Soft supersymmetry breaking as the sole origin of neutrino masses and lepton number violation

We discuss a scenario in which the supergravity induced soft terms, conventionally used for breaking supersymmetry, also lead to non-zero Majorana neutrino masses. The soft terms lead to the spontaneous violation of the lepton number at the gravitino mass scale $m_{3/2}$ which in turn leads to (i) the Majorana masses of ${\cal O} (m_{3/2})$ for the right-handed neutrinos and (ii) the $R$-parity breaking at the same scale. The former contributes to light neutrino masses through the type I seesaw mechanism, while the latter adds to it through neutrino-neutralino mixing. Both contributions can scale inversely with respect to $m_{3/2}$ given that gaugino and Higgsino masses are also of order $m_{3/2}$. Together, these two contributions adequately explain observed neutrino masses and mixing. One realization of the scenario also naturally leads to a $\mu$ parameter of ${\cal O} (m_{3/2})$. Despite the lepton number symmetry breaking close to the weak scale, the Majoron in the model exhibits very weak coupling to leptons, satisfying existing constraints on Majoron-lepton interactions. The right-handed neutrinos in the model have a large coupling to Higgsinos. This coupling and the relatively large heavy-light neutrino mixing induced through the seesaw mechanism may lead to the observable signals at colliders in terms of displaced vertices.Comment: V2: Added discussion, updated reference list, published versio

From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic

Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on \emph{proof} (as opposed to truth). There are two major approaches to P-tS: proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former is a semantics of arguments, and the latter is a semantics of logical constants in a logic. This paper demonstrates that the B-eS for intuitionistic propositional logic (IPL) encapsulates the declarative content of a basic version of P-tV. Such relationships have been considered before yielding incompleteness results. This paper diverges from these approaches by accounting for the constructive, hypothetical setup of P-tV. It explicates how the B-eS for IPL works

Modeling of Subwavelength Gratings: Near-Field Behavior

Subwavelength gratings, with period shorter than the incident wavelength, have garnered significant attention in the fields of photonics, optoelectronics, and image sensor technology. In this research, we delve into the scattering characteristics of these gratings by employing the 2-dimensional point dipole approximation. Additionally, we propose a version of perturbation theory that relies on Fourier decomposition to obtain analytical expressions for the near-field behavior. We validate our models using numerical techniques such as boundary and finite element analysis. Notably, we explore how parameters like the grating period and slit width affect field enhancements. We demonstrate that our models produce qualitatively accurate results even for narrow slits.Comment: 16 pages, 9 figures, bibliography 29 source

Topology optimization and boundary observation for clamped plates

We indicate a new approach to the optimization of the clamped plates with holes. It is based on the use of Hamiltonian systems and the penalization of the performance index. The alternative technique employing the penalization of the state system, cannot be applied in this case due to the (two) Dirichlet boundary conditions. We also include numerical tests exhibiting both shape and topological modifications, both creating and closing holes

General Relativistic Chronometry with Clocks on Ground and in Space

One of geodesy's main tasks is to determine the gravity field of the Earth. High precision clocks have the potential to provide a new tool in a global determination of the Earth's gravitational potential based on the gravitational redshift. Towards this clock-based gravimetry or chronometry in stationary spacetimes, exact expressions for the relativistic redshift and the timing between observers in various configurations are derived. These observers are assumed to be equipped with standard clocks and move along arbitrary worldlines. It is shown that redshift measurements, involving clocks on ground and/or in space, can be used to determine the (mass) multipole moments of the underlying spacetime. Results shown here are in agreement with the Newtonian potential determination from, e.g., the so-called energy approach. The framework of chronometric geodesy is exemplified in different exact vacuum spacetimes for illustration and future gravity field recovery missions may use clock comparisons as an additional data channel for advanced data fusion.Comment: 15 pages, 4 figure

The evolution of collision debris near the ν6\nu_6 secular resonance and its role in the origin of terrestrial water

This work presents novel findings that broadens our understanding of the amount of water that can be transported to Earth. The key innovation lies in the combined usage of Smoothed Particle Hydrodynamics (SPH) and $N$-body codes to assess the role of collision fragments in water delivery. We also present a method for generating initial conditions that enables the projectile to impact at the designated location on the target's surface with the specified velocity. The primary objective of this study is to simulate giant collisions between two Ceres-sized bodies by SPH near the $\nu_6$ secular resonance and follow the evolution of the ejected debris by numerical $N$-body code. With our method 6 different initial conditions for the collision were determined and the corresponding impacts were simulated by SPH. Examining the orbital evolution of the debris ejected after collisions, we measured the amount of water delivered to Earth, which is broadly 0.001 ocean equivalents of water, except in one case where one large body transported 7\% oceans of water to the planet. Based on this, and taking into account the frequency of collisions, the amount of delivered water varies between 1.2 and 8.3 ocean's worth of water, depending on the primordial disk mass. According to our results, the prevailing external pollution model effectively accounts for the assumed water content on Earth, whether it's estimated at 1 or 10 ocean's worth of water.Comment: 15 pages, 13 figure

