Singular Density Research Articles

Photon absorption of two-dimensional nonsymmorphic Dirac semimetals

Two-dimensional Dirac semimetals have attracted much attention because of their linear energy dispersion and non-trivial Berry phase. Graphene-like 2D Dirac materials are gapless only within certain approximations, e.g., if spin-orbit coupling (SOC) is neglected. It has recently been reported that materials with nonsymmorphic crystal lattice possess symmetry-enforced Dirac-like band dispersion around certain high-symmetry momenta even in the presence of SOC. Here we calculate the optical absorption coefficient of nonsymmorphic semimetals, such as $\alpha$-bismuthene, which hosts two anisotropic Dirac cones with different Fermi velocities along $x$ and $y$ directions.We find that the optical absorption coefficient depends strongly on the anisotropy factor and the photon polarization. When a magnetic field is applied perpendicular to the plane of the material, the absorption coefficient also depends on an internal parameter we termed the mixing angle of the band structure. We further find that an in-plane magnetic field, while leaving the system gapless, can induce a Van-Hove singularity in the joint density of states: this causes a significant enhancement of the optical absorption at the frequency of the singularity for one direction of polarization but not for the orthogonal one, making the optical properties even more strongly dependent on polarization. Due to the anisotropy present in our model, the Dirac cones at two high-symmetry momenta in the Brillouin zone contribute very differently to the optical absorbance. Consequently, it might be possible to preferentially populate one valley or the other by varying photon polarization and frequency. These results suggest that nonsymmorphic 2D Dirac semimetals are excellent candidate materials for tunable magneto-optic devices.

Tolman IV fluid sphere in [formula omitted] gravity

In this article, we studied the behavior of relativistic spherical objects considering Tolman IV spacetime in modified f(R,T) gravity for the uncharged perfect fluid matter. We have chosen the matter Lagrangian as Lm=−p to develop our present model. In particular, for this investigation we have reported for the compact object LMC X−4 [Mass=(1.04±0.09)M⊙; Radius= 8.301−0.2+0.2 Km] in our paper. The effect of the coupling parameter β on the local matter distribution of compact stars has been investigated in this paper. It can be seen that with greater values of β, the sound speed and adiabatic index are higher. On contrary, the mass function takes lower value for higher values of β. Our obtained solution does not admit singularities in the matter density, pressure and metric functions. According to our graphical analysis, this new stellar model satisfies all physical requirements anticipated in a realistic star.

Existence of weak solutions of diffuse interface models for magnetic fluids

AbstractIn this article we collect some recent results on the global existence of weak solutions for diffuse interface models involving incompressible magnetic fluids. We consider both the cases of matched and unmatched specific densities. For the model involving fluids with identical densities we consider the free energy density to be a double well potential whereas for the unmatched density case it is crucial to work with a singular free energy density.

Bottling the champagne: dynamics and radiation trapping of wind-driven bubbles around massive stars

ABSTRACT In this paper, we make predictions for the behaviour of wind bubbles around young massive stars using analytic theory. We do this in order to determine why there is a discrepancy between theoretical models that predict that winds should play a secondary role to photoionization in the dynamics of H iiregions, and observations of young H iiregions that seem to suggest a driving role for winds. In particular, regions such as M42 in Orion have neutral hydrogen shells, suggesting that the ionizing radiation is trapped closer to the star. We first derive formulae for wind bubble evolution in non-uniform density fields, focusing on singular isothermal sphere density fields with a power-law index of -2. We find that a classical ‘Weaver’-like expansion velocity becomes constant in such a density distribution. We then calculate the structure of the photoionized shell around such wind bubbles, and determine at what point the mass in the shell cannot absorb all of the ionizing photons emitted by the star, causing an ‘overflow’ of ionizing radiation. We also estimate perturbations from cooling, gravity, magnetic fields and instabilities, all of which we argue are secondary effects for the conditions studied here. Our wind-driven model provides a consistent explanation for the behaviour of M42 to within the errors given by observational studies. We find that in relatively denser molecular cloud environments around single young stellar sources, champagne flows are unlikely until the wind shell breaks up due to turbulence or clumping in the cloud.

