based on a model potential. Moreover, we have developed an evaluation method for the interaction energy arising from the overlap of the steric layer coating spheroidal particles. This is based on a sphere-connected particle model, but some modifications are introduced in order to express an appropriate repulsive interaction energy at the deepest overlapping position. We have investigated the phase change in a magnetic spheroidal particle suspension for a two-dimensional system by means of Monte Carlo simulations. In the case of no external magnetic field, if the magnetic particle-particle interaction is sufficiently strong to favour cluster formation, long raft-like clusters tend to be formed in a dilute situation. With decreasing values of area fraction, a chain-like structure in a dense situation transforms into a raft-like structure within a narrow range of the particle area fraction. Similarly, the raft-like clusters are preferred in a weak applied magnetic field, but an increase in the field strength induces a phase change from a raft-like into a chain-like structure.

Highlights of the present paper:

1. A simple assessment method has been proposed for the overlap between two spheroidal particles.

2. The particle overlap assessment is free from a complex mathematical manipulation regarding vectors and matrices.

3. A modified sphere-connected model has been proposed in order to more accurately evaluate a repulsive interaction due to the overlap of the steric layers coating spheroidal particles.

4. 2D Monte Carlo simulations have been performed to elucidate the phenomenon of a phase change by magnetic spheroidal particles on a material plane surface.

5. A phase change between a raft-like and a chain-like aggregate structure is able to be controlled by the area fraction of particles and an external magnetic field.

     

Modeling DNA and Virus Trafficking in the Cell Cytoplasm

Cytosol trafficking is a limiting step of viral infection or DNA delivery. Starting from the cell surface, most viruses have to travel through a crowded and risky environment in order to reach a small nuclear pore. This work is dedicated to estimating the probability p _N of a viral arrival success and, in that case, the mean time τ _N it takes. Viral movement is described by a stochastic equation, containing both a drift and a Brownian component. The drift part represents the movement along microtubules, while the Brownian component corresponds to the free diffusion. The success of a viral infection is limited by a killing activity occurring inside the cytoplasm. We model the killing activity by a steady state killing rate k. Because nuclear pores occupy a small fraction of the nuclear area, we use this property to obtain asymptotic estimates of p _N and τ _N as a function of the diffusion constant D, the amplitude of the drift B and the killing rate k. This paper is dedicated to my wife Nathalie Rouach. D. H. is supported by the program “Chaire d’Excellence.” D.H is incumbent to the Haas Russell Chair     

Existence and invariance of twisted products on a symplectic manifold

It is now well-known [1] that the twisted product on the functions defined on a symplectic manifold, play a fundamental role in an invariant approach of quantum mechanics. We prove here a general existence theorem of such twisted products. If a Lie group G acts by symplectomorphisms on a symplectic manifold and if there is a G-invariant symplectic connection, the manifold admits G-invariant Vey twisted products. In particular, if a homogeneous space G/H admits an invariant linear connection, T ^*(G/H) admits a G-invariant Vey twisted product. For the connected Lie group G, the group T ^*G admits a symplectic structure, a symplectic connection and a Vey twisted product which are bi-invariant under G.     

Spectral bundles and the DRY-Conjecture

Supersymmetric heterotic string models, built from a Calabi-Yau threefold X endowed with a stable vector bundle V, usually start from a phenomenologically motivated choice of a bundle V_v in the visible sector, the spectral cover construction on an elliptically fibered X being a prominent example. The ensuing anomaly mismatch between c₂(V_v) and c₂(X), or rather the corresponding differential forms, is often ‘solved’, on the cohomological level, by including a fivebrane. This leads to the question whether the difference can be alternatively realized by a further stable bundle. The ‘DRY’-conjecture of Douglas, Reinbacher and Yau in math.AG/0604597 gives a sufficient condition on cohomology classes on X to be realized as the Chern classes of a stable sheaf. In 1010.1644 [hep-th], we showed that infinitely many classes on X exist for which the conjecture is true. In this note, we give the sufficient condition for the mentioned fivebrane classes to be realized by a further stable bundle in the hidden sector. Using a result obtained in 1011.6246 [hep-th], we show that corresponding bundles exist, thereby confirming this version of the DRY-Conjecture.     

