In this work we analyse the convergence of solutions of the Poisson equation with Neumann boundary conditions in a thin domain with highly oscillatory behavior $\mathcal{U}^\varepsilon$ contained in the sphere $\mathbb{S}^2$. Using the Multiple Scales method, we obtain the homogenized limit problem and analyse the convergence of solutions, as $\varepsilon$ tends to $0$. Introducing appropriate correctors, we show strong convergence and give error estimates.

We give a general lower bound on the frequency of sign changes in the real coefficients of L-functions of the Selberg class. We in particular recover existing results in the cases of GL(2) and GL(3), and obtain new bounds in the case of GSp(4).

Let $F$ be a non-archimedean local field such that $4|q-1$, with $q$ the order of the residue field of $F$, and let $(M^0,σ^0)$ be the depth-zero cuspidal pair for the twisted Levi subgroup $G^0$ of $\mathrm{SL}_8$ arising from quadratic and quartic field extensions, as defined in the recent article by Adler-Fintzen-Ohara [AFO]. Then the corresponding Bernstein block is described by a twisted Hecke algebra $\mathcal{H}^0$. We describe $\mathcal{H}^0$ explicitly as a noncommutative $\mathbb{C}$-algebra with generators and relations. We describe explicitly the simple modules of $\mathcal{H}^0$. All the simple modules are $2$-dimensional. The primitive spectrum of $\mathcal{H}^0$ is then an explicit complex algebraic variety $\mathfrak{X}$. The maximal compact real form of $\mathfrak{X}$ is homeomorphic to a Klein bottle. This Klein bottle is a model of the unitary principal series of $G^0$ attached to the cuspidal pair $(M^0, σ^0)$. We make a full comparison with the classical situation in which $G = \mathrm{SL}_8$ and $(M,σ)$ is a cuspidal pair for $G$. The supercuspidal representation $σ$ is constructed from the same quadratic and quartic extensions of $F$. Let $\mathfrak{s}$ be the point in the Bernstein spectrum $\mathfrak{B} G$ determined by $(M,σ)$ and let $\mathfrak{s}^0$ be the point in the Bernstein spectrum $\mathfrak{B} G^0$ determined by $(M^0, σ^0)$. We compare the two points $\mathfrak{s}$ and $\mathfrak{s}^0$ and show explicitly that the corresponding Bernstein varieties are isomorphic. In that case, the Klein bottle re-appears, this time floating in the tempered dual of $\mathrm{SL}_8$.

In 1987, Alavi, Malde, Schwenk and Erdős conjectured that the independence polynomials of trees are unimodal. Subsequently, many researchers proposed strengthening this conjecture to log-concavity. In 2023, Kadrawi, Levit, Yosef, and Mizrachi discovered independence polynomials of trees of order 26 that are not log-concave, which led them to construct two infinite families of such polynomials, denoted by $T_{3,m,n}$ and $T_{3,m,n}^*$. In this paper, we show that these two infinite families also satisfy the unimodal conjecture raised by Alavi, Malde, Schwenk, and Erdős.

Parallel programming in high-performance computing depends on low-level APIs such as MPI, requiring users to manage synchronization and resources manually. Several correctness checking tools exist to help bug-free code development, though most target a single programming model, limiting their applicability. Our previous work, the static analysis tool CoVer, leverages a contract-based approach enabling users to specify custom error-checking rules and support emerging or unconventional programming models without requiring extensive new tooling. However, static analysis cannot fully reason about runtime-dependent behavior such as pointer aliasing or indirect control flow. To address this, we present CoVer-Dynamic, a dynamic analysis extension that reuses CoVer's contract language to provide a unified static-dynamic verification framework. By enforcing the same contracts at runtime, CoVer-Dynamic improves classification accuracy and eliminates false positives on standardized MPI and OpenSHMEM benchmarks, while detecting errors beyond static analysis only. Our evaluation shows that CoVer-Dynamic consistently outperforms the state-of-the-art correctness checker MUST, averaging a 2x speedup. Finally, our results show limitations in the expressiveness of the contract language, motivating future work to support more error classes.

