Heavy right-handed neutrinos are highly motivated due to their connection with the origin of neutrino masses via the seesaw mechanism. If the right-handed neutrino Majorana mass is at or below the weak scale, direct experimental discovery of these states is possible in laboratory experiments. However, there is no basis to expect right-handed neutrinos to be so light since the Majorana mass is a technically natural parameter and could comfortably reside at any scale, including at scales far above the weak scale. Here we explore the possibility that the right-handed neutrino Majorana mass originates from electroweak symmetry breaking. Working within an effective theory with two Higgs doublets, a nonzero lepton number is assigned to the bilinear operator built from the two Higgs fields, which is then coupled to the right-handed neutrino mass operator. In tandem with the neutrino Yukawa coupling, following electroweak symmetry breaking a seesaw mechanism operates, generating the light Standard Model neutrino masses along with right-handed neutrinos with masses below the electroweak scale. This scenario leads to novel phenomenology in the Higgs sector, which may be probed at the LHC and at future colliders. There are also interesting prospects for neutrinoless double beta decay and lepton flavor violation. We also explore some theoretical aspects of the scenario, including the technical naturalness of the effective field theory and ultraviolet completions of the right-handed neutrino Majorana mass.

We present a reduced-scaling auxiliary-field quantum Monte Carlo (AFQMC) framework designed for large molecular systems and ensembles, with or without coupling to optical cavities. Our approach leverages the natural block sparsity of the Cholesky decomposition (CD) of electron repulsion integrals in molecular ensembles and employs tensor hypercontraction (THC) to efficiently compress low-rank Cholesky blocks. By representing the Cholesky vectors in a mixed format, keeping high-rank blocks in block-sparse form and compressing low-rank blocks with THC, we reduce the scaling of exchange-energy evaluation from quartic to robust cubic in the number of molecular orbitals N, while lowering memory from cubic toward quadratic. Benchmark analyses on one-, two-, and three-dimensional molecular ensembles (up to ∼1,200 orbitals) show that (a) the number of nonzeros in Cholesky tensors grows linearly with system size across dimensions; (b) the average numerical rank increases sublinearly and does not saturate at these sizes; and (c) rank heterogeneity─some blocks nearly full rank and many low rank, naturally motivates the proposed mixed block sparsity and THC scheme for efficient calculation of exchange energy. We demonstrate that the mixed scheme yields cubic wall-time scaling with favorable prefactors and preserves AFQMC accuracy.

We examine the linear stability of a shear flow driven by wind stress at the free surface and rotation at the lower boundary, mimicking oceanic flows influenced by surface winds and the Earth’s rotation. The linearised eigenvalue problem is solved using the Chebyshev spectral collocation method and a long-wave asymptotic analysis. Our results reveal new long-wave instability modes that emerge for non-zero rotational Reynolds numbers. It is observed that the most unstable mode, characterised by the lowest critical parameters, corresponds to long-wave spanwise disturbances with vanishing streamwise wavenumber. The asymptotic analysis, which shows excellent agreement with numerical results, analytically confirms the existence of this instability. Thus, the present study demonstrates the hitherto unreported combined influence of wind stress and the Earth’s rotation on ocean dynamics.

We extract the equation of state of hot quark matter from a holographic 2 + 1 flavor quantum chromodynamics (QCD) model, which could form the core of a stable compact star. By adding a thin hadron shell, a new type of hybrid star is constructed. With the temperature serving as a parameter, the EoS varies and we obtain stable stars with mass ranging from about 5 to 30 solar masses, and the maximum compactness around 0.2. The I-Love-Q-C relations are further discussed, and compared with the neutron star cases. These compact stars are candidates for black hole mimickers, which could be observed by gravitational waves and distinguished by properties like nonzero tidal Love number and electromagnetic signals.

Let p≥3 be a prime number. A Fermat curve over Q of exponent p is defined by an equation of the form axp+byp+czp=0, where a, b, c are non-zero rational numbers. We prove in this article that there exist infinitely many Fermat curves defined over Q, of exponent p, pairwise non Q-isomorphic, contradicting the Hasse principle.

