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In this paper, we shall give a characterization of all monotonically decreasing sequence of positive terms, whose sum converge and then introduce a Transformation which can be used to accelerate the convergence of a large class of logarithmically convergent series.
Knowledge about the evaporation loss of light elements is important to our understanding of chondrule formation processes. The evaporative loss of light elements (such as B and Li) as a function of cooling rate is of special interest because recent investigations of the distribution of Li, Be and B in meteoritic chondrules have revealed that Li varies by 25 times, and B and Be varies by about 10 times. Therefore, if we can extrapolate and interpolate with confidence the evaporation loss of B and Li (and other light elements such as K, Na) at a wide range of cooling rates of interest based upon limited experimental data, we would be able to assess the full range of scenarios relating to chondrule formation processes. Here, we propose that evaporation loss of light elements as a function of cooling rate should obey the logarithmic law.
The versatility of the family of generalized logarithmic spirals is improved by introducing a degree of freedom in the solution. The low-thrust acceleration profile now includes a control term that affects both the magnitude and the direction of the thrust. Exact and fully analytic solutions to the trajectory, the velocity, the time of flight, etc. are made available. Two integrals of motion are preserved. The first one is a generalization of the equation of the energy and depends on the values of the control parameter. The second one relates to the equation of the angular momentum. The problem of finding spiral transfers between two arbitrary state vectors reduces to solving one algebraic equation with one unknown. The degree of freedom allows fixing the time of flight of the transfer. If the time of flight is fixed, then there are two equations with two unknowns. No other iterative procedures are required. Coast arcs can be introduced in the solution naturally. An explicit expression for the maximum acceleration reached along the transfer is provided. Thanks to the symmetry properties of the solution a simple algorithm for generating periodic orbits is presented. An arbitrary number of intermediate nodes can be introduced to improve the flexibility of the solution when facing optimization problems. An example of a low-thrust gravity-assist Earth-Mars-Ceres trajectory shows that the solution is comparable to that obtained with other preliminary design techniques.
We explore the CO2 dependence of effective climate sensitivity (SG) with symmetric abrupt and transient CO2 forcing, spanning the range 1/8×, 1/4×, 1/2×, 2×, 4×, and 8×CO2, using two state-of-the-art fully coupled atmosphere-ocean-sea-ice-land models. In both models, under abrupt CO2 forcing, we find an asymmetric response in surface temperature and SG. The surface global warming at 8×CO2 is more than one third larger than the corresponding cooling at 1/8×CO2, and SG is CO2 dependent, increasing non-monotonically from 1/8×CO2 to 8×CO2. We find similar CO2 dependence in the transient runs, forced with -1%yr−1CO2 and +1%yr−1CO2 up to 1/8×CO2 and 8×CO2, respectively. The non-logarithmic radiative forcing – not the changing feedbacks – primarily explains the dependence of SG on CO2, particularly at low CO2 levels. The changing feedbacks, however, explain SG’s non-monotonic behavior.
Clog is a library of charged particle stopping powers and related Coulomb logarithm processes in a plasma. The stopping power is a particularly useful quantity for plasma physics, as it measures the energy loss of per unit length of charged particle as it traverses a plasma. Clog's primary stopping power is the BPS (Brown-Preston-Singleton) theory.
We describe in detail how a d log representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized unitarity. For the examples we study, the alphabet of the differential equation is related to special points in kinematic space, described by certain cut equations which encode the geometry of the Feynman integral. At one loop, we reproduce the motivic formulae described by Goncharov [1] that reappeared in the context of Feynman integrals in [2–4]. The d log representation allows us to generalize the differential equations to higher loops and motivates the study of certain mixed-dimension integrals.
The low-temperature thermodynamics of near-extremal rotating black holes has recently been revisited to incorporate one-loop contributions that are dominant in this regime. We discuss these quantum corrections to the gravitational path integral for asymptotically Anti de-Sitter black holes in four and five dimensions. In four dimensions we explicitly consider Kerr-AdS 4 , Kerr-Newman-AdS 4 and the rotating black hole in $\mathcal{N}$ = 4 gauged supergravity with two scalars and two electric charges turned on. In five dimensions we explicitly address the asymptotically flat Myers-Perry black hole and the Kerr-AdS5 black hole. In every case we find that tensor modes contribute $\frac{3}{2}$logT Hawking to the low-temperature thermodynamics. We identify the root cause of this universality in two facts: (i) the universal presence of a SL(2, $\mathbb{R}$) subgroup of isometries in the near-horizon geometry and (ii) a set of cancellations in the Lichnerowicz operator. We show that these two conditions hold for near-extremal black holes in asymptotically flat and asymptotically AdS spacetimes of various dimensions.
Using the known resummation of virtual corrections together with knowledge of the leading-log structure of real radiation in a parton shower, we derive analytic expressions for the resummed real radiation after they have been integrated over all of phase space. Performing a numerical analysis for both the 13 TeV LHC and a 100 TeV pp collider, we show that resummation of the real corrections is at least as important as resummation of the virtual corrections, and that this resummation has a sizable effect for partonic center of mass energies exceeding √s=O(few TeV). For partonic center of mass energies √s≳10 TeV, which can be reached at a 100 TeV collider, resummation becomes an O(1) effect and needs to be included even for rough estimates of the cross-sections.
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By studying Rozansky-Witten theory with non-compact target spaces we find new connections with knot invariants whose physical interpretation was not known. Furthermore, this opens up several new avenues, which include a new formulation of q-series invariants of 3-manifolds in terms of affine Grassmannians and a generalization of Akutsu-Deguchi-Ohtsuki knot invariants.
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