Shock-induced cavitation and wavefront analysis inside a water droplet

The objective of this study is to develop a basic understanding of the interaction of shock waves with density inhomogeneities. We consider the particular instance of a planar air shock impinging on a spherical water droplet and discuss to what extent this interaction can lead to the inception of cavitation inside the droplet. The effort centers on early phases of the interaction, which are analyzed using both ray theory and a hydrodynamic code. Within the context of ray theory, the occurrence of focusing is examined in detail, and parametric equations are derived for the transmitted wavefront and its multiple internal reflections. It is found that wave patterns predicted by ray calculations compare extremely well with the more accurate numerical solutions from simulations. In particular, it is shown that the internal wavefront assumes a complex time-dependent shape whose dominant feature is the existence of cusp singularities. These singular points are shown to trace out surfaces that are the caustics of the associated system of rays. From the singularities of the energy flux density of the refracted wave, the parametric equations of the caustic surface associated with the kth reflected wavefront are deduced. As a consequence of the focusing process, simulations show the formation of negative-pressure regions in the internal flow field. These low-pressure zones are identified as possible spots at which cavitation may occur, depending on the magnitude of pressure reached. Finally, numerical results provide quantitative information on the dependence of negative-pressure peaks upon incident-shock-wave strength.

Unusual Features of QCD Low-Energy Modes in the Infrared Phase.

It was recently proposed that there is a phase in thermal QCD (IR phase) at temperatures well above the chiral crossover, featuring elements of scale invariance in the infrared (IR). Here, we study the effective spatial dimensions d_{IR} of Dirac low-energy modes in this phase, in the context of pure-glue QCD. Our d_{IR} is based on the scaling of mode support toward thermodynamic limit, and hence is an IR probe. Ordinary extended modes, such as those at high energy, have d_{IR}=3. We find d_{IR}<3 in the spectral range whose lower edge coincides with λ_{IR}=0, the singularity of spectral density defining the IR phase, and the upper edge with λ_{A}, the previously identified Anderson-like nonanalyticity. Details near λ_{IR} are unexpected in that only exact zero modes are d_{IR}=3, while a thin spectral layer near zero is d_{IR}=2, followed by an extended layer of d_{IR}=1 modes. With only integer values appearing, d_{IR} may have a topological origin. We find similar structure at λ_{A}, and associate its adjacent thin layer (d_{IR}⪆2) with Anderson-like criticality. Our analysis reveals the manner in which nonanalyticities at λ_{IR} and λ_{A}, originally identified in other quantities, appear in d_{IR}(λ). This dimension structure may be important for understanding the near-perfect fluidity of the quark-gluon medium seen in accelerator experiments. The role of λ_{A} in previously conjectured decoupling of IR component is explained.

Configuration entropy in the soft wall AdS/QCD model and the Wien law

The soft wall AdS/QCD holographic model provides simple estimates for the spectra of light mesons and glueballs satisfying linear Regge trajectories. It is also an interesting tool to represent the confinement/deconfinement transition of a gauge theory, that is pictured as a Hawking-Page transition from a dual geometry with no horizon to a black hole space. A very interesting tool to analyze stability of general physical systems that are localized in space is the configuration (or complexity) entropy (CE). This quantity, inspired in Shannon information entropy, is defined in terms of the energy density of the system in momentum space. The purpose of this work is to use the CE to investigate the stability of the soft wall background as a function of the temperature. A nontrivial aspect is that the geometry is an anti-de Sitter black hole, that has a singular energy density. In order to make it possible to calculate the CE, we first propose a regularized form for the black hole energy density. Then, calculating the CE, it is observed that its behavior is consistently related to the black hole instability in anti-de Sitter space. Another interesting result that emerges from this analysis is that the regularized energy density shows a behavior similar to the Wien law, satisfied by black body radiation. That means: the momentum kmax where the energy density is maximum, varies with the temperature T obeying the relation: T/kmax=constant in the deconfined phase.

Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain

When the quantum critical transverse-field Ising chain is perturbed by a longitudinal field, a quantum integrable model emerges in the scaling limit with massive excitations described by the exceptional $E_{8}$ Lie algebra. Using the corresponding analytical form factors of the quantum $E_{8}$ integrable model, we systematically study the spin dynamic structure factor of the perturbed quantum critical Ising chain, where particle channels with total energy up to 5$m_1$ ($m_1$ being the mass of the lightest $E_{8}$ particle) are exhausted. In addition to the significant single-particle contributions to the dynamic spectrum, each two-particle channel with different masses is found to exhibit an edge singularity at the threshold of the total mass and decays with an inverse square root of energy, which is attributed to the singularity of the two-particle density of states at the threshold. The singularity is absent for particles with equal masses due to a cancellation mechanism involving the structure of the form factors. As a consequence, the dynamic structure factor displays a cascade of bumping peaks in the continuum region with clear singular features which can serve as a solid guidance for the material realization of the quantum $E_{8}$ model.

