Alternative derivation of the relativistic contribution to perihelic precession

An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for approximately elliptical motion. The method of solution makes use of coordinate transformations and the correspondence principle, rather than the standard perturbative approach. The form of the resulting orbit equation is similar to that derived from Newtonian mechanics and includes first-order corrections to Kepler's orbits due to general relativity. The associated relativistic contribution to perihelic precession agrees with established first-order results. The reduced radius for the circular orbit is in agreement to first-order with that calculated from the Schwarzschild effective potential. The method of solution is understandable by undergraduate students.Comment: 12 pages, 2 figures. Accepted for publication in the American Journal of Physic

Fourth order indirect integration method for black hole perturbations: even modes

On the basis of a recently proposed strategy of finite element integration in time domain for partial differential equations with a singular source term, we present a fourth order algorithm for non-rotating black hole perturbations in the Regge-Wheeler gauge. Herein, we address even perturbations induced by a particle plunging in. The forward time value at the upper node of the $(r^*,t)$ grid cell is obtained by an algebraic sum of i) the preceding node values of the same cell, ii) analytic expressions, related to the jump conditions on the wave function and its derivatives, iii) the values of the wave function at adjacent cells. In this approach, the numerical integration does not deal with the source and potential terms directly, for cells crossed by the particle world line. This scheme has also been applied to circular and eccentric orbits and it will be object of a forthcoming publication.Comment: This series of papers deals with EMRI for LISA. With the respect to the v1 version, the algorithm has been improved; convergence tests and references have been added; v2 is composed by 23 pages, and 6 figures. Paper accepted by Class. Quantum Gravity for the special issue on Theory Meets Data Analysis at Comparable and Extreme Mass Ratios (Capra and NRDA) at Perimeier Institute in June 201

A System Dynamics Approach to the Efficacy of Oxime Therapy in Sub Lethal Exposure to Sarin Gas

The 2010 National Security Strategy states, The effective dissemination of a lethal agent would endanger the lives of thousands of people and have unprecedented economic, societal, and political consequences. We must continue to work at home with first responders and health officials to reduce the risk associated with high-consequence threats . Nerve agents, such as Sarin gas, are considered high consequence threats. The threat of use of agents such as Sarin is as much a threat today as any other time in our history. However, the suggested treatment protocol is not as precise as it could be. Debate exists over the dosing and timing of atropine and oxime treatment when combating the effects caused by exposure to nerve agents. Oxime treatment has proved to be less than effective under several situations. The research presented in this paper used a physiologically based pharmacokinetic model to determine if the current treatment protocol prescribed by the Center for Disease Control (CDC) and the U.S Army is effective in treating victims suffering from acute exposure symptoms. Then the model was used to determine what treatment should be applied to victims suffering from mild exposure symptoms. The results indicate that the current treatment prescribed by the CDC and U.S. Army is effective; however treatment with oxime therapy was not effective in alleviating symptoms for someone suffering from mild exposure. By applying these results a treatment protocol was developed for someone suffering from mild exposure symptoms to Sarin gas

Mean-payoff Automaton Expressions

Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic mean-payoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions

Evolutionary Selection of Behavioral Rules in a Cournot Model: A Local Bifurcation Analysis

Evolutionary game theory;heterogeneous behavioral rules;Cournot competition;nonlinear dynamics;bifurcation theory

Universal homogeneous causal sets

Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete space-time in quantum gravity. We show that the class C of all countable past-finite causal sets contains a unique causal set (U,<) which is universal (i.e., any member of C can be embedded into (U,<)) and homogeneous (i.e., (U,<) has maximal degree of symmetry). Moreover, (U,<) can be constructed both probabilistically and explicitly. In contrast, the larger class of all countable causal sets does not contain a universal object.Comment: 14 page

Development of the Mississippian-Pennsylvanian Unconformity in Indiana

In very early Pennsylvanian time the place nowcalled Indiana was the locus of subaerial erosion. About 8,000 square miles of this landscape is preserved in western Indiana beneath the rocks of the Pennsylvanian System. Data from 20,000 wells provide the evidence to reconstruct this surface and to describe its geomorphology. Six ancient physiographic regions that show clear relationships of landform to outcropping Mississippian bedrock have been identified. From north to south a distinctive topography is associated with each of the ancient outcrop areas of (1) the Borden Group, (2) the Sanders and Blue River Groups, (3) the West Baden Group, (4) the Stephensport Group, (5) the Tar Springs Formation through the Menard Limestone, and ( 6) the Palestine Sandstone through the Grove Church Shale. In northern Indiana the Mississippian-Pennsylvanian unconformity may represent as much as 8 million years of erosion. In southern Indiana that same unconformity may represent less than 3 million years of erosion

Where communities intermingle, diversity grows - The evolution of topics in ecosystem service research

We analyze how the content of ecosystem service research has evolved since the early 1990s. Conducting a computational bibliometric content analysis we process a corpus of 14,118 peer-reviewed scientific article abstracts on ecosystem services (ES) from Web of Science records. To provide a comprehensive content analysis of ES research literature, we employ a latent Dirichlet allocation algorithm. For three different time periods (1990-2000, 2001-2010, 2011-2016), we derive nine main ES topics arising from content analysis and elaborate on how they are related over time. The results show that natural science-based ES research analyzes oceanic, freshwater, agricultural, forest, and soil ecosystems. Pollination and land cover emerge as traceable standalone topics around 2001. Social science ES literature demonstrates a reflexive and critical lens on the role of ES research and includes critiques of market-oriented perspectives. The area where social and natural science converge most is about land use systems such as agriculture. Overall, we provide evidence of the strong natural science foundation, the highly interdisciplinary nature of ES research, and a shift in social ES research towards integrated assessments and governance approaches. Furthermore, we discuss potential reasons for observable topic developments.Peer reviewe

The theory of the exponential differential equations of semiabelian varieties

The complete first order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arises from an amalgamation-with-predimension construction in the style of Hrushovski. The theory includes necessary and sufficient conditions for a system of equations to have a solution. The necessary condition generalizes Ax's differential fields version of Schanuel's conjecture to semiabelian varieties. There is a purely algebraic corollary, the "Weak CIT" for semiabelian varieties, which concerns the intersections of algebraic subgroups with algebraic varieties.Comment: 53 pages; v3: Substantial changes, including a completely new introductio

Evolutionary design of a full-envelope full-authority flight control system for an unstable high-performance aircraft

The use of an evolutionary algorithm in the framework of H1 control theory is being considered as a means for synthesizing controller gains that minimize a weighted combination of the infinite norm of the sensitivity function (for disturbance attenuation requirements) and complementary sensitivity function (for robust stability requirements) at the same time. The case study deals with a complete full-authority longitudinal control system for an unstable high-performance jet aircraft featuring (i) a stability and control augmentation system and (ii) autopilot functions (speed and altitude hold). Constraints on closed-loop response are enforced, that representing typical requirements on airplane handling qualities, that makes the control law synthesis process more demanding. Gain scheduling is required, in order to obtain satisfactory performance over the whole flight envelope, so that the synthesis is performed at different reference trim conditions, for several values of the dynamic pressure, used as the scheduling parameter. Nonetheless, the dynamic behaviour of the aircraft may exhibit significant variations when flying at different altitudes, even for the same value of the dynamic pressure, so that a trade-off is required between different feasible controllers synthesized at different altitudes for a given equivalent airspeed. A multiobjective search is thus considered for the determination of the best suited solution to be introduced in the scheduling of the control law. The obtained results are then tested on a longitudinal non-linear model of the aircraft