Leaps and bounds towards scale separation

In a broad class of gravity theories, the equations of motion for vacuum compactifications give a curvature bound on the Ricci tensor minus a multiple of the Hessian of the warping function. Using results in so-called Bakry-Émery geometry, we put rigorous general bounds on the KK scale in gravity compactifications in terms of the reduced Planck mass or the internal diameter. We reexamine in this light the local behavior in type IIA for the class of supersymmetric solutions most promising for scale separation. We find that the local O6-plane behavior cannot be smoothed out as in other local examples; it generically turns into a formal partially smeared O4.

Local Behavior of Lap-Spliced Deformed Rebars in Reinforced Concrete Beams

Twelve full-scale reinforced concrete beams with two tension lap splices were constructed and tested under a four-point loading test. Half of these beams had shorter lap splices than that recommended by American Concrete Institute Building Code ACI 318-19; they failed by bond loss between steel and concrete at the lap splice region before rebar yielding. The other half of the beams were designed with a lap splice length slightly exceeding that recommended by ACI 318-19; they failed by rebar yielding and exhibited a ductile behavior. Several strain gauges were attached to the longitudinal bars in the lap splice region to study the local behavior of deformed bars during loading. The strain in a rebar was maximum at the loaded end of the lap splice and progressively decreased toward the unloaded end because the rebar at this end could not sustain any load. Stress flow discontinuity occurred at the loaded end and caused stress concentration. The effect of this concentration was investigated based on test results. The comparison of bond strengths calculated by existing equations and those of tested specimens indicated that the results agreed well.

New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem

For the spatially-distributed Fermi–Pasta–Ulam (FPU) equation, irregular solutions are studied that contain components rapidly oscillating in the spatial variable, with different asymptotically large modes. The main result of this paper is the construction of families of special nonlinear systems of the Schrödinger type—quasinormal forms—whose nonlocal dynamics determines the local behavior of solutions to the original problem, as t→∞. On their basis, results are obtained on the asymptotics in the main solution of the FPU equation and on the interaction of waves moving in opposite directions. The problem of “perturbing” the number of N elements of a chain is considered. In this case, instead of the differential operator, with respect to one spatial variable, a special differential operator, with respect to two spatial variables appears. This leads to a complication of the structure of an irregular solution.

The accelerated Gisin state: its non-locality, quantum correlations and efficiency to perform quantum masking

The local and non local behavior of the accelerated Gisin state are investigated either before or after filtering process. It is shown that, the possibility of predicting the non-local behavior is forseen at large values of the weight of the Gisin and acceleration parameters. Due to the filtering process, the non-locality behavior of the Gisin state is predicted at small values of the weight parameter. The amount of non classical correlations are quantified by means of the local quantum uncertainty (LQU)and the concurrence, where the LQU is more sensitive to the non-locality than the concurrence. The phenomenon of the sudden changes is displayed for both quantifiers. Our results show that, the accelerated Gisin state could be used to mask information, where all the possible partitions of the masked state satisfy the masking criteria. Moreover, there is a set of states, which satisfy the masking condition, that is generated between each qubit and its masker qubit. For this set, the amount of the non-classical correlations increases as the acceleration parameter increases . Further, the filtering process improves these correlations, where their maximum bounds are much larger than those depicted for non-filtered states.

Constructing totally p-adic numbers of small height

Bombieri and Zannier gave an effective construction of algebraic numbers of small height inside the maximal Galois extension of the rationals which is totally split at a given finite set of prime numbers. They proved, in particular, an explicit upper bound for the lim inf of the height of elements in such fields. We generalize their result in an effective way to maximal Galois extensions of number fields with given local behavior at finitely many places.

Global and Local Behavior of the System of Piecewise Linear Difference Equations xn+1 = |xn| − yn − b and yn+1 = xn − |yn| + 1 Where b ≥ 4

The aim of this article is to study the system of piecewise linear difference equations xn+1=|xn|−yn−b and yn+1=xn−|yn|+1 where n≥0. A global behavior for b=4 shows that all solutions become the equilibrium point. For a large value of |x0| and |y0|, we can prove that (i) if b=5, then the solution becomes the equilibrium point and (ii) if b≥6, then the solution becomes the periodic solution of prime period 5.