Solving Differential Equations in R: Package deSolve

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR), DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1) to demonstrate the potential of using R for dynamic modeling, (2) to highlight typical uses of the different methods implemented and (3) to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to RâÂÂs high-level procedures. deSolve is the successor of package odesolve which will be deprecated in the future; it is free software and distributed under the GNU General Public License, as part of the R software project.

Minimal Seesaw as an Ultraviolet Insensitive Cure for the Problems of Anomaly Mediation

We show that an intermediate scale supersymmetric left-right seesaw scenario with automatic R-parity conservation can cure the problem of tachyonic slepton masses that arises when supersymmetry is broken by anomaly mediation, while preserving ultraviolet insensitivity. The reason for this is the existence of light B - L = 2 higgses with yukawa couplings to the charged leptons. We find these theories to have distinct predictions compared to the usual mSUGRA and gauge mediated models as well as the minimal AMSB models. Such predictions include a condensed gaugino mass spectrum and possibly a correspondingly condensed sfermion spectrum.Comment: 19 pages, 1 figur

Development of a bedrest muscle stress apparatus

In attempting further to define the deleterious effects of spaceflight on the human body, measurement systems and techniques were devised to determine the loss of skeletal muscle strength and tone as a result of spaceflight exposure. In order to determine how the muscle degradation process progresses with time during nonuse, a system for measuring muscle stress during bedrest was developed. The Bedrest Muscle Stress Apparatus is configured to slip snugly over the foot board of a standard hospital bed. Data collected with this device correlated well with pre- and post-bedrest data collected with the original skeletal muscle stress apparatus

Evidence for room temperature superconductivity at graphite interfaces

In the last 43 years several hints were reported suggesting the existence of granular superconductivity above room temperature in different graphite-based systems. In this paper some of the results are reviewed, giving special attention to those obtained in water and n-heptane treated graphite powders, commercial and natural bulk graphite samples with different characteristics as well as transmission electron microscope (TEM) lamellae. The overall results indicate that superconducting regions exist and are localized at certain internal interfaces of the graphite structure. The existence of the rhombohedral graphite phase in all samples with superconducting-like properties suggests its interfaces with the Bernal phase as a possible origin for the high-temperature superconductivity, as theoretical calculations predict. High precision electrical resistance and magnetization measurements were used to identify a transition at $T_c \gtrsim 350~$K. To check for the existence of true zero resistance paths in the samples we used local magnetic measurements, which results support the existence of superconducting regions at such high temperatures.Comment: 10 pages, 9 figures, 2nd International Workshop "Towards Room Temperature Superconductivity: Superhydrides and more", Orange California May 2017. To be published in "Quantum Studies: Mathematics and Foundations" (Springer Nature

Induced Magnetic Ordering by Proton Irradiation in Graphite

We provide evidence that proton irradiation of energy 2.25 MeV on highly-oriented pyrolytic graphite samples triggers ferro- or ferrimagnetism. Measurements performed with a superconducting quantum interferometer device (SQUID) and magnetic force microscopy (MFM) reveal that the magnetic ordering is stable at room temperature.Comment: 3 Figure

A natural little hierarchy for RS from accidental SUSY

We use supersymmetry to address the little hierarchy problem in Randall-Sundrum models by naturally generating a hierarchy between the IR scale and the electroweak scale. Supersymmetry is broken on the UV brane which triggers the stabilization of the warped extra dimension at an IR scale of order 10 TeV. The Higgs and top quark live near the IR brane whereas light fermion generations are localized towards the UV brane. Supersymmetry breaking causes the first two sparticle generations to decouple, thereby avoiding the supersymmetric flavour and CP problems, while an accidental R-symmetry protects the gaugino mass. The resulting low-energy sparticle spectrum consists of stops, gauginos and Higgsinos which are sufficient to stabilize the little hierarchy between the IR scale and the electroweak scale. Finally, the supersymmetric little hierarchy problem is ameliorated by introducing a singlet Higgs field on the IR brane.Comment: 37 pages, 3 figures; v2: minor corrections, version published in JHE

A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Magnetic-Field-Driven Superconductor-Insulator-Type Transition in Graphite

A magnetic-field-driven transition from metallic- to semiconducting-type behavior in the basal-plane resistance takes place in highly oriented pyrolytic graphite at a field $H_c \sim 1~$kOe applied along the hexagonal c-axis. The analysis of the data reveals a striking similarity between this transition and that measured in thin-film superconductors and Si MOSFET's. However, in contrast to those materials, the transition in graphite is observable at almost two orders of magnitude higher temperatures.Comment: 4 Figure