Isotropic Space Research Articles

The Negative Baryon Acoustic Oscillation Shift in the Lyα Forest from Cosmological Simulations

We present the first measurement of the Lyα forest baryon acoustic oscillations (BAO) shift parameter from cosmological simulations. In particular, we generate a suite of 1000 accurate effective field-level bias-based Lyα forest simulations of volume V=(1h−1Gpc)3 at z = 2, both in real and redshift space, calibrated upon two fixed-and-paired cosmological hydrodynamic simulations. To measure the BAO, we stack the 3D power spectra of the 1000 different realizations, compute the average, and use a model accounting for a proper smooth-peak component decomposition of the power spectrum, to fit it via an efficient Markov Chain Monte Carlo scheme estimating the covariance matrices directly from the simulations. We report the BAO shift parameters to be α=0.9969−0.0014+0.0014 and α=0.9905−0.0027+0.0027 in real and redshift space, respectively. We also measure the bias b lya and the BAO broadening parameter Σnl, finding blya=−0.1786−0.0001+0.0001 and Σnl=3.87−0.20+0.20 in real space, and blya=−0.073−0.004+0.005 and Σnl=6.55−0.22+0.23 in redshift space. Moreover, we measure the linear Kaiser factor βlya=1.39−0.18+0.24 from the isotropic redshift space fit. Overall, we find evidence for a negative shift of the BAO peak at the ∼2.2σ and ∼3.5σ levels in real and redshift space, respectively. This work sets new important theoretical constraints on the Lyα forest BAO scale and offers a potential solution to the tension emerging from previous observational analysis, in light of ongoing and upcoming Lyα forest spectroscopic surveys, such as DESI, the Prime Focus Spectrograph Survey, and WEAVE-QSO.

Analytical analysis of the interaction between cavities and a crack in bonded isotropic and anisotropic half spaces under SH wave

Interaction between two cavities and a linear crack subjected to elastic shear horizontally (SH) wave is investigated analytically in this work. Two cavities are buried in two bounded half spaces respectively and the cross-section of each cavity has a different shape. The media of two half spaces are isotropic and anisotropic respectively, and the complex function method is applied to first solve the wave equation in each medium. Then, with the help of image principle, Green’s functions and wave field expressions in each separated half space are constructed. Subsequently, utilizing “conjunction” technique, a series of Fredholm integral equations containing undetermined forces at the interface are obtained and reduced in order to be solved. Dynamic stress distribution is mainly considered to discuss the interaction between the cavities and the crack. Finally, a parametric study on dynamic stress concentration factor (DSCF) and dynamic stress intensity factor (DSIF) presents the interaction is affected by several dimensionless factors simultaneously.

Classifications of THA-surfaces in I^3

In classical differential geometry, the problem of obtaining Gaussian and mean curvatures of a surface is one of the most important problems. A surface M2 in I3 is a THA-surface of first type if it can be parameterized by r(s, t) = (s, t, Af(s + at)g(t) + B(f(s + at) + g(t))). A surface M2 in I3 is a THA- surface of second type if it can be parameterized by r(s, t) = (s, Af(s + at)g(t) + B(f(s + at) + g(t)), t), where A and B are non-zero real numbers [16, 17, 18]. In this paper, we classify two types THA-surfaces in the 3-dimensional isotropic space I3 and study THA-surfaces with zero curvature in I3.

Cosmographic and matter bounce scenario in modified torsion gravity

In this manuscript, we investigate the matter bounce cosmological implications in the context of f(T,τ) gravity (T represents the torsion scalar whereas τ is the trace of the energy–momentum tensor). We construct the field equations for spatially flat homogeneous and isotropic space–time with perfect fluid configuration. We consider the two particular forms of scale factor inspired by loop-quantum cosmology to investigate the matter bounce mechanism. In this regard, we examine the graphical behavior of cosmological as well as dynamical parameters at and in the neighborhood of bounce point. Furthermore, the stability via perturbation technique and energy conditions are also discussed. It is concluded that all the cosmographic tests favor the bouncing cosmology for an appropriate choice of model parameters. It is worth mentioning that considered models are stable and energy conditions are violated at the bouncing point as well as in its vicinity leading to a successful bouncing scenario.