Matter-antimatter asymmetry induced by non-linear electrodynamics

In this work, we propose an economical model to address some open cosmological problems such as the absence of the initial cosmological singularity, an early acceleration of the Universe and the generation of matter–antimatter asymmetry. The model is based on a scenario in which the early Universe consists of a non-linear electrodynamics (NLED) fields. It is found that the NLED model has an equation of state which shows that the Universe undergoes an early epoch acceleration to a radiation era given by . We show that the singularities in the energy density, pressure and curvature are absent at early stages. In our scenario, the baryon asymmetry is generated by the non-linearity parameter β. Additionally, we calculate the resulting baryon asymmetry and discuss how a successful gravitational baryogenesis is obtained for different values of the model’s parameter space.

Three dimensional reconstruction to visualize atrial fibrillation activation patterns on curved atrial geometry.

BackgroundThe rotational activation created by spiral waves may be a mechanism for atrial fibrillation (AF), yet it is unclear how activation patterns obtained from endocardial baskets are influenced by the 3D geometric curvature of the atrium or ‘unfolding’ into 2D maps. We develop algorithms that can visualize spiral waves and their tip locations on curved atrial geometries. We use these algorithms to quantify differences in AF maps and spiral tip locations between 3D basket reconstructions, projection onto 3D anatomical shells and unfolded 2D surfaces.MethodsWe tested our algorithms in N = 20 patients in whom AF was recorded from 64-pole baskets (Abbott, CA). Phase maps were generated by non-proprietary software to identify the tips of spiral waves, indicated by phase singularities. The number and density of spiral tips were compared in patient-specific 3D shells constructed from the basket, as well as 3D maps from clinical electroanatomic mapping systems and 2D maps.ResultsPatients (59.4±12.7 yrs, 60% M) showed 1.7±0.8 phase singularities/patient, in whom ablation terminated AF in 11/20 patients (55%). There was no difference in the location of phase singularities, between 3D curved surfaces and 2D unfolded surfaces, with a median correlation coefficient between phase singularity density maps of 0.985 (0.978–0.990). No significant impact was noted by phase singularities location in more curved regions or relative to the basket location (p>0.1).ConclusionsAF maps and phase singularities mapped by endocardial baskets are qualitatively and quantitatively similar whether calculated by 3D phase maps on patient-specific curved atrial geometries or in 2D. Phase maps on patient-specific geometries may be easier to interpret relative to critical structures for ablation planning.

Product Matrix Processes With Symplectic and Orthogonal Invariance via Symmetric Functions

Abstract We apply symmetric function theory to study random processes formed by singular values of products of truncations of Haar distributed symplectic and orthogonal matrices. These product matrix processes are degenerations of Macdonald processes introduced by Borodin and Corwin. Through this connection, we obtain explicit formulae for the distribution of singular values of a deterministic matrix multiplied by a truncated Haar orthogonal or symplectic matrix under conditions where the latter factor acts as a rank $1$ perturbation. Consequently, we generalize the recent Kieburg–Kuijlaars–Stivigny formula for the joint singular value density of a product of truncated unitary matrices to symplectic and orthogonal symmetry classes. Specializing to products of two symplectic matrices with a rank $1$ perturbative factor, we show that the squared singular values form a Pfaffian point process.

Magnetic nulls in interacting dipolar fields

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance$\varDelta _d$. Electron inertia ensures$\varDelta _d\gtrsim c/\omega _{pe}$. The lines that lie within a magnetic flux tube of radius$\varDelta _d$at the place where the field strength$B$is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where$B=0$vanishes, then distinguishable lines come no closer to the null than$\approx (a^2c/\omega _{pe})^{1/3}$, where$a$is a characteristic spatial scale of the magnetic field. The behaviour of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.

