Fluctuations and Instabilities of Ferromagnetic Domain Wall pairs in an External Magnetic Field

Soliton excitations and their stability in anisotropic quasi-1D ferromagnets are analyzed analytically. In the presence of an external magnetic field, the lowest lying topological excitations are shown to be either soliton-soliton or soliton-antisoliton pairs. In ferromagnetic samples of macro- or mesoscopic size, these configurations correspond to twisted or untwisted pairs of Bloch walls. It is shown that the fluctuations around these configurations are governed by the same set of operators. The soliton-antisoliton pair has exactly one unstable mode and thus represents a critical nucleus for thermally activated magnetization reversal in effectively one-dimensional systems. The soliton-soliton pair is stable for small external fields but becomes unstable for large magnetic fields. From the detailed expression of this instability threshold and an analysis of nonlocal demagnetizing effects it is shown that the relative chirality of domain walls can be detected experimentally in thin ferromagnetic films. The static properties of the present model are equivalent to those of a nonlinear sigma-model with anisotropies. In the limit of large hard-axis anisotropy the model reduces to a double sine-Gordon model.Comment: 15 pages RevTex 3.0 (twocolumn), 9 figures available on request, to appear in Phys Rev B, Dec (1994

Macroscopic Quantum Tunneling of Ferromagnetic Domain Walls

Quantum tunneling of domain walls out of an impurity potential in a mesoscopic ferromagnetic sample is investigated. Using improved expressions for the domain wall mass and for the pinning potential, we find that the cross-over temperature between thermal activation and quantum tunneling is of a different functional form than found previously. In materials like Ni or YIG, the crossover temperatures are around 5 mK. We also find that the WKB exponent is typically two orders of magnitude larger than current estimates. The sources for these discrepancies are discussed, and precise estimates for the transition from three-dimensional to one-dimensional magnetic behavior of a wire are given. The cross-over temperatures from thermal to quantum transitions and tunneling rates are calculated for various materials and sample sizes.Comment: 10 pages, 2 postscript figures, REVTe

A Product Formula for the Normalized Volume of Free Sums of Lattice Polytopes

The free sum is a basic geometric operation among convex polytopes. This note focuses on the relationship between the normalized volume of the free sum and that of the summands. In particular, we show that the normalized volume of the free sum of full dimensional polytopes is precisely the product of the normalized volumes of the summands.Comment: Published in the proceedings of 2017 Southern Regional Algebra Conferenc

Statistical Mechanics of Nonuniform Magnetization Reversal

The magnetization reversal rate via thermal creation of soliton pairs in quasi-1D ferromagnetic systems is calculated. Such a model describes e.g. the time dependent coercivity of elongated particles as used in magnetic recording media. The energy barrier that has to be overcome by thermal fluctuations corresponds to a soliton-antisoliton pair whose size depends on the external field. In contrast to other models of first order phase transitions such as the phi^4 model, an analytical expression for this energy barrier is found for all values of the external field. The magnetization reversal rate is calculated using a functional Fokker-Planck description of the stochastic magnetization dynamics. Analytical results are obtained in the limits of small fields and fields close to the anisotropy field. In the former case the hard-axis anisotropy becomes effectively strong and the magnetization reversal rate is shown to reduce to the nucleation rate of soliton-antisoliton pairs in the overdamped double sine-Gordon model. The present theory therefore includes the nucleation rate of soliton-antisoliton pairs in the double sine-Gordon chain as a special case. These results demonstrate that for elongated particles, the experimentally observed coercivity is significantly lower than the value predicted by the standard theories of N\'eel and Brown.Comment: 21 pages RevTex 3.0 (twocolumn), 6 figures available on request, to appear in Phys Rev B, Dec (1994