Stress Field Features in Vicinity of Interfacial Circular Inclusion Under Mixed Contact Conditions with Piecewise Homogeneous Transversely Isotropic Space

Stress Field Features in Vicinity of Interfacial Circular Inclusion Under Mixed Contact Conditions with Piecewise Homogeneous Transversely Isotropic Space

On n-Dimensional Maxwell and Dirac Equations in Curved Space-Time and Its Applications in SO(P,Q) Group Theoretic Image Processing

Maxwell equations in p time and q spatial dimensions are formulated. Properties of the Green’s function for the associated (p,q)-wave operator are derived based on contour integration. The notions of electric and magnetic fields in (p,q)-dimensions is explored by analogy with four dimensional physics and the problem of far field computation of the radiation field generated by charges and currents in \((1,n-1)\) space-time is analyzed. SO(p,q) invariance properties of the Maxwell equations are deduced and used to formulate SO(p,q)-group theoretic image processing problems in (p,q)-dimensions. Dirac’s equation in (p,q)-dimensional space-time is derived using the Clifford algebra of the Dirac gamma matrices. SO(p,q)-invariance of the Dirac equation based on the spinor representation of \(SO(p,q)\) is mentioned. The Maxwell’s equations in (p,q)-dimensional curved space-time is analyzed using perturbation theory in the context of maximally symmetric spaces which play a fundamental role in \((p,q)\)-dimensional cosmological models for homogeneous and isotropic spaces. The Einstein-Maxwell equations for (p,q)-dimensional gravity and electromagnetism is studied and used to derive the equations of motion of point charges carrying mass moving under mutual gravitational and electromagnetic interactions in general relativity. Finally, Dirac’s equation in (p,q)-dimensional curved space-time interacting with the (p,q)-dimensional electromagnetic field is looked at. \(U(1)\)-Gauge, local SO(p,q) Lorentz and diffeomorphism invariance of this equation is analyzed. Local \(SO(p,q)\) invariance of the curved space-time Dirac equation is deduced based on transformation properties of the Dirac matrices under the spinor representation. The appendix presents some applications of group representation theoretic statistical image processing on a manifold to the situation when the image field is described by the six component electromagnetic field tensor on which the Lorentz group acts.

Bayesian Inversion of MDJ Seismograms for Source Parameters and Yields of DPRK Underground Nuclear Explosions 2 to 6

AbstractThe Democratic People’s Republic of Korea (DPRK) conducted six underground nuclear explosions at the Punggye-ri nuclear test site at Mount Mantap, a granite peak. Test 1 was separate from tests 2 to 6, which were within about 1 km of each other. Using seismograms recorded at Mudanjiang (MDJ) seismic station in China, I propose a new approach to obtain source parameters, source time functions and yields of events 2 to 6, assuming they share the same Green’s function from Punggye-ri to MDJ. Each source is modelled as a spherical cavity in a homogeneous isotropic elastic full space, with four independent parameters constrained by published data on the properties of granite and analysis of the recorded MDJ seismograms. The effect of the ground surface is included as a planar reflection that modifies the pressure at the cavity boundary. The Green’s function for each event is estimated by deconvolving the seismogram for the estimated source time function. Very fast simulated annealing (VFSA) is used to search the parameter space to minimise the root-mean square difference among the estimated Green’s functions and their mean. The estimated Green’s functions are similar and differ in amplitude by less than a factor of 2. Green’s functions from Punggye-ri to other seismic stations may be obtained by deconvolving the seismograms for the corresponding source time functions. Mapping the nonlinear zones surrounding each explosion indicates that this part of the site was destroyed by the underground nuclear tests before its official destruction on 24 May 2018.

Linear Monte Carlo quadrature with optimal confidence intervals

We study the numerical integration of functions from isotropic Sobolev spaces Wps([0,1]d) using finitely many function evaluations within randomized algorithms, aiming for the smallest possible probabilistic error guarantee ε>0 at confidence level 1−δ∈(0,1). For spaces consisting of continuous functions, non-linear Monte Carlo methods with optimal confidence properties have already been known, in few cases even linear methods that succeed in that respect. In this paper we promote a method called stratified control variates (SCV) and by it show that already linear methods achieve optimal probabilistic error rates in the high smoothness regime without the need to adjust algorithmic parameters to the uncertainty δ. We also analyse a version of SCV in the low smoothness regime where Wps([0,1]d) may contain functions with singularities. Here, we observe a polynomial dependence of the error on δ−1 in contrast to the logarithmic dependence in the high smoothness regime.