Random matrix approach to the boson peak and Ioffe-Regel criterion in amorphous solids

We present a random matrix approach to study the general vibrational properties of stable amorphous solids with translational invariance using the correlated Wishart ensemble. Within this approach, both analytical and numerical methods can be applied. Applying the random matrix theory to the correlated Wishart ensemble, we found the analytical form of the vibrational density of states and the dynamical structure factor. The ratio between the number of bonds and the number of degrees of freedom controls the Ioffe-Regel frequency, which determines the crossover between low-frequency propagating phonons and diffusons at higher frequencies. The reduced vibrational density of states shows the boson peak, whose frequency is close to the Ioffe-Regel crossover. In the isostatic case, we obtain the low-frequency cusplike singularity of the vibrational density of states, which was observed numerically. We also present a simple numerical random matrix model with finite interaction radius, whose properties rapidly converge to the analytical results with increasing the interaction radius. For a finite interaction radius, the numerical model demonstrates the presence of quasilocalized vibrations with a power-law low-frequency density of states.

Cycle length statistics during human atrial fibrillation reveal refractory properties of the underlying substrate: a combined in silico and clinical test of concept study.

The treatment of atrial fibrillation beyond pulmonary vein isolation has remained an unsolved challenge. Targeting regions identified by different substrate mapping approaches for ablation resulted in ambiguous outcomes. With the effective refractory period being a fundamental prerequisite for the maintenance of fibrillatory conduction, this study aims at estimating the effective refractory period with clinically available measurements. A set of 240 simulations in a spherical model of the left atrium with varying model initialization, combination of cellular refractory properties, and size of a region of lowered effective refractory period was implemented to analyse the capabilities and limitations of cycle length mapping. The minimum observed cycle length and the 25% quantile were compared to the underlying effective refractory period. The density of phase singularities was used as a measure for the complexity of the excitation pattern. Finally, we employed the method in a clinical test of concept including five patients. Areas of lowered effective refractory period could be distinguished from their surroundings in simulated scenarios with successfully induced multi-wavelet re-entry. Larger areas and higher gradients in effective refractory period as well as complex activation patterns favour the method. The 25% quantile of cycle lengths in patients with persistent atrial fibrillation was found to range from 85 to 190 ms. Cycle length mapping is capable of highlighting regions of pathologic refractory properties. In combination with complementary substrate mapping approaches, the method fosters confidence to enhance the treatment of atrial fibrillation beyond pulmonary vein isolation particularly in patients with complex activation patterns.

Nine years of SMOS sea surface salinity global maps at the Barcelona Expert Center

Abstract. After more than 10 years in orbit, the Soil Moisture and Ocean Salinity (SMOS) European mission is still a unique, high-quality instrument for providing soil moisture over land and sea surface salinity (SSS) over the oceans. At the Barcelona Expert Center (BEC), a new reprocessing of 9 years (2011–2019) of global SMOS SSS maps has been generated. This work presents the algorithms used in the generation of BEC global SMOS SSS product v2.0, as well as an extensive quality assessment. Three SMOS SSS fields are distributed: a high-resolution level-3 product (with DOI https://doi.org/10.20350/digitalCSIC/12601, Olmedo et al., 2020a) consisting of binned SSS in 9 d maps at 0.25∘×0.25∘; low-resolution level-3 SSS computed from the binned salinity by applying a smoothing spatial window of 50 km radius; and level-4 SSS (with DOI https://doi.org/10.20350/digitalCSIC/12600, Olmedo et al., 2020b) consisting of daily 0.05∘×0.05∘ maps that are computed by multifractal fusion with sea surface temperature maps. For the validation of BEC SSS products, we have applied a battery of tests aimed at the assessment of quality of the products both in value and in structure. First, we have compared BEC SSS products with near-to-surface salinity measurements provided by Argo floats. Secondly, we have assessed the geophysical consistency of the products characterized by singularity analysis, and the effective spatial resolutions are also estimated by means of power density spectra and singularity density spectra. Finally, we have calculated full maps of SSS errors by using correlated triple collocation. We have compared the performance of the BEC SMOS product with other satellite SSS and reanalysis products. The main outcomes of this quality assessment are as follows. (i) The bias between BEC SMOS and Argo salinity is lower than 0.02 psu at a global scale, while the standard deviation of their difference is lower than 0.34 and 0.27 psu for the high- and low-resolution level-3 fields (respectively) and 0.24 psu for the level-4 salinity. (ii) The effective spatial resolution is around 40 km for all SSS products and regions. (iii) The results from triple collocation show the BEC SMOS level-4 product as the product with the lowest estimated salinity error in most of the global ocean and the BEC SMOS high-resolution level-3 as the one with the lowest estimated salinity error in regions strongly affected by rainfall and continental freshwater discharge.

