Behavior of Friedmann-Lemaître-Robertson-Walker Singularities

In Stoica (Int. J. Theor. Phys. 55, 71–80, 2016) a regularization procedure is suggested for regularizing Big Bang singularities in Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes. We argue that this procedure is only appliable to one case of Big Bang singularities and does not affect other types of singularities.     

Solutions of time-fractional Kudryashov–Sinelshchikov equation arising in the pressure waves in the liquid with gas bubbles

In this paper, analytical approximate solutions for time-fractional Kudryashov–Sinelshchikov equation have been obtained. Two different techniques have been implemented to calculate the solutions, namely, homotopy analysis method and residual power series method. The approximate solutions are represented numerically and graphically for different values of fractional order of derivative. The numerical results are expressed in Tables 1, 2, 3 and 4 which show that the approximate solutions are in good agreement with the exact solution. The comparative study of the numerical results reveal that both methods are reliable and effective tools for the solution of time-fractional Kudryashov–Sinelshchikov equation.     

Late time acceleration in f(G) model

Late time transition is obtained with a function of Gauss Bonnet curvature $f(G)$ in the Einstein Hilbert action with a matter field in a FLRW spacetime assuming an ansatz without a specific $f(G)$ . Late time accelerating expansion is either a phantom era without Big Rip singularity or a quintessence era or a de-Sitter era of expansion. The equation of state parameter, jerk and snap parameters support observational data and the function $f(G)$ obtained from the solution supports earlier works.     

On the Backward Stability of the Schwarzschild Black Hole Singularity

We study the backwards-in-time stability of the Schwarzschild singularity from a dynamical PDE point of view. More precisely, considering a spacelike hypersurface \({\Sigma_0}\) in the interior of the black hole region, tangent to the singular hypersurface \({\{r = 0\}}\) at a single sphere, we study the problem of perturbing the Schwarzschild data on \({\Sigma_0}\) and solving the Einstein vacuum equations backwards in time. We obtain a local backwards well-posedness result for small perturbations lying in certain weighted Sobolev spaces. No symmetry assumptions are imposed. The perturbed spacetimes all have a singularity at a “collapsed” sphere on \({\Sigma_0}\), where the leading asymptotics of the curvature and the metric match those of their Schwarzschild counterparts to a suitably high order. As in the Schwarzschild backward evolution, the pinched initial hypersurface \({\Sigma_0}\) ‘opens up’ instantly, becoming a regular spacelike (cylindrical) hypersurface. This result thus yields classes of examples of non-symmetric vacuum spacetimes, evolving forward-in-time from regular initial data, which form a Schwarzschild type singularity at a collapsed sphere. We rely on a precise asymptotic analysis of the Schwarzschild geometry near the singularity which turns out to be at the threshold that our energy methods can handle.     

Geodesics Toward Corners in First Passage Percolation

For stationary first passage percolation in two dimensions, the existence and uniqueness of semi-infinite geodesics directed in particular directions or sectors has been considered by Damron and Hanson (Commun Math Phys 325(3):917–963, 2014), Ahlberg and Hoffman (Random coalescing geodesics in first-passage percolation, arXiv:1609.02447 [math.PR]), and others. However the main results do not cover geodesics in the direction of corners of the limit shape \(\mathcal {B}\), where two facets meet. We construct an example with the following properties: (i) the limiting shape is an octagon, (ii) semi-infinite geodesics exist only in the four axis directions, and (iii) in each axis direction there are multiple such geodesics. Consequently, the set of points of \(\partial \mathcal {B}\) which are in the direction of some geodesic does not have all of \(\mathcal {B}\) as its convex hull.     

Wall-crossing between stable and co-stable ADHM data

We prove formula between Nekrasov partition functions defined from stable and co-stable ADHM data for the plane following method by Nakajima and Yoshioka (Kyoto J Math 51(2):263–335, 2011) based on the theory of wall-crossing formula developed by Mochizuki (Donaldson type invariants for algebraic surfaces: transition of moduli stacks, Lecture notes in mathematics, vol 1972, Springer, Berlin, 2009). This formula is similar to conjectures by Ito et al. [J High Energy Phys 2013(5):045, 2013, (4.1), (4.2)] for \(A_{1}\) singularity.     

