Dynamics of semiclassical Bloch wave - packets

The semiclassical approximation for electron wave-packets in crystals leads to equations which can be derived from a Lagrangian or, under suitable regularity conditions, in a Hamiltonian framework. In the plane, these issues are studied %in presence of external fields using the method of the coadjoint orbit applied to the ``enlarged'' Galilei group.Comment: 15 pages, Talk given at Nonlinear Physics. Theory and Experiment. IV,Gallipoli (Lecce), Italy - June 22 - July 1, 200

Non-commutative mechanics and Exotic Galilean symmetry

In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological contexts are covered. The non-commutativity of the particle position coordinates are a natural consequence. Some explicit examples are considered.Comment: 15 pages, Talk given at Nonlinear Physics. Theory and Experiment VI,Gallipoli (Lecce), Italy, June 23 - July 3, 201

Increased release time of antibiotics from bone allografts through a novel biodegradable coating

Theuse of bone allografts is contraindicated in septic revision surgery due to the high risk of graft reinfection.Antibiotic release from the graft may solve the problem and these combinations can theoretically be used for prevention or even therapy of infection.The present study investigated whether amoxicillin, ciprofloxacin, and vancomycin alone or in combination with chitosan or alginate are suitable for short-term or long-term bone coating. Human bone allografts were prepared from femoral head and lyophilized. Antibiotic coating was achieved by incubating the grafts in antibiotic solution and freeze-drying again. Two biopolymers chitosan and alginate were used for creating sustained-release implantable coatings and the drug release profile was characterized in vitro by spectrophotometry. Using lyophilization with or without chitosan only resulted in short-term release that lasted up to 48 hours. Alginate coating enabled a sustained release that lasted for 8 days with amoxicillin, 28 days with ciprofloxacin coating, and 50 days with vancomycin coating. Using only implantable biodegradable allograft and polymers, a sustained release of antibiotics was achieved with ciprofloxacin and vancomycin for several weeks. Since the calculated daily release of the antibiotic was lower than the recommended IV dose, the calcium alginate coated bone graft can support endoprosthesis revision surgery

Transverse Shifts in Paraxial Spinoptics

The paraxial approximation of a classical spinning photon is shown to yield an "exotic particle" in the plane transverse to the propagation. The previously proposed and observed position shift between media with different refractive indices is modified when the interface is curved, and there also appears a novel, momentum [direction] shift. The laws of thin lenses are modified accordingly.Comment: 3 pages, no figures. One detail clarified, some misprints corrected and references adde

Spinor vortices in non-relativistic Chern-Simons theory

The non-relativistic `Dirac' equation of L\'evy-Leblond is used to describe a spin {\small 1/2} particle interacting with a Chern-Simons gauge field. Static, purely magnetic, self-dual spinor vortices are constructed. The solution can be `exported' to a uniform magnetic background field.Comment: 7 pages, Plain Te

Lowest weight representations of super Schrodinger algebras in low dimensional spacetime

We investigate the lowest weight representations of the super Schrodinger algebras introduced by Duval and Horvathy. This is done by the same procedure as the semisimple Lie algebras. Namely, all singular vectors within the Verma modules are constructed explicitly then irreducibility of the associated quotient modules is studied again by the use of singular vectors. We present the classification of irreducible Verma modules for the super Schrodinger algebras in (1+1) and (2+1) dimensional spacetime with N = 1, 2 extensions.Comment: 10pages, talk given at GROUP28 conference New Castle 26-30th July 2010, reference adde

Path Integrals and Their Application to Dissipative Quantum Systems

Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time Path Integral Dissipative Systems - Introduction - Environment as Collection of Harmonic Oscillators - Effective Action Damped Harmonic Oscillator - Partition Function - Ground State Energy and Density of States - Position Autocorrelation FunctionComment: 55 pages, 13 figures. To be published in "Coherent Evolution in Noisy Environments", Lecture Notes in Physics (http://link.springer.de/series/lnpp/) (Springer Verlag, Berlin-Heidelberg-New York

Celestial Mechanics, Conformal Structures, and Gravitational Waves

The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly constant null vector. Such a spacetime admits a Bargmann structure and corresponds physically to a generalized pp-wave. Bargmann electromagnetism in five dimensions comprises the two Galilean electro-magnetic theories (Le Bellac and L\'evy-Leblond). At the quantum level, the $N$-body Schr\"odinger equation retains the form of a massless wave equation. We exploit the conformal symmetries of such spacetimes to discuss some properties of the Newtonian $N$-body problem: homographic solutions, the virial theorem, Kepler's third law, the Lagrange-Laplace-Runge-Lenz vector arising from three conformal Killing 2-tensors, and motions under inverse square law forces with a gravitational constant $G(t)$ varying inversely as time (Dirac). The latter problem is reduced to one with time independent forces for a rescaled position vector and a new time variable; this transformation (Vinti and Lynden-Bell) arises from a conformal transformation preserving the Ricci-flatness (Brinkmann). A Ricci-flat metric representing $N$ non-relativistic gravitational dyons is also pointed out. Our results for general time-dependent $G(t)$ are applicable to the motion of point particles in an expanding universe. Finally we extend these results to the quantum regime.Comment: 26 pages, LaTe

The Effects of Hyperacute Serum on the Elements of the Human Subchondral Bone Marrow Niche

Mesenchymal stem cells (MSCs) are widely used in laboratory experiments as well as in human cell therapy. Their culture requires animal sera like fetal calf serum (FCS) as essential supplementation; however, animal sera pose a risk for clinical applications. Human blood derivatives, for example, platelet-rich plasma (PRP) releasates, are potential replacements of FCS; however, it is unclear which serum variant has the best effect on the given cell or tissue type. Additionally, blood derivatives are commonly used in musculoskeletal diseases like osteoarthritis (OA) or osteonecrosis as "proliferative agents" for the topical MSC pool. Hyperacute serum (HAS), a new serum derivative, has been designed to approximate the natural coagulation cascade with a single-step, additive-free preparation method. We investigated the effects of HAS on monolayer MSC cultures and in their natural niche, in 3D subchondral bone and marrow explants. Viability measurements, RT-qPCR evaluation for gene expression and flow cytometry for cell surface marker analysis were performed to compare the effects of FCS-, PRP-, or HAS-supplemented culture media. Monolayer MSCs showed significantly higher metabolic activity following 5 days' incubation in HAS, and osteoblast-specific mRNA expression was markedly increased, while cells also retained their MSC-specific cell surface markers. A similar effect was observed on bone and marrow explants, which was further confirmed with confocal microscopy analysis. Moreover, markedly higher bone marrow preservation was observed with histology in case of HAS supplementation compared to FCS. These findings indicate possible application of HAS in regenerative solutions of skeletal diseases like OA or osteonecrosis