With no binary neutron star (BNS) merger detected yet during the fourth observing run (O4) of the LIGO-Virgo-KAGRA (LVK) gravitational wave (GW) detector network, despite the time volume (VT) surveyed with respect to the end of O3 having increased by more than a factor of three, a pressing question is how likely the detection of at least one BNS merger is in the remainder of the run. I present here a simple and general method of addressing such a question, which constitutes the basis for the predictions that have been presented in the LVK Public Alerts User Guide during the hiatus between the O4a and O4b parts of the run. The method, which can be applied to neutron star–black hole (NSBH) mergers as well, is based on simple Poisson statistics and on an estimate of the ratio of the VT span by the future run to that span by previous runs. An attractive advantage of this method is that its predictions are independent of the mass distribution of the merging compact binaries, which is very uncertain at the present moment. The results, not surprisingly, show that the most likely outcome of the final part of O4 is the absence of any BNS merger detection. Still, the probability of a non-zero number of detections is 34−46%. For NSBH mergers, the probability of at least one additional detection is 64−71%. The prospects for the next observing run, O5, are more promising, with predicted numbers of NBNS,O5 = 2.8−21+44, and NSBH detections of NNSBH,O5 = 65−38+61 (median and 90% symmetric credible range), based on the current LVK detector target sensitivities for the run. The calculations presented here also lead to an update of the LVK local BNS merger rate density estimate that accounts for the absence of BNS merger detections in O4 so far, which reads 2.8 Gpc−3 yr−1 ≤ R0 ≤ 480 Gpc−3 yr−1.

ABSTRACT Pseudopathology in paleontology refers to postmortem bone alteration mimicking osseous features of disease. Differentiating pathologies from pseudopathologies is critical in the investigation of paleopathology, as misattribution can produce erroneous conclusions regarding diseases and life history. In this paper, we describe several examples of pseudopathologies from a Cretaceous commingled monospecific bonebed of Edmontosaurus annectens (Lance Formation, WY). In addition to 96 documented real pathologies or injuries uncovered in examination of over 3000 fossil bone specimens, multiple pseudopathologies were observed. Most of these were bone fractures or patterned erosions of bone material resulting from most likely taphonomic processes. Bone proliferation characterizing the living response to premortem injuries is one clue. Absent this response, perimortem injuries and postmortem changes due to scavenging, weathering, and other factors should be considered. CT imaging of one astragalus showed intense focal radiodensity surrounding the two large lesions, sharply distinct from the surrounding bone. When compared against histological thin sections and SEM-EDS scanning, what appeared in CT as dense sclerotic reactive bone suggested postmortem migration of minerals subsequent to erosive insect boring, a gradient potentially related to the unique microenvironment thereby created affecting subsequent permineralization. Evidence from our analysis of this assemblage supports that even diagnoses supported by non-invasive imaging such as CT scans should, when possible, be tested by histological analysis. Otherwise, a distinctly and disturbingly non-zero number of erroneous conclusions are to be expected from any survey of paleopathology, particularly given the numbers of intervening processes separating a fresh carcass from permineralized bone.

Abstract For cardinals $\mathfrak {a}$ and $\mathfrak {b}$ , we write $\mathfrak {a}=^\ast \mathfrak {b}$ if there are sets A and B of cardinalities $\mathfrak {a}$ and $\mathfrak {b}$ , respectively, such that there are partial surjections from A onto B and from B onto A. $=^\ast $ -equivalence classes are called surjective cardinals. In this article, we show that $\mathsf {ZF}+\mathsf {DC}_\kappa $ , where $\kappa $ is a fixed aleph, cannot prove that surjective cardinals form a cardinal algebra, which gives a negative solution to a question proposed by Truss [J. Truss, Ann. Pure Appl. Logic 27, 165–207 (1984)]. Nevertheless, we show that surjective cardinals form a “surjective cardinal algebra”, whose postulates are almost the same as those of a cardinal algebra, except that the refinement postulate is replaced by the finite refinement postulate. This yields a smoother proof of the cancellation law for surjective cardinals, which states that $m\cdot \mathfrak {a}=^\ast m\cdot \mathfrak {b}$ implies $\mathfrak {a}=^\ast \mathfrak {b}$ for all cardinals $\mathfrak {a},\mathfrak {b}$ and all nonzero natural numbers m.

We provide further evidence that information is preserved during black hole evaporation and may be recoverable, provided quantum gravitational effects resolve the singularity. We demonstrate that due to quantum gravity effects, black holes acquire quantum hair, manifested by nonzero tidal Love numbers, revealing a distinct internal structure similar to neutron stars. Interestingly, the magnitude of these Love numbers is Planck-scale suppressed, implying significant tidal deformation in the late stage of evaporation. Depending on the final state of the black hole, information may be retrieved through correlations in Hawking radiation, baby universes or via remnants.