On subordination conditions for systems of minimal di erential operators

In this paper, we provide a review of results on apriori estimates for systems of minimal differential operators in the scale of spaces \(L^p(\Omega),\) where \(p\in[1,\infty].\) We present results on the characterization of elliptic and \(l\)-quasielliptic systems using apriori estimates in isotropic and anisotropic Sobolev spaces \(W_{p,0}^l(\mathbb
 R^n),\)\(p\in[1,\infty].\) For a given set \(l=(l_1,\dots,l_n)\in\mathbb
 N^n\) we prove criteria for the existence of \(l\)-quasielliptic and weakly coercive systems and indicate wide classes of weakly coercive in \(W_{p,0}^l(\mathbb
 R^n),\) \(p\in[1,\infty],\) nonelliptic, and nonquasielliptic systems. In addition, we describe linear spaces of operators that are subordinate in the \(L^\infty(\mathbb R^n)\)-norm to the tensor product of two elliptic differential polynomials.

Influence of Concentrated Forces on an Interface Inclusion under the Conditions of Smooth Contact in the Inhomogeneous Transversely Isotropic Space

Influence of Concentrated Forces on an Interface Inclusion under the Conditions of Smooth Contact in the Inhomogeneous Transversely Isotropic Space

Rayleigh waves in isotropic elastic materials with micro-voids

In this paper, we show that a general method introduced by Fu and Mielke allows to give a complete answer on the existence and uniqueness of a subsonic solution describing the propagation of surface waves in an isotropic half space modelled with the linear theory of isotropic elastic materials with micro-voids. Our result is valid for the entire class of materials admitting real wave propagation which include auxetic materials (negative Poisson’s ratio) and composite materials with negative-stiffness inclusions (negative Young’s modulus). Moreover, the used method allows to formulate a simple and complete numerical strategy for the computation of the solution.

Shear Waves in an Elastic Plate with a Hole Resting on a Rough Base

The article is devoted to the analytical and numerical study of the pattern of propagation and attenuation, due to Coulomb friction, of shear waves in an infinite elastic thin plate with a circular orifice of radius r0 lying on a rough base. Considering the friction forces and their influence on the sample of wave propagation in extended rods or thin plates is important for calculating the stress–strain state in them and the size of the area of motion. An exact analytical solution of a nonlinear boundary value problem for tangential stresses and velocities is obtained in quadratures by the Laplace transform, with respect to time. It turned out that the complete exhaustion of the wave front of a strong rupture occurs at a finite distance r* from the center of the orifice, and an elementary formula is given for this distance (the case of tangential shock stresses suddenly applied to the orifice boundary is considered). For various ratios of the magnitude of the limiting friction force to the amplitude of the applied load, the stopping (trailing) wave fronts are calculated. After passing them, a state of static equilibrium between the elastic and friction forces with a nonlinear distribution of residual stresses is established in the region r0≤r≤r*. For the first time, a precise analytical solution was obtained for the boundary value problem of the propagation of elastic shear waves in an infinite isotropic space with a cylindrical cavity, when a tangential shock load is set on its surface.

The geometry of discrete asymptotic-geodesic 4-webs in isotropic 3-space

The geometry of webs has been investigated over more than a century driven by still open problems. In our paper we contribute to extending the knowledge on webs from the perspective of the geometry of webs on surfaces in three dimensional space. Our study of AGAG-webs is motivated by architectural applications of gridshell structures where four families of manufactured curves on a curved surface are realizations of asymptotic lines and geodesic lines. We describe all discrete AGAG-webs in isotropic space and propose a method to construct them. Furthermore, we prove that some sub-nets of an AGAG-web are timelike minimal surfaces in Minkowski space and can be embedded into a one-parameter family of discrete isotropic Voss nets.

Spinor Representation in Isotropic 3-Space via Laguerre Geometry

We give a detailed description of the geometry of isotropic space, in parallel to those of Euclidean space within the realm of Laguerre geometry. After developing basic surface theory in isotropic space, we define spin transformations, directly leading to the spinor representation of conformal surfaces in isotropic space. As an application, we obtain the Weierstrass-type representation for zero mean curvature surfaces, and the Kenmotsu-type representation for constant mean curvature surfaces, allowing us to construct many explicit examples.