Deformation Theory of Periodic Monopoles (With Singularities)

Cherkis and Kapustin (Commun Math Phys 218(2): 333–371, 2001 and Commun Math Phys 234(1):1–35, 2003) introduced periodic monopoles (with singularities), i.e. monopoles on \({\mathbb{R}^{2} \times \mathbb{S}^{1}}\) possibly singular at a finite collection of points. In this paper we show that for generic choices of parameters the moduli spaces of periodic monopoles (with singularities) with structure group \({SO(3)}\) are either empty or smooth hyperkähler manifolds. Furthermore, we prove an index theorem and therefore compute the dimension of the moduli spaces.     

Random Forests and Networks Analysis

Wilson (Proceedings of the twenty-eight annual acm symposium on the theory of computing, pp. 296–303, 1996) in the 1990s described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works (Avena and Gaudillière in A proof of the transfer-current theorem in absence of reversibility, in Stat. Probab. Lett. 142, 17–22 (2018); Avena and Gaudillière in J Theor Probab, 2017.  https://doi.org/10.1007/s10959-017-0771-3; Avena et al. in Approximate and exact solutions of intertwining equations though random spanning forests, 2017. arXiv:1702.05992v1; Avena et al. in Intertwining wavelets or multiresolution analysis on graphs through random forests, 2017. arXiv:1707.04616, to appear in ACHA (2018)) we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: (1) a random-walk-based notion of well-distributed points in a graph, (2) a framework to describe metastable-like dynamics in finite settings by means of Markov intertwining dualities, (3) coarse graining schemes for networks and associated processes, (4) wavelets-like pyramidal algorithms for graph signals.     

Optimal Symmetric Ternary Quantum Encryption Schemes

In this paper, we present two definitions of the orthogonality and orthogonal rate of an encryption operator, and we provide a verification process for the former. Then, four improved ternary quantum encryption schemes are constructed. Compared with Scheme 1 (see Section 2.3), these four schemes demonstrate significant improvements in term of calculation and execution efficiency. Especially, under the premise of the orthogonal rate ε as secure parameter, Scheme 3 (see Section 4.1) shows the highest level of security among them. Through custom interpolation functions, the ternary secret key source, which is composed of the digits 0, 1 and 2, is constructed. Finally, we discuss the security of both the ternary encryption operator and the secret key source, and both of them show a high level of security and high performance in execution efficiency.     

$$$$-Dimensional charged black holes with scalar hair in Einstein–Power–Maxwell Theory

In \((2+1)\)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter \(k=1\) and \(k\ne 1\)), in the Einstein–Power–Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with \(k\ne 1\), we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.     

Application of time transfer function to McVittie spacetime: gravitational time delay and secular increase in astronomical unit

We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann–Lemaître–Robertson–Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte et al. (Class Quantum Gravity 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class Quantum Gravity 25:145020, 2008), which is originally related to Synge’s world function Ω(x _A , x _B ) and enables to circumvent the integration of the null geodesic equation. We re-examine the global cosmological effect on light propagation in the solar system. The round-trip time of a light ray/signal is given by the functions of not only the spacial coordinates but also the emission time or reception time of light ray/signal, which characterize the time-dependency of solutions. We also apply the obtained results to the secular increase in the astronomical unit, reported by Krasinsky and Brumberg (Celest Mech Dyn Astron 90:267, 2004), and we show that the leading order terms of the time-dependent component due to cosmological expansion is 9 orders of magnitude smaller than the observed value of dAU/dt, i.e., 15 ± 4 (m/century). Therefore, it is not possible to explain the secular increase in the astronomical unit in terms of cosmological expansion.     

Reconstruction of a kinetic k-essence Lagrangian from a modified of dark energy equation of state

In this paper the Lagrangian density of a purely kinetic k-essence model that describes the behavior of dark energy described by four parameterized equations of state proposed by Cooray and Huterer (Astrophys J 513:L95, 1999), Zhang and Wu (Mod Phys Lett A 27:1250030, 2012), Linder (Phys Rev Lett 90:091301, 2003), Efstathiou (Mon Not R Astron Soc 310:842, 2000), and Feng and Lu (J Cosmol Astropart Phys 1111:34, 2011) has been reconstructed. This reconstruction is performed using the method outlined by de Putter and Linder (Astropart Phys 28:263, 2007), which makes it possible to solve the equations that relate the Lagrangian density of the k-essence with the given equation of state (EoS) numerically. Finally, we discuss the observational constraints for the models based on 1049 SNIa data points from the Pantheon data set compiled by Scolnic et al. (Astrophys J 859(2):101, 2018)     