Shannon Entropy Loss in Mixed-Radix Conversions

This paper models a translation for base-2 pseudorandom number generators (PRNGs) to mixed-radix uses such as card shuffling. In particular, we explore a shuffler algorithm that relies on a sequence of uniformly distributed random inputs from a mixed-radix domain to implement a Fisher–Yates shuffle that calls for inputs from a base-2 PRNG. Entropy is lost through this mixed-radix conversion, which is assumed to be surjective mapping from a relatively large domain of size 2J to a set of arbitrary size n. Previous research evaluated the Shannon entropy loss of a similar mapping process, but this previous bound ignored the mixed-radix component of the original formulation, focusing only on a fixed n value. In this paper, we calculate a more precise formula that takes into account a variable target domain radix, n, and further derives a tighter bound on the Shannon entropy loss of the surjective map, while demonstrating monotonicity in a decrease in entropy loss based on increased size J of the source domain 2J. Lastly, this formulation is used to specify the optimal parameters to simulate a card-shuffling algorithm with different test PRNGs, validating a concrete use case with quantifiable deviations from maximal entropy, making it suitable to low-power implementation in a casino.     

Antiferromagnetic correlations in the cubic heavy fermion compound CeInCu2

CeInCu₂ is a heavy fermion compound close to magnetic instability. The electrical resistivity has aT ² behaviour between 1 and 2.5 K. and the AC field susceptibility has a faint maximum at 0.9 K, indicating the onset of coherence near 1 K for this compound. The magnetoresistance keeps a negative sign down to 0.3 K. Neutron inelastic scattering give a crystal field splitting of 90 K, with a doublet ground state, and a residual quasielastic linewidth of 0.3 meV.We have studied the resistivity, susceptibility and specific heat of some dilute solutions La_1–xCe_xInCu₂ and Y_1–xCe_xInCu₂. The spin-dependent part of the resistivity may be decomposed into a single impurity term plus a pair interaction term, the magnitude of which folows a Curie-Weiss law, as in classical spin glassesCuMn orAuFe.The magnetisation and susceptibility at low temperatures may be represented within the resonant level model, taking into account antiferromagnetic interactions. Finally, the specific heat of CeInCu₂ shows a bump near 2.3 K, absent for dilute solutions, which may also be interpreted by introducing a magnetic interaction term.     

A comment on the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T.D. Frank

The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and nonlinear Fokker-Planck equations, Physica A 331 (2004) 391]. Our comment centers on the claims of a “non-linear Markov process” and a “non-linear Fokker-Planck equation.” First, memory in transition densities is misidentified as a Markov process. Second, the paper assumes that one can derive a Fokker-Planck equation from a Chapman-Kolmogorov equation, but no proof was offered that a Chapman-Kolmogorov equation exists for the memory-dependent processes considered. A “non-linear Markov process” is claimed on the basis of a non-linear diffusion pde for a 1-point probability density. We show that, regardless of which initial value problem one may solve for the 1-point density, the resulting stochastic process, defined necessarily by the conditional probabilities (the transition probabilities), is either an ordinary linearly generated Markovian one, or else is a linearly generated non-Markovian process with memory. We provide explicit examples of diffusion coefficients that reflect both the Markovian and the memory-dependent cases. So there is neither a “non-linear Markov process”, nor a “non-linear Fokker-Planck equation” for a conditional probability density. The confusion rampant in the literature arises in part from labeling a non-linear diffusion equation for a 1-point probability density as “non-linear Fokker-Planck,” whereas neither a 1-point density nor an equation of motion for a 1-point density can define a stochastic process. In a closely related context, we point out that Borland misidentified a translation invariant 1-point probability density derived from a non-linear diffusion equation as a conditional probability density. Finally, in the Appendix A we present the theory of Fokker-Planck pdes and Chapman-Kolmogorov equations for stochastic processes with finite memory.     