Anisotropic seabed soil failure description and three-dimensional simulation method

In order to find out the underlying effect of anisotropy on the failure characteristics from the mesoscopic mechanism, using the concept of fabric tensor and assumption of mutual mapping between isotropic space and anisotropic space, a compound stress is proposed based on the combination of ordinary stress and fabric tensor. This compound stress can be used to describe the primary anisotropic properties effectively. For the difference in the effect of stress-induced anisotropy on shear strength of various geotechnical materials in the deviatoric plane, a generalized failure criterion is proposed. This failure criterion can effectively describe various criteria forms from Von-Mises criterion to SMP criterion within a relatively large range. The hydrostatic pressure effect can also be indicated by the shape of the power function on the meridional plane. A primary anisotropy generalized failure criterion can be obtained when the compound stress is used to describe the new generalized failure criterion and the corresponding transformation stress method has been proposed. This method can consider the effect of native induced anisotropy and stress induced anisotropy on the shear strength simultaneously. The comparison between predicted and tested results shows that the proposed anisotropic generalized stress failure criterion and its transformation method can be applied to the geotechnical engineering practice simply, its rationality and applicability have also been verified.

Generating and Characterization Loft Surface by Type-2-Bishop Frame in Isotropic Space

Generating and Characterization Loft Surface by Type-2-Bishop Frame in Isotropic Space

Catenaries and Singular Minimal Surfaces in the Simply Isotropic Space

Catenaries and Singular Minimal Surfaces in the Simply Isotropic Space

Sampling numbers of smoothness classes via ℓ1-minimization

Using techniques developed recently in the field of compressed sensing we prove new upper bounds for general (nonlinear) sampling numbers of (quasi-)Banach smoothness spaces in L2. In particular, we show that in relevant cases such as mixed and isotropic weighted Wiener classes or Sobolev spaces with mixed smoothness, sampling numbers in L2 can be upper bounded by best n-term trigonometric widths in L∞. We describe a recovery procedure from m function values based on ℓ1-minimization (basis pursuit denoising). With this method, a significant gain in the rate of convergence compared to recently developed linear recovery methods is achieved. In this deterministic worst-case setting we see an additional speed-up of m−1/2 (up to log factors) compared to linear methods in case of weighted Wiener spaces. For their quasi-Banach counterparts even arbitrary polynomial speed-up is possible. Surprisingly, our approach allows to recover mixed smoothness Sobolev functions belonging to SprW(Td) on the d-torus with a logarithmically better rate of convergence than any linear method can achieve when 1<p<2 and d is large. This effect is not present for isotropic Sobolev spaces.

Influence of Concentrated Forces and Heat Sources on the Distribution of Stresses in the Interface of Two Different Transversely Isotropic Half Spaces

Influence of Concentrated Forces and Heat Sources on the Distribution of Stresses in the Interface of Two Different Transversely Isotropic Half Spaces

The Topography of Memory: The Constitutive Relation Between Body Memory and Place Memory

A new interest in space emerged in contemporary studies of body memory. According to Merleau-Ponty, the lived body constitutes a close connection between place and memory. The real or even imagined movements of the body contribute to the recollection of places. Recently, Edward S. Casey and Thomas Fuchs highlighted the constitutive role of the body in remembering. First, the paper intends to show the intertwined relation between body memory and place memory. For instance, Casey regards Proust’s madeleine experience as an instance of place memory, and he argues that the body can sustain and recollect place memories. According to Casey, modern philosophy neglected the concept of place, in which the lived body is dwelling, and introduced the concept of site; that is, the geometrical extension of a homogeneous and isotropic space. Second, the paper examines the psychological and emotional aspects of place memories. According to Fuchs, body and place memory constitute a horizontal unconscious that consists of the zones of attraction and avoidance of the lived space. Finally, the paper argues that place memory has much to offer to the phenomenological investigation of the self. Place memory eventuates the recollection of distant memories in an affectively charged form. This type of memory establishes an affective connection with the past and contributes to the preservation of personal identity.