Jacobi equations using a variational principle

A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for the system. The approach can be of help in finding constants of motion in the Jacobi equations as well as in analysing the stability of the systems and can be related to the vertical extension of the Lagrangian formalism. To exemplify two of such aspects, we uncover a constant of motion in the Jacobi equations of autonomous systems and we recover the well-known sufficient conditions of stability of two dimensional orbits in classical mechanics.Comment: 7 pages, no figure

Electronic structure of periodic curved surfaces -- topological band structure

Electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface characterized completely in terms of "navels") but represent the topology of real systems such as zeolites and negative-curvature fullerene. The band structure turns out to be primarily determined by the topology of the surface, i.e., how the wavefunction interferes on a multiply-connected surface, so that the bands are little affected by the way in which we confine the electrons on the surface (thin-slab limit or zero thickness from the outset). Another curiosity is that different minimal surfaces connected by the Bonnet transformation (such as Schwarz's P- and D-surfaces) possess one-to-one correspondence in their band energies at Brillouin zone boundaries.Comment: 6 pages, 8 figures, eps files will be sent on request to [email protected]

From Euclidean to Minkowski space with the Cauchy-Riemann equations

We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from calculated Green's functions in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes is many times unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore we suggest to use the Cauchy-Riemann equations, that perform the analytical continuation without assuming global information on the function in the entire complex plane, only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge Quantum Chromodynamics, that is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations to high-frequency noise, that makes difficult to achieve good accuracy. We also point out a few curiosities related to the Wick rotation.Comment: 12 pages in EPJ double-column format, 16 figures. This version: added paragraph, two reference

Lagrangian Description of the Variational Equations

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. Our main result establishes that both the Euler-Lagrange equations and the corresponding variational equations of the original system can be viewed as the Lagrangian vector field associated with the first prolongation of the original LagrangianAfter discussing certain features of the formulation, we introduce the so-called inherited constants of the motion and relate them to the Noether constants of the extended system

Disease-specific, neurosphere-derived cells as models for brain disorders

There is a pressing need for patient-derived cell models of brain diseases that are relevant and robust enough to produce the large quantities of cells required for molecular and functional analyses. We describe here a new cell model based on patient-derived cells from the human olfactory mucosa, the organ of smell, which regenerates throughout life from neural stem cells. Olfactory mucosa biopsies were obtained from healthy controls and patients with either schizophrenia, a neurodevelopmental psychiatric disorder, or Parkinson's disease, a neurodegenerative disease. Biopsies were dissociated and grown as neurospheres in defined medium. Neurosphere-derived cell lines were grown in serum-containing medium as adherent monolayers and stored frozen. By comparing 42 patient and control cell lines we demonstrated significant disease-specific alterations in gene expression, protein expression and cell function, including dysregulated neurodevelopmental pathways in schizophrenia and dysregulated mitochondrial function, oxidative stress and xenobiotic metabolism in Parkinson's disease. The study has identified new candidate genes and cell pathways for future investigation. Fibroblasts from schizophrenia patients did not show these differences. Olfactory neurosphere-derived cells have many advantages over embryonic stem cells and induced pluripotent stem cells as models for brain diseases. They do not require genetic reprogramming and they can be obtained from adults with complex genetic diseases. They will be useful for understanding disease aetiology, for diagnostics and for drug discovery

Challenges in Complex Systems Science

FuturICT foundations are social science, complex systems science, and ICT. The main concerns and challenges in the science of complex systems in the context of FuturICT are laid out in this paper with special emphasis on the Complex Systems route to Social Sciences. This include complex systems having: many heterogeneous interacting parts; multiple scales; complicated transition laws; unexpected or unpredicted emergence; sensitive dependence on initial conditions; path-dependent dynamics; networked hierarchical connectivities; interaction of autonomous agents; self-organisation; non-equilibrium dynamics; combinatorial explosion; adaptivity to changing environments; co-evolving subsystems; ill-defined boundaries; and multilevel dynamics. In this context, science is seen as the process of abstracting the dynamics of systems from data. This presents many challenges including: data gathering by large-scale experiment, participatory sensing and social computation, managing huge distributed dynamic and heterogeneous databases; moving from data to dynamical models, going beyond correlations to cause-effect relationships, understanding the relationship between simple and comprehensive models with appropriate choices of variables, ensemble modeling and data assimilation, modeling systems of systems of systems with many levels between micro and macro; and formulating new approaches to prediction, forecasting, and risk, especially in systems that can reflect on and change their behaviour in response to predictions, and systems whose apparently predictable behaviour is disrupted by apparently unpredictable rare or extreme events. These challenges are part of the FuturICT agenda

Effectiveness of recovered magnesium phosphates as fertilizers in neutral and slightly alkaline soils

Magnesium phosphates such as struvite (MgNH4PO4 · 6H2O) can be recovered from municipal, industrial, and agricultural wastewaters. However, limited information is available on the beneficial reuse of these recovered products; research has focused on low pH soils. Th is study determined whether recovered struvite and dittmarite (MgNH4PO4 · H2O) were effective P fertilizers in neutral to slightly alkaline soils. In addition to commercially available triple superphosphate (TSP) and certified organic rock phosphate (RP), recovered struvite, dittmarite, and a heterogeneous recovered phosphate were evaluated in a laboratory dissolution study and as fertilizers for spring wheat (Triticum aestivum L.) in a greenhouse study. Struvite and dittmarite were much more soluble than RP, but less soluble than TSP. Laboratory dissolution kinetics were fast, with most materials nearing equilibrium within 7 to 14 d. At a soil pH of 6.5, both dittmarite and struvite increased the average plant P concentration over the control. Struvite and dittmarite performance was similar to TSP. There were no significant differences in plant dry matter (DM) production or total P uptake at pH 6.5. In the limed soil (pH 7.6), many treatments had plant P concentrations significantly lower than the control, but most fertilizers increased DM production over the control; all fertilizers generally performed similarly to one another. These findings support previous work showing recovered Mg phosphates to be effective in acidic soils, and provide evidence that they are also effective in slightly alkaline soils. Recovered Mg phosphates could become a useful alternative for P fertilization in arid and semiarid environments

From chemical gardens to chemobrionics

Chemical gardens in laboratory chemistries ranging from silicates to polyoxometalates, in applications ranging from corrosion products to the hydration of Portland cement, and in natural settings ranging from hydrothermal vents in the ocean depths to brinicles beneath sea ice. In many chemical-garden experiments, the structure forms as a solid seed of a soluble ionic compound dissolves in a solution containing another reactive ion. In general any alkali silicate solution can be used due to their high solubility at high pH. The cation should not precipitate with the counterion of the metal salt used as seed. A main property of seed chemical-garden experiments is that initially, when the fluid is not moving under buoyancy or osmosis, the delivery of the inner reactant is diffusion controlled. Another experimental technique that isolates one aspect of chemical-garden formation is to produce precipitation membranes between different aqueous solutions by introducing the two solutions on either side of an inert carrier matrix. Chemical gardens may be grown upon injection of solutions into a so-called Hele-Shaw cell, a quasi-two-dimensional reactor consisting in two parallel plates separated by a small gap

Equine Protozoal Myeloencephalitis: An Updated Consensus Statement with a Focus on Parasite Biology, Diagnosis, Treatment, and Prevention

Equine protozoal myeloencephalitis (EPM) remains an important neurologic disease of horses. There are no pathognomonic clinical signs for the disease. Affected horses can have focal or multifocal central nervous system (CNS) disease. EPM can be difficult to diagnose antemortem. It is caused by either of 2 parasites, Sarcocystis neurona and Neospora hughesi, with much less known about N. hughesi. Although risk factors such as transport stress and breed and age correlations have been identified, biologic factors such as genetic predispositions of individual animals, and parasite-specific factors such as strain differences in virulence, remain largely undetermined. This consensus statement update presents current published knowledge of the parasite biology, host immune response, disease pathogenesis, epidemiology, and risk factors. Importantly, the statement provides recommendations for EPM diagnosis, treatment, and prevention