Abstract In this study, we investigate the intricate interplay between the entanglement entropy of initial multipartite states characterized by a nonzero particle number q and the dynamics of an expanding universe. Our analysis demonstrates that spacetime expansion significantly enhances the particle production rate associated with such states, yielding an amplification factor of $$q + 1 + \frac{q}{|\beta |^2}$$ q + 1 + q | β | 2 compared to the vacuum scenario. This result indicates that the presence of multipartite excitations in the asymptotic past leads to markedly increased cosmological particle generation in the asymptotic future. Furthermore, we show that the entanglement entropy of these states grows substantially under expansion, far surpassing the entropy arising from vacuum fluctuations alone. These findings suggest that multipartite initial states serve as highly effective probes for encoding and extracting information about the dynamical history of spacetime.

Abstract The mobility edge (ME) is a critical concept in Anderson localized systems, which marks the boundary between extended and localized states. Although the ME and localization phenomena have been extensively investigated in non-Hermitian (NH) quasiperiodic tight-binding models, they remain limited to NH continuum systems. Here, we study the ME and localization behaviors in a one-dimensional (1D) NH quasiperiodic continuous system, which is described by a Schrödinger equation with an incommensurable one-site potential and an imaginary vector potential. We find that the ME is located in the real spectrum and falls between the localized and extended states. Additionally, we show that under the periodic boundary condition, the energy spectrum always exhibits an open curve representing high-energy extended eigenstates characterized by a non-zero integer winding number. This complex spectrum topology is closely connected with the non-Hermitian skin effect (NHSE) observed under open boundary conditions, where the eigenstates of the bulk bands accumulate at the boundaries. We also analyze the critical behavior of the localization transition and obtain the critical potential strength accompanied by the critical exponent ν ≃ 1 / 3 . Furthermore, we investigate the expansion dynamics to dynamically probe the existence of NHSE and MEs, and outline a possible experimental implementation. Our study provides valuable inspiration for exploring MEs and localization behaviors in NH quasiperiodic continuous systems.

This paper aims at treating a study on the order of every element of higher 100, 105, and 107 orders of group for multiplication composition. But the composition in G is associative; the multiplication composition is very significant in the order of elements of a group. We develop the order of a group o(G), higher order of groups in different types of order and the order of elements o(a) of a group in real numbers. Let G be a group and let a^n ∈ G be of infinite order n, then find Highest Common Factor (i.e., (n, m) denotes H.C.F of n and m). The Highest Common Factor of two numbers is the “smallest non-zero common number” which is a multiple of both the numbers. So o(a^m) = n / H.C.F(n, m), where (n, m) denotes the H.C.F of n and m. If a ∈ G is of order n, then there exists an integer m for which a^m = e if m is a multiple of n, in general we use this. Then we develop orders of elements of a cyclic group and every element of higher order of a group. After that we find out the order of every element of a group for the higher orders of the group for being binary operation.

This paper investigates the effect of heat capacity variations across the compact flame, calculated using detailed chemical reactions in combustion processes, on the acoustic coupling and thermoacoustic modes in a general combustor. For thermoacoustic analyses, the acoustic jump conditions across compact flames are recast to account for changes in heat capacities and specific heat ratios at a non-zero Mach number. Two coefficients defined by heat capacity and specific heat ratio in jump conditions show a strong dependence on temperature jump ratios and equivalence ratios within premixed flames. The modified coupling index and thermoacoustic modes of a longitudinal combustor separated by the unsteady flame are then studied by embedding modified jump conditions in the wave-based model. For a large coupling index, heat capacities within reacting thermoacoustic systems can no longer be considered as constant or averaged parameters between adjacent modules, but as varying with fuel types and operating conditions. A parametric study examines the modified coupling index and thermoacoustic modes for changing temperature jump ratios, surface area ratios, and flame models. Results show that traditional jump conditions cannot be safely applied to the hydrogen flames with significant variations in heat capacity, even when the reduced acoustic coupling index is sufficiently small. With a choked outlet boundary, more resonant modes are introduced due to the indirect noise generated by entropy waves and are strongly dependent on variations in heat capacities. Finally, the experimental validation is performed using a well-documented laboratory combustor.