Berry's phase and Quantum Dynamics of Ferromagnetic Solitons

We study spin parity effects and the quantum propagation of solitons (Bloch walls) in quasi-one dimensional ferromagnets. Within a coherent state path integral approach we derive a quantum field theory for nonuniform spin configurations. The effective action for the soliton position is shown to contain a gauge potential due to the Berry phase and a damping term caused by the interaction between soliton and spin waves. For temperatures below the anisotropy gap this dissipation reduces to a pure soliton mass renormalization. The gauge potential strongly affects the quantum dynamics of the soliton in a periodic lattice or pinning potential. For half-integer spin, destructive interference between soliton states of opposite chirality suppresses nearest neighbor hopping. Thus the Brillouin zone is halved, and for small mixing of the chiralities the dispersion reveals a surprising dynamical correlation: Two subsequent band minima belong to different chirality states of the soliton. For integer spin, the Berry phase is inoperative and a simple tight-binding dispersion is obtained. Finally it is shown that external fields can be used to interpolate continuously between the Bloch wall dispersions for half-integer and integer spin.Comment: 20 pages, RevTex 3.0 (twocolumn), to appear in Phys. Rev. B 53, 3237 (1996), 4 PS figures available upon reques

Do High-Velocity Clouds trace the Dark Matter subhalo population?

Within the cosmological concordance model, Cold Dark Matter (CDM) subhalos form the building blocks which merge hierarchically to more massive galaxies. Since intergalactic gas is accreted by massive galaxies, observable e.g. as high- velocity clouds (HVCs) around the Milky Way, with extremely low metallicities, these can be suggested to represent the baryonic content of primordial Dark Matter (DM) subhalos. Another possibility of their origin is that they stem from disrupted satellite galaxies, but in this case, these gas clouds move unaccompanied by a bound DM structure. Since HVCs are observed with long gas tails and with irregular substructures, numerical models are performed aiming at exploring their structure and compare them with observations. If HVCs are engulfed by DM subhalos, their gas must leave the DM gravitational potential and reflect this in their dynamics. On the other hand, the evolution and survival of pure gas models must be tested to distinguish between DM-dominated and DM-free clouds and to allow conclusions on their origin. The models demonstrate that purely baryonic HVCs with low masses are disrupted by ram-pressure stripping and Kelvin-Helmholtz instabilities, while more massive ones survive, losing their initially spherical shape and develop significant substructures including cometary elongations in the column density distribution ("head-tail structure"). On the contrary, HVCs with DM subhalos survive with more than 90% of their gas mass still bound and spherically shaped, approaching the Galactic disk like bullets. In addition, we find that velocity gradients along the cometary head-tail structures does not necessarily offer a possibility to distinguish between DM-dominated and purely gaseous HVCs. Comparison of models with observations let us conclude that HVCs are not embedded in a DM substructure and do not trace the cosmological subhalo population.Comment: Accepted for publication in A&

Two New X-ray/Optical/Radio Supernova Remnants in M31

We compare a deep (37 ks) Chandra ACIS-S image of the M31 bulge to Local Group Survey narrow-band optical data and Very Large Array (VLA) radio data of the same region. Our precisely registered images reveal two new optical shells with X-ray counterparts. These shells have sizes, [S II]/H-alpha flux ratios, and X-ray spectral properties typical of supernova remnants (SNRs) with ages of 9$^{+3}_{-4}$ and 17$^{+6}_{-9}$ kyr. Analysis of complementary VLA data reveals the radio counterparts, further confirming that they are SNRs. We discuss and compare the properties and morphologies of these SNRs at the different wavelengths.Comment: 18 pages, 5 figures, accepted for publication in Ap

A Collaborative Model for Accelerating the Discovery and Translation of Cancer Therapies

Preclinical studies using genetically engineered mouse models (GEMM) have the potential to expedite the development of effective new therapies; however, they are not routinely integrated into drug development pipelines. GEMMs may be particularly valuable for investigating treatments for less common cancers, which frequently lack alternative faithful models. Here, we describe a multicenter cooperative group that has successfully leveraged the expertise and resources from philanthropic foundations, academia, and industry to advance therapeutic discovery and translation using GEMMs as a preclinical platform. This effort, known as the Neurofibromatosis Preclinical Consortium (NFPC), was established to accelerate new treatments for tumors associated with neurofibromatosis type 1 (NF1). At its inception, there were no effective treatments for NF1 and few promising approaches on the horizon. Since 2008, participating laboratories have conducted 95 preclinical trials of 38 drugs or combinations through collaborations with 18 pharmaceutical companies. Importantly, these studies have identified 13 therapeutic targets, which have inspired 16 clinical trials. This review outlines the opportunities and challenges of building this type of consortium and highlights how it can accelerate clinical translation. We believe that this strategy of foundation-academic-industry partnering is generally applicable to many diseases and has the potential to markedly improve the success of therapeutic development

On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin