Biot-Savart-like law in electrostatics

The Biot-Savart law is a well-known and powerful theoretical tool used to calculate magnetic fields due to currents in magnetostatics. We extend the range of applicability and the formal structure of the Biot-Savart law to electrostatics by deriving a Biot-Savart-like law suitable for calculating electric fields. We show that, under certain circumstances, the traditional Dirichlet problem can be mapped onto a much simpler Biot-Savart-like problem. We find an integral expression for the electric field due to an arbitrarily shaped, planar region kept at a fixed electric potential, in an otherwise grounded plane. As a by-product we present a very simple formula to compute the field produced in the plane defined by such a region. We illustrate the usefulness of our approach by calculating the electric field produced by planar regions of a few nontrivial shapes.Comment: 14 pages, 6 figures, RevTex, accepted for publication in the European Journal of Physic

Possible potentials responsible for stable circular relativistic orbits

Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In the present article an attempt has been made to generalize Bertrand's theorem to the central force problem of relativistic systems. The stability criterion for potentials which can produce stable, circular orbits in the relativistic central force problem has been deduced and a general solution of it is presented in the article. It is seen that the inverse square law passes the relativistic test but the kind of force required for simple harmonic motion does not. Special relativistic effects do not allow stable, circular orbits in presence of a force which is proportional to the negative of the displacement of the particle from the potential center.Comment: 11 pages, Latex fil

Managing structural uncertainty in health economic decision models: a discrepancy approach

Healthcare resource allocation decisions are commonly informed by computer model predictions of population mean costs and health effects. It is common to quantify the uncertainty in the prediction due to uncertain model inputs, but methods for quantifying uncertainty due to inadequacies in model structure are less well developed. We introduce an example of a model that aims to predict the costs and health effects of a physical activity promoting intervention. Our goal is to develop a framework in which we can manage our uncertainty about the costs and health effects due to deficiencies in the model structure. We describe the concept of `model discrepancy': the difference between the model evaluated at its true inputs, and the true costs and health effects. We then propose a method for quantifying discrepancy based on decomposing the cost-effectiveness model into a series of sub-functions, and considering potential error at each sub-function. We use a variance based sensitivity analysis to locate important sources of discrepancy within the model in order to guide model refinement. The resulting improved model is judged to contain less structural error, and the distribution on the model output better reflects our true uncertainty about the costs and effects of the intervention

Stokes-space formalism for Bragg scattering in a fiber

Optical frequency conversion by four-wave mixing (Bragg scattering) in a fiber is considered. The evolution of this process can be modeled using the signal and idler amplitudes, which are complex, or Stokes-like parameters, which are real. The Stokes-space formalism allows one to visualize power and phase information simultaneously, and produces a simple evolution equation for the Stokes parameters

Kinetic pinning and biological antifreezes

Biological antifreezes protect cold-water organisms from freezing. An example are the antifreeze proteins (AFPs) that attach to the surface of ice crystals and arrest growth. The mechanism for growth arrest has not been heretofore understood in a quantitative way. We present a complete theory based on a kinetic model. We use the `stones on a pillow' picture. Our theory of the suppression of the freezing point as a function of the concentration of the AFP is quantitatively accurate. It gives a correct description of the dependence of the freezing point suppression on the geometry of the protein, and might lead to advances in design of synthetic AFPs.Comment: 4 pages, 4 figure

Derivation of the Lorentz Force Law, the Magnetic Field Concept and the Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation

It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. This formalism, making essential use of the 4-vector electromagnetic potential concept, provides a short derivation of the Lorentz force law of classical electrodynamics, the conventional definition of the magnetic field, in terms of spatial derivatives of the 4--vector potential and the Faraday-Lenz Law. An important distinction between the physical meanings of the space-time and energy-momentum 4--vectors is pointed out.Comment: 15 pages, no tables 1 figure. Revised and extended version of physics/0307133 Some typos removed and minor text improvements in this versio

Improving Medication Management after a Hospitalization with Pharmacist Home Visits and Electronic Personal Health Records: An Observational Study

Background: Substantial opportunity exists to improve medication management in the period following a hospital discharge. The objective of this study was to assess and improve medication management during care transitions through pharmacist home visits and the use of an electronic personal health record (ePHR) system. Methods: Recently discharged patients aged 50 years or older and having a chronic medical condition were offered the opportunity to meet with a pharmacist in the home setting to review medication instructions and receive a demonstration of an ePHR system. Patients agreeable to using the ePHR system were offered pharmacist support with setting up the ePHR system, having emphasis on documenting and reviewing medication regimens. Medication-related problems identified by the pharmacist during the visit were categorized according to ePHR use and by other characteristics. Results: Thirty recently discharged patients with chronic disease were visited by a pharmacist over a 6-month period. The percentage of medication-related problems identified by the pharmacist was greater among those patients who agreed to use the ePHR system, as compared with patients whose visit did not include use of the ePHR (75% versus 40%, respectively; P=0.06). Differing types of medication-related problems were identified, including therapy duplications, lack of use of clinically important therapies, and patient nonadherence. Conclusion: For some patients, the home setting can be a suitable venue for medication review and education after discharge from hospital. Assisting patients with setting up the ePHR system may enhance pharmacists’ ability to identify and resolve medication-related problems that may lead to rehospitalization

Genetic steps to organ laterality in zebrafish.

All internal organs are asymmetric along the left-right axis. Here we report a genetic screen to discover mutations which perturb organ laterality. Our particular focus is upon whether, and how, organs are linked to each other as they achieve their laterally asymmetric positions. We generated mutations by ENU mutagenesis and examined F3 progeny using a cocktail of probes that reveal early primordia of heart, gut, liver and pancreas. From the 750 genomes examined, we isolated seven recessive mutations which affect the earliest left-right positioning of one or all of the organs. None of these mutations caused discernable defects elsewhere in the embryo at the stages examined. This is in contrast to those mutations we reported previously (Chen et al., 1997) which, along with left-right abnormalities, cause marked perturbation in gastrulation, body form or midline structures. We find that the mutations can be classified on the basis of whether they perturb relationships among organ laterality. In Class 1 mutations, none of the organs manifest any left-right asymmetry. The heart does not jog to the left and normally leftpredominant BMP4 in the early heart tube remains symmetric. The gut tends to remain midline. There frequently is a remarkable bilateral duplication of liver and pancreas. Embryos with Class 2 mutations have organotypic asymmetry but, in any given embryo, organ positions can be normal, reversed or randomized. Class 3 reveals a hitherto unsuspected gene that selectively affects laterality of heart. We find that visceral organ positions are predicted by the direction of the preceding cardiac jog. We interpret this as suggesting that normally there is linkage between cardiac and visceral organ laterality. Class 1 mutations, we suggest, effectively remove the global laterality signals, with the consequence that organ positions are effectively symmetrical. Embryos with Class 2 mutations do manifest linkage among organs, but it may be reversed, suggesting that the global signals may be present but incorrectly orientated in some of the embryos. That laterality decisions of organs may be independently perturbed, as in the Class 3 mutation, indicates that there are distinctive pathways for reception and organotypic interpretation of the global signals

Single-ion and exchange anisotropy effects and multiferroic behavior in high-symmetry tetramer single molecule magnets

We study single-ion and exchange anisotropy effects in equal-spin $s_1$ tetramer single molecule magnets exhibiting $T_d$, $D_{4h}$, $D_{2d}$, $C_{4h}$, $C_{4v}$, or $S_4$ ionic point group symmetry. We first write the group-invariant quadratic single-ion and symmetric anisotropic exchange Hamiltonians in the appropriate local coordinates. We then rewrite these local Hamiltonians in the molecular or laboratory representation, along with the Dzyaloshinskii-Moriay (DM) and isotropic Heisenberg, biquadratic, and three-center quartic Hamiltonians. Using our exact, compact forms for the single-ion spin matrix elements, we evaluate the eigenstate energies analytically to first order in the microscopic anisotropy interactions, corresponding to the strong exchange limit, and provide tables of simple formulas for the energies of the lowest four eigenstate manifolds of ferromagnetic (FM) and anitiferromagnetic (AFM) tetramers with arbitrary $s_1$. For AFM tetramers, we illustrate the first-order level-crossing inductions for $s_1=1/2,1,3/2$, and obtain a preliminary estimate of the microscopic parameters in a Ni$_4$ from a fit to magnetization data. Accurate analytic expressions for the thermodynamics, electron paramagnetic resonance absorption and inelastic neutron scattering cross-section are given, allowing for a determination of three of the microscopic anisotropy interactions from the second excited state manifold of FM tetramers. We also predict that tetramers with symmetries $S_4$ and $D_{2d}$ should exhibit both DM interactions and multiferroic states, and illustrate our predictions for $s_1=1/2, 1$.Comment: 30 pages, 14 figures, submitted to Phys. Rev.

Making Sense of the Legendre Transform

The Legendre transform is an important tool in theoretical physics, playing a critical role in classical mechanics, statistical mechanics, and thermodynamics. Yet, in typical undergraduate or graduate courses, the power of motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms. We review and modify the presentation of Legendre transforms in a way that explicates the formal mathematics, resulting in manifestly symmetric equations, thereby clarifying the structure of the transform algebraically and geometrically. Then we bring in the physics to motivate the transform as a way of choosing independent variables that are more easily controlled. We demonstrate how the Legendre transform arises naturally from statistical mechanics and show how the use of dimensionless thermodynamic potentials leads to more natural and symmetric relations.Comment: 11 pages, 3 figure