Abstract Study question Can PGT accurately distinguish between zero and non-zero copies of SMN1 in embryos without individual probe development or the need for linkage analyses? Summary answer PGT with Capillary Electrophoresis (CE) detects SMN1 and SMN2 deletions, helping reduce SMA risk, especially for patients at risk of being silent carriers. What is known already Spinal muscular atrophy (SMA) is primarily caused by the loss of both SMN1 gene copies inherited from carrier parents. For intended parents with 1 + 0 carrier status, PGT-M using probe development or linkage analysis is commonly performed. However, this approach is ineffective for silent carriers. A more effective method would directly assess SMN1 copy numbers to identify affected embryos. The proposed approach enables the identification of embryos affected by SMA due to SMN1 loss, providing families with additional risk reduction options and enhancing embryo selection for a lower SMA risk. Study design, size, duration Fifty samples with known SMN1 status were analyzed, with DNA diluted to picogram levels to mimic embryo biopsies. A whole genome amplification (WGA) method was used to generate DNA for standard PGT and SMA testing via capillary electrophoresis. The WGA approach, validated to minimize allele dropout, enables accurate detection of SMN1 and SMN2 gene copies. Participants/materials, setting, methods Coriell cell lines and embryos with known SMN1/SMN2 status were analyzed. Capillary electrophoresis was used to assess the existence of SMN1 and SMN2 copies. Final SMN1/SMN2 results were confirmed using Polymerase Chain Reaction Restriction Fragment Length Polymorphism (PCR-RFLP), ensuring reliable assessment for preimplantation genetic testing. Main results and the role of chance 99% concordance was achieved on the SMN1 and SMN2 results. PCR-RFLP confirmed both SMN1 and SMN2 copy number results.PGT for the presence or absence of loss of SMN1 can allow intended parents to select an embryo unaffected with SMA without probe development. Limitations, reasons for caution The current study is intended as proof of concept that PGT direct assessment resolves the challenge of detecting zero vs non-zero copy number samples of SMN1 and SMN2PGT-M options are limited for intended parents with silent SMA carrier status (2 + 0) since traditional linkage analysis requires confirmed carrier status. Wider implications of the findings The new PGT assay incorporates CE to detect SMN1 loss, reducing SMA risk. Additionally,post-amplification DNA is typically sufficient for standard PGT and SMA testing, allowing analysis after euploid embryo selection Trial registration number No

Planar linear flows are a one-parameter family, with the parameter $\hat {\alpha }\in [-1,1]$ being a measure of the relative magnitudes of extension and vorticity; $\hat {\alpha } = -1$ , $0$ and $1$ correspond to solid-body rotation, simple shear flow and planar extension, respectively. For a neutrally buoyant spherical drop in a hyperbolic planar linear flow with $\hat {\alpha }\in (0,1]$ , the near-field streamlines are closed for $\lambda \gt \lambda _c = 2 \hat {\alpha } / (1 - \hat {\alpha })$ , $\lambda$ being the drop-to-medium viscosity ratio; all streamlines are closed for an ambient elliptic linear flow with $\hat {\alpha }\in [-1,0)$ . We use both analytical and numerical tools to show that drop deformation, as characterized by a non-zero capillary number ( $Ca$ ), destroys the aforementioned closed-streamline topology. While inertia has previously been shown to transform closed Stokesian streamlines into open spiralling ones that run from upstream to downstream infinity, the streamline topology around a deformed drop, for small but finite $Ca$ , is more complicated. Only a subset of the original closed streamlines transforms to open spiralling ones, while the remaining ones densely wind around a configuration of nested invariant tori. Our results contradict previous efforts pointing to the persistence of the closed streamline topology exterior to a deformed drop, and have important implications for transport and mixing.

In this paper, we exhaustively investigate the quasinormal modes (QNMs) of a probe scalar field over a d-dimensional regular black hole (BH) characterized by the parameter A. The quasinormal frequencies (QNFs) exhibit different behaviors with respect to the parameter A for d=4 and d>44$$\\end{document}]]>. Firstly, the trends of QNFs with respect to A exhibit completely opposite patterns for the case of d=4 and d>44$$\\end{document}]]>. Secondly, in the four-dimensional regular BH, a non-monotonic behavior with respect to A is observed in the imaginary part of the fundamental modes with vanishing angular quantum number. In contrast, for nonzero angular quantum number or d>44$$\\end{document}]]>, non-monotonic behavior is observed only in the overtones. Thirdly, an overtone outburst accompanied by an oscillatory patter is observed only in the case of d>44$$\\end{document}]]>, but not in d=4.

We compute the baryon asymmetry in decay and scattering processes involving the electromagnetically charge-neutral fermion χ that carries the nonzero baryon number and interacts with quarklike fermions U, D via a vector-vector dimension-six effective operator, in the theory we developed in our earlier work. Majorana masses for the χ break the baryon number and split the Dirac fermion χ into a pair of Majorana fermions Xn with an indefinite baryon number. We identify loop amplitudes for Xn decay and scattering processes that are sensitive to the baryon number violation. The phases in the Majorana mass and couplings, in conjunction with the phase from intermediate on-shell states, lead to C and CP violation in these processes. For some representative parameter choices, we numerically compute the decay and scattering baryon asymmetries between the process and its conjugate process and find that the asymmetry generated is very interesting for explaining the baryon asymmetry of the Universe. Published by the American Physical Society 2025

Abstract It has been noted that lower type of an entire function completely ignores the value of lower order. The question arises for entire functions of irregular growth that what happens when we replace order by an arbitrary nonzero finite number. Here in this article our aim is to solve this problem by defining new lower ( p , q ) \left(p,q) -type by using a ( p , q ) \left(p,q) -scale, ( p ≥ q ≥ 1 ) \left(p\ge q\ge 1) for an entire function. Moreover, a relationship has been established between lower ( p , q ) \left(p,q) -type of entire function solutions of linear homogeneous partial differential equation of second order with coefficients occurring in series expansion and Laguerre polynomial approximation errors in sup norm.