Vertically emitting, dye-doped polymer laser in the green (λ ∼ 536 nm) with a second order distributed feedback grating fabricated by replica molding

Lasing in the green from a distributed feedback (DFB) structure, based upon a second order grating fabricated by replica molding in a dye-doped UV curable polymer, has been demonstrated. For a Bragg grating having a periodicity and depth of 360 ± 2 nm and 78 ± 5 nm, respectively, a coumarin 540-polymer laser operates at 535.6 nm, which is in agreement with calculations of the photonic band diagram for the structure. The fabricated laser exhibits a linewidth of 0.15 nm, a threshold pump fluence of ∼0.7 mJ cm⁻² at 355 nm, and a slope efficiency of ∼14%. Incorporation of the dye gain medium into a one- (or two-) dimensional photonic crystal and fabrication of the grating by replica molding at room temperature provides an inexpensive approach to fabricating polymer-based DFB lasers on flexible substrates of large area.     

Nanocrystalline nickel films with lotus leaf texture for superhydrophobic and low friction surfaces

Nanostructured Ni films with high hardness, high hydrophobicity and low coefficient of friction (COF) were fabricated. The surface texture of lotus leaf was replicated using a cellulose acetate film, on which a nanocrystalline (NC) Ni coating with a grain size of 30 ± 4 nm was electrodeposited to obtain a self-sustaining film with a hardness of 4.42 GPa. The surface texture of the NC Ni obtained in this way featured a high density (4 × 10³ mm⁻²) of conical protuberances with an average height of 10.0 ± 2.0 μm and a tip radius of 2.5 ± 0.5 μm. This structure increased the water repellency and reduced the COF, compared to smooth NC Ni surfaces. The application of a short-duration (120 s) electrodeposition process that deposited “Ni crowns” with a larger radius of 6.0 ± 0.5 μm on the protuberances, followed by a perfluoropolyether (PFPE) solution treatment succeeded in producing a surface texture consisting of nanotextured protuberances that resulted in a very high water contact angle of 156°, comparable to that of the superhydrophobic lotus leaf. Additionally, the microscale protuberances eliminated the initial high COF peaks observed when smooth NC Ni films were tested, and the PFPE treatment resulted in a 60% reduction in the steady-state COFs.     

How to test for diagonalizability: the discretized PT-invariant square-well potential

Given a non-Hermitian matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note explains how to determine the minimal polynomial of a matrix without going through its characteristic polynomial. The approach is applied to a quantum mechanical particle moving in a square well under the influence of a piece-wise constant PT-symmetric potential. Upon discretizing the configuration space, the system is described by a matrix of dimension three which turns out not to be diagonalizable for a critical strength of the interaction. The systems develops a three-fold degenerate eigenvalue, and two of the three eigenfunctions disappear at this exceptional point, giving a difference between the algebraic and geometric multiplicity of the eigenvalue equal to two. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Using capillary forces to estimate the adhesion strength of Magnaporthe grisea spores on glass

The Magnaporthe grisea is a fungus whose spores strongly adhere to plant leaves, and to solid surfaces in general. In this note, we give an estimate of the adhesion force, F_det, of a spore on a glass surface, in water. F_det is defined as the force to be applied to a spore to pull it out from the surface. In our experiments, spores are detached from the glass in a few milliseconds by means of a capillary force. The latter is provided by a water/air or a water/oil interface, in contact with the spore body. We thus find F_det of the order of 10⁻⁶ N.     

Symmetry and Topology in Quantum Logic

A test space is a collection of non-empty sets, usually construed as the catalogue of (discrete) outcome sets associated with a family of experiments. Subject to a simple combinatorial condition called algebraicity, a test space gives rise to a “quantum logic”—that is, an orthoalgebra. Conversely, all orthoalgebras arise naturally from algebraic test spaces. In non-relativistic quantum mechanics, the relevant test space is the set ℱ F(H) of frames (unordered orthonormal bases) of a Hilbert space H. The corresponding logic is the usual one, i.e., the projection lattice L(H) of H. The test space ℱ F(H) has a strong symmetry property with respect to the unitary group of H, namely, that any bijection between two frames lifts to a unitary operator. In this paper, we consider test spaces enjoying the same symmetry property relative to an action by a compact topological group. We show that such a test space, if algebraic, gives rise to a compact, atomistic topological orthoalgebra. We also present a construction that generates such a test space from purely group-theoretic data, and obtain a simple criterion for this test space to be algebraic. PACS: 02.10.Ab; 02.20.Bb; 03.65.Ta.