$$\mathrm{SL}(2, \mathbb {C})$$ group action on cohomological field theories

We introduce the \(\mathrm {SL} (2,\mathbb {C})\) group action on a partition function of a cohomological field theory via a certain Givental’s action. Restricted to the small phase space we describe the action via the explicit formulae on a CohFT genus g potential. We prove that applied to the total ancestor potential of a simple-elliptic singularity the action introduced coincides with the transformation of Milanov–Ruan changing the primitive form (cf. Milanov and Ruan in Gromov–Witten theory of elliptic orbifold \(\mathbb {P}^{1}\) and quasi-modular forms, arXiv:1106.2321, 2011).     

Analytic study of self-gravitating polytropic spheres with light rings

Ultra-compact objects describe horizonless solutions of the Einstein field equations which, like black-hole spacetimes, possess null circular geodesics (closed light rings). We study analytically the physical properties of spherically symmetric ultra-compact isotropic fluid spheres with a polytropic equation of state. It is shown that these spatially regular horizonless spacetimes are generally characterized by two light rings \(\{r^{\text {inner}}_{\gamma },r^{\text {outer}}_{\gamma }\}\) with the property \(\mathcal{C}(r^{\text {inner}}_{\gamma })\le \mathcal{C}(r^{\text {outer}}_{\gamma })\), where \(\mathcal{C}\equiv m(r)/r\) is the dimensionless compactness parameter of the self-gravitating matter configurations. In particular, we prove that, while black-hole spacetimes are characterized by the lower bound \(\mathcal{C}(r^{\text {inner}}_{\gamma })\ge 1/3\), horizonless ultra-compact objects may be characterized by the opposite dimensionless relation \(\mathcal{C}(r^{\text {inner}}_{\gamma })\le 1/4\). Our results provide a simple analytical explanation for the interesting numerical results that have recently presented by Novotný et al. (Phys Rev D 95:043009, 2017).     

Deflection of light by black holes and massless wormholes in massive gravity

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov, JHEP 0904:100, 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass M and an extra parameter S namely ‘scalar charge’. These black hole reduce to the standard Schwarzschild black hole solutions when the scalar charge is zero and the mass is positive. In addition, a parameter \(\lambda \) in the metric characterizes so-called ‘hair’. The geodesic equations are used to examine the behavior of the deflection angle in four relevant cases of the parameter \(\lambda \). Then, by introducing a simple coordinate transformation \(r^\lambda =S+v^2\) into the black hole metric, we were able to find a massless wormhole solution of Einstein–Rosen (ER) (Einstein and Rosen, Phys Rev 43:73, 1935) type with scalar charge S. The programme is then repeated in terms of the Gauss–Bonnet theorem in the weak field limit after a method is established to deal with the angle of deflection using different domains of integration depending on the parameter \(\lambda \). In particular, we have found new analytical results corresponding to four special cases which generalize the well known deflection angles reported in the literature. Finally, we have established the time delay problem in the spacetime of black holes and wormholes, respectively.     

Critical Behavior of the Annealed Ising Model on Random Regular Graphs

In Giardinà et al. (ALEA Lat Am J Probab Math Stat 13(1):121–161, 2016), the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in Can (Annealed limit theorems for the Ising model on random regular graphs, arXiv:1701.08639, 2017), we generalized their results to the class of all random regular graphs. In this paper, we study the critical behavior of this model. In particular, we determine the critical exponents and prove a non standard limit theorem stating that the magnetization scaled by \(n^{3/4}\) converges to a specific random variable, with n the number of vertices of random regular graphs.     