Nanofluids have the proven capacity to significantly improve the thermal efficiency of a heat exchanging system due to the presence of conductive nanoparticles. The aim of this study is to simulate the forced convection on a non-Newtonian hybrid with a nanofluid (Al2O3-TiO2-H2O) in a hexagonal enclosure by the Galerkin finite element method (GFEM). The physical model is a hexagonal enclosure in two dimensions, containing a heated cylinder embedded at the center. The bottom, middle left, and right walls of the enclosure are all considered cold (Tc), while the top wall is considered to be moving, and the remaining middle, upper left, and right walls have the adiabatic condition. The Prandtl number (Pr = 6.2), Reynolds number (Re = 50, 100, 300 and 500), power law index (n = 0.6, 0.8, 1.0, 1.2 and 1.4), volume fractions of nanoparticles (ϕ = 0.00, 0.01, 0.02, 0.03 and 0.04), and Hartmann numbers (Ha = 0, 10, 20 and 30) are considered in the model. The findings are explained in terms of sensitivity tests and statistical analysis for various Re numbers, n, and Ha numbers employing streamlines, isotherms, velocity profiles, and average Nusselt numbers. It is observed that the inclusion of ϕ improves the convective heat transfer at the surging values of Re. However, if the augmenting heat transfer requires any control mechanism, integrating a non-zero Ha number is found to stabilize the system for the purpose of thermal efficacy.

<sec>Dicke model, as an important many-body model in quantum optics, describes the interaction between multiple identical two-level atoms and a quantized electromagnetic field. This spin-boson model shows collective phenomena in light-matter interaction systems and can undergo a second-order quantum phase transition from a normal phase to a superradiant phase when the coupling strength between the two-level atoms and the optical field exceeds a critical value. Dicke model embodies unique many-body quantum theories. And it has been widely studied and obtained many significant research results in quantum information, quantum process, and other quantum systems. Meanwhile, Dicke model also has wide applications in quantum optics and condensed matter physics.</sec><sec>The extended Dicke model, describing the interaction of a Bose-Einstein condensate in an optical cavity, provides a remarkable platform for studying extraordinary quantum phase transitions in theory and experiment. Based on the recent experiment on non-Hermitian coupling between two long-lived atomic spin waves in an optical cavity, in this work we use spin-coherent-state variational method and present the macroscopic quantum-state energy of the non-Hermitian Dicke model.</sec><sec>The spin coherent state variational method has an advantage in the theoretical research of macroscopic quantum states, especially in the normal and the inverted pseudospin states. In the variational method, optical coherent states and atomic extremum spin coherent states are used as the trial wave functions. A Hermitian transformation operator is proposed to diagonalize the non-Hermitian Hamiltonian, which is different from the ordinary quantum mechanics where the transformation operator must be unitary. Herein, the energy function is not necessarily real in the entire coupling region. Beyond an exceptional point, the spectrum becomes complex and introducing biorthogonal sets of atomic extremum states is necessary to evaluate the average quantities.</sec><sec>The normal phase (for the zero average photon number) possesses real energy and atomic population. The non-Hermitian interaction destroys the superradiant phase (for the stable nonzero average photon number) and leads to the absence of quantum phase transition. However, the introduced atom-photon interaction, which is induced by the pump field experimentally, can change the situation, dramatically. The pump field can balance the loss by the non-Hermitian atom-photon interaction to achieve the superradiant phase.</sec><sec>An interesting double exceptional point are observed in the energy functional. There is the real spectrum below the first exceptional point and beyond the second exceptional point, while there is a complex spectrum between these two exceptional points. The superradiant phase appears only beyond a critical value, which is related to the nonlinear interaction and the pump laser. A new and inverted quantum phase transition from the superradiant phase to the normal phase, is observed by modulating the atom-field coupling strength. The superradiant phase of the population inversion state appears for a negative effective frequency and a large atom-photon interaction. The influence of the dissipative coupling may be observed in cold atom experiment in an optical cavity. All the parameters adopted in this work are the actual experimental parameters.</sec>