Tunable ultrafast thermionic emission from femtosecond-laser hot spot on a metal surface: role of laser polarization and angle of incidence

Ultrafast laser induced thermionic emission from metal surfaces has several applications. Here, we investigate the role of laser polarization and angle of incidence on the ultrafast thermionic emission process from laser driven gold coated glass surface. The spatio-temporal evolution of electron and lattice temperatures are obtained using an improved three-dimensional (3D) two-temperature model (TTM) which takes into account the 3D laser pulse profile focused obliquely onto the surface. The associated thermionic emission features are described through modified Richardson-Dushman equation, including dynamic space charge effects and are included self-consistently in our numerical approach. We show that temperature dependent reflectivity influences laser energy absorption. The resulting peak electron temperature on the metal surface monotonically increases with angle of incidence for P polarization, while for S polarization it shows opposite trend. We observe that thermionic emission duration shows strong dependence on angle of incidence and contrasting polarization dependent behaviour. The duration of thermionic current shows strong correlation to the intrinsic electron-lattice thermalization time, in a fluence regime well below the damage threshold of gold. The observations and insights have important consequences in designing ultrafast thermionic emitters based on a metal based architecture.Comment: 17 pages, 7 figures, 1 tabl

No Evidence for More Earth-sized Planets in the Habitable Zone of Kepler's M versus FGK Stars

Reliable detections of Earth-sized planets in the habitable zone remain elusive in the Kepler sample, even for M dwarfs. The Kepler sample was once thought to contain a considerable number of M dwarf stars ($T_\mathrm{eff} < 4000$ K), which hosted enough Earth-sized ($[0.5,1.5]$ R$_\oplus$) planets to estimate their occurrence rate ($\eta_\oplus$) in the habitable zone. However, updated stellar properties from Gaia have shifted many Kepler stars to earlier spectral type classifications, with most stars (and their planets) now measured to be larger and hotter than previously believed. Today, only one partially-reliable Earth-sized candidate remains in the optimistic habitable zone, and zero in the conservative zone. Here we performed a new investigation of Kepler's Earth-sized planets orbiting M dwarf stars, using occurrence rate models with considerations of updated parameters and candidate reliability. Extrapolating our models to low instellations, we found an occurrence rate of $\eta_\oplus={8.58}_{-8.22}^{+17.94}\%$ for the conservative habitable zone (and ${14.22}_{-12.71}^{+24.96}\%$ for the optimistic), consistent with previous works when considering the large uncertainties. Comparing these estimates to those from similarly comprehensive studies of Sun-like stars, we found that the current Kepler sample does not offer evidence to support an increase in $\eta_\oplus$ from FGK to M stars. While the Kepler sample is too sparse to resolve an occurrence trend between early and mid-to-late M dwarfs for Earth-sized planets, studies including larger planets and/or data from the K2 and TESS missions are well-suited to this task.Comment: 22 pages, 11 figures, 2 tables; Accepted for publication in A

Language Models as Zero-Shot Trajectory Generators

Large Language Models (LLMs) have recently shown promise as high-level planners for robots when given access to a selection of low-level skills. However, it is often assumed that LLMs do not possess sufficient knowledge to be used for the low-level trajectories themselves. In this work, we address this assumption thoroughly, and investigate if an LLM (GPT-4) can directly predict a dense sequence of end-effector poses for manipulation skills, when given access to only object detection and segmentation vision models. We study how well a single task-agnostic prompt, without any in-context examples, motion primitives, or external trajectory optimisers, can perform across 26 real-world language-based tasks, such as "open the bottle cap" and "wipe the plate with the sponge", and we investigate which design choices in this prompt are the most effective. Our conclusions raise the assumed limit of LLMs for robotics, and we reveal for the first time that LLMs do indeed possess an understanding of low-level robot control sufficient for a range of common tasks, and that they can additionally detect failures and then re-plan trajectories accordingly. Videos, code, and prompts are available at: https://www.robot-learning.uk/language-models-trajectory-generators.Comment: 19 pages, 21 figure

Uniform representation of the turbulent velocity profile in an open channel

A uniform representation of the mean turbulent velocity profile in the sum of a wall function and a wake function is applied to an open channel, quantitatively determining its components. The open channel is thus found to coherently fit in to the same theoretical picture previously drawn for plane Couette, plane closed channel and circular pipe flow, and to share with them a universal law of the wall and a universal logarithmic law with a common value of von K\'arm\'an's constant.Comment: submitted to the Journal of Fluid Mechanic