Ultrafast Soft X-ray Probing of Gas Phase Molecular Dynamics

The molecular ability to selectively and efficiently convert sunlight into other forms of energy like heat, bond change, or charge separation is truly remarkable. The decisive steps in these transformations often happen on a femtosecond timescale and require transitions among different electronic states that violate the Born-Oppenheimer approximation (BOA) [1 W. Domcke, D. Yarkony, and H. Köppel, Conical Intersections Electronic Structure, Dynamics &; Spectroscopy, World Scientific, Singapore (2004).[Crossref] , [Google Scholar]]. Non-BOA transitions pose challenges to both theory and experiment. From a theoretical point of view, excited state dynamics and nonadiabatic transitions both are difficult problems [2 F. Plasser, Theor. Chem. Acc. 131, 233902 (2012).[Crossref], [Web of Science ®] , [Google Scholar], 3 J. C. Tully, J. Chem. Phys. 137, 22A301 (2012).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] (see Figure 1(a)). However, the theory on non-BOA dynamics has advanced significantly over the last two decades. Full dynamical simulations for molecules of the size of nucleobases have been possible for a couple of years [4 H. R. Hudock, J. Phys. Chem. A 111, 8500–8508 (2007).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 5 J. J. Szymczak, J. Phys. Chem. A 113, 12686–12693 (2009).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] and allow predictions of experimental observables like photoelectron energy [6 S. Ullrich, Phys. Chem. Chem. Phys. 6, 2796 (2004).[Crossref], [Web of Science ®] , [Google Scholar]] or ion yield [7 H. Tao, J. Chem. Phys. 134, 244306 (2011).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]–9 M. Assmann, T. Weinacht, and S. Matsika, J. Chem. Phys. 144, 34301 (2016).[Crossref], [Web of Science ®] , [Google Scholar]]. The availability of these calculations for isolated molecules has spurred new experimental efforts to develop methods that are sufficiently different from all optical techniques. For determination of transient molecular structure, femtosecond X-ray diffraction [10 M. P. Minitti, Phys. Rev. Lett. 114, 255501 (2015).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 11 J. Küpper, Phys. Rev. Lett. 112, 083002 (2014). [Google Scholar]] and electron diffraction [12 J. Yang, Nat. Commun. 7, 11232 (2016).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] have been implemented on optically excited molecules.     

On the type N twisting vacuum solution of the Einstein equations

One of the problems in the catalogue of solutions to the vacuum solutions of the Einstein equations is the dearth of solutions to what is known as the type N twisting metric. Were it to be found in its general form it would then, according to the Peeling theorem of Sachs (Proc R Soc Lond A270:103, 1962), describe the asymptotic gravitational field of an isolated source. The only known mathematical solution was found by Hauser (Phys Rev Lett 33:1112, 1974) and (Phys Rev Lett 33:1525, 1974). In this article the general equations are reduced to one third order complex equation for one complex variable plus one simple condition.     

The Evolution of High-Throughput Macromolecular Crystallography at Synchrotrons

On May 11 and 12, 2000, the Stanford Synchrotron Radiation Laboratory, as it was then known, hosted a “Workshop on Techniques for Automated Mounting, Viewing and Centering Pre-Cooled Protein Crystals” [1 http://www-ssrl.slac.stanford.edu/conferences/workshops/px-robotics/. [Google Scholar], 2 E. Abola, Nature Structural Biology 7, 973–977 (2000).[Crossref], [PubMed] , [Google Scholar]]. The 12 presentations during the meeting all focused on the impact that automation could have on the performance of synchrotron beamlines and thus on research in structural biology. Two principal themes ran through the workshop: (1) robotics to mount crystals on a diffractometer; and (2) methods to place a crystal in the X-ray beam. Five conceptual and prototype robotic systems for automated mounting were described—the original ACTOR from Abbott Laboratories, later modified and marketed by Rigaku/MSC, and the systems which in final form become the ALS [3 G. Snell, Structure 12, 537–545 (2004).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], EMBL/ESRF SC3 [4 F. Cipriani, Acta Cryst. D62(10), 1251–1259 (2006). [Google Scholar]], APS/SBC [5 D. Shu, AIP Conference Proceedings 705(1), 1201–1204 (2004).[Crossref] , [Google Scholar]], and SSRL SAM robots [6 A. E. Cohen, J. Appl. Cryst. 5(6), 720–726 (2002).[Crossref], [Web of Science ®] , [Google Scholar]]. By December of that year, the ACTOR had been installed for testing at Sector 32 of the Advanced Photon Source (Figure 1). Within three years, by the end of 2003, several of these robots, plus the commercial MARcsc from MAR Research, had been deployed to handle frozen protein crystals at beamlines for macromolecular crystallography (MX). Currently, at least 13 distinct robot types, not including variants of the ALS automounter, are employed at synchrotron beamlines to transfer crystals from storage to beam position.     

A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems

In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.