Half-metallic ferromagnetism in layered CdOHCl induced by hole doping

Next-generation spintronic devices will benefit from low-dimensionality, ferromagnetism, and half–metallicity, possibly controlled by electric fields. We find these technologically–appealing features to be combined with an exotic microscopic origin of magnetism in doped CdOHCl, a van der Waals material from which 2D layers may be exfoliated. By means of first principles simulations, we predict homogeneous hole–doping to give rise to p-band magnetism in both the bulk and monolayer phases and interpret our findings in terms of Stoner instability: as the Fermi level is tuned via hole–doping through singularities in the 2D-like density of states, ferromagnetism develops with large saturation magnetization of 1 µ B per hole, leading to a half-metallic behaviour for layer carrier densities of the order of 1014 cm−2. Furthermore, we put forward electrostatic doping as an additional handle to induce magnetism in monolayers and bilayers of CdOHCl. Upon application of critical electric fields perpendicular to atomically–thin-films (as low as 0.2 and 0.5 V Å−1 in the bilayer and monolayer case, respectively), we envisage the emergence of a magnetic half-metallic state. The different behaviour of monolayer vs bilayer systems, as well as an observed asymmetric response to positive and negative electric fields in bilayers, are interpreted in terms of intrinsic polarity of CdOHCl atomic stacks, a distinctive feature of the material. In perspective, given the experimentally accessible magnitude of critical fields in bilayer of CdOHCl, one can envisage p band magnetism to be exploited in miniaturized spintronic devices.

Random Hamiltonians with arbitrary point interactions in one dimension

We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we prove the following dichotomy: Either every realization of the random operator has purely absolutely continuous spectrum or spectral and exponential dynamical localization hold. In particular, we establish Anderson localization for Schrödinger operators with Bernoulli-type random singular potential and singular density.

Calibration of the Heston stochastic local volatility model: A finite volume scheme

The two most popular equity and FX derivatives pricing models in banking practice are the local volatility model and the Heston model. While the former has the appealing property that it can be calibrated exactly to any given set of arbitrage free European vanilla option prices, the latter delivers more realistic smile dynamics. In this paper, we combine both modeling approaches to the Heston stochastic local volatility model. We build upon a theoretical framework that has been already developed and focus on the numerical model calibration which requires special care in the treatment of mixed derivatives and in cases where the Feller condition is not met in the Heston model leading to a singular transition density at zero volatility. We propose a finite volume scheme to calibrate the model after a suitable transformation of the model equation and demonstrate its accuracy in numerical test cases using real market data.

Evolution of spin density vectors in a strongly focused composite field

The evolution of the spin density vectors (SDVs) is studied in a strongly focused composite field. It is found that the SDVs can be spiral along the propagation axis, and they are perpendicular to the ys direction on the ys axis. This behavior is governed by the Gouy phase difference between the field polarization components. The 60° rotation of the spatial distribution of the transverse SDVs is also generated, which is found to be controlled by the Gouy phase difference between the field orbital angular momentum modes. Additionally, the spin density singularities are observed in the evolution of the SDVs.

Shell-crossing in a ΛCDM Universe

ABSTRACT Perturbation theory is an indispensable tool for studying the cosmic large-scale structure, and establishing its limits is therefore of utmost importance. One crucial limitation of perturbation theory is shell-crossing, which is the instance when cold-dark-matter trajectories intersect for the first time. We investigate Lagrangian perturbation theory (LPT) at very high orders in the vicinity of the first shell-crossing for random initial data in a realistic three-dimensional Universe. For this, we have numerically implemented the all-order recursion relations for the matter trajectories, from which the convergence of the LPT series at shell-crossing is established. Convergence studies performed at large orders reveal the nature of the convergence-limiting singularities. These singularities are not the well-known density singularities at shell-crossing but occur at later times when LPT already ceased to provide physically meaningful results.