A Generalized Inoue--Bombieri (GIB) manifold $M$ is a compact quotient of a connected Riemannian product $\mathbb{R}^q \times (N,g _N)$ by a discrete subgroup of $\mathrm{Sim}(\mathbb{R}^q) \times \mathrm{Isom}(N,g_N)$. The flat factor induces a transversely Riemannian foliation whose leaf closures determine, up to a natural geometric modification, a torus fibration $M \to X$. The main goal of this article is to study the associated monodromy representation $ρ: π_1(X) \to \mathrm{GL}(n,\mathbb{Z})$. We prove that the image of $ρ$ is a subgroup of a cocompact arithmetic lattice of a reductive group, and we discuss which groups may be realized as monodromy groups of GIB manifolds. When $(N,g_N)$ is a symmetric space of non-compact type, the monodromy itself is arithmetic. Moreover, one may describe the fibration and the monodromy in terms of parabolic subgroups of the isometry group of $(N,g_N)$. This yields new examples of GIB manifolds, as well as obstructions, and opens the way toward a complete classification in this particular case.

We initiate the study of single-sample bilateral trade with a broker, drawing an analogy to the setting of single-sample bilateral trade without a broker considered in Babaioff et al. (2020) and Cai and Wu (2023). Our model captures the three-sided interaction in which a broker mediates trade between a buyer and seller, each described by a valuation distribution from which a single sample can be drawn. We consider two settings in particular: one where the valuation distributions of the buyer and seller are identical and one where the valuation distributions are stochastically ordered. We analyze simple mechanisms that rely only on a single sample from each agent's distribution and show that these mechanisms achieve constant-factor approximations to the first-best gains-from-trade (GFT), first-best social welfare (SW), and optimal profit under the standard monotone-hazard-rate assumption. We then complement these results with matching or nearly matching upper bounds on the GFT and SW of our mechanisms. Notably, in both settings, we observe fairly small losses in the approximation factors to the first-best GFT and first-best SW due to the existence of the broker (benchmarked against the corresponding approximation factors in the setting without a broker). Furthermore, our results stand in stark contrast to those of Hajiaghayi et al. (2025), who show inapproximability results under a strategic broker with full distributional knowledge. Our results provide insight into the design of data-efficient brokerage mechanisms for online marketplaces and decentralized trading platforms, where intermediaries must facilitate trade under severe informational constraints. They highlight how even minimal data can enable robust and incentive-compatible brokerage in uncertain markets for both the broker and the market participants.

A promising way to scale up superconducting quantum computers is to link different devices together using propagating photons. Correspondingly, accurately modeling the quantum information transfer in such quantum interconnects is critical to advancing this emerging technology. To accomplish this, a full-wave quantum numerical model is essential for describing the few-photon transport characteristics of various components. Unfortunately, validating the accuracy of such numerical models remains a difficult challenge due to the lack of appropriate analytical solutions for standard component types. Recently, progress has been made on creating the first-ever analytical quantum full-wave solutions for a superconducting circuit quantum device. These efforts considered the case of two-photon transport through an empty rectangular waveguide cavity and the interactions of photons inside a closed rectangular waveguide cavity with a transmon qubit formed by a Josephson junction connected across the terminals of a small wire dipole antenna. Here, we advance these efforts by considering the one- and two-photon transport properties through a rectangular waveguide cavity containing a qubit in this form when the cavity is interfaced with via two coaxial ports. Such devices can be used in various ways for quantum interconnects, such as to form parts of a quantum memory or a photon source. We perform this analysis leveraging a quantum input-output theory formalism to derive the relevant single- and two-photon transport characteristics of interest. We then examine the signatures of the nonlinear quantum scattering effects in the good and bad cavity regimes of cavity quantum electrodynamics. In the future, these analytical results can be used to validate numerical full-wave quantum solvers for modeling quantum interconnects.

The stellar mass dependence of the unbiased giant planet occurrence rate may be the best statistical tool to constrain the formation of such planets. This rate rises and falls as a function of stellar mass, peaking around stars of $\sim 1.7{-}2 \Ms$. In this work, we carry out a population synthesis study, using pebble-driven core accretion model of planet formation, to investigate the planet formation conditions that may be responsible for this stellar-mass dependence. We use the inferred giant planet occurrence rated of three combined homogenised radial velocity surveys (EXPRESS, PPPS, and Lick giant star survey) to constrain the models. We find that we can produce a synthetic giant planet population with closely aligned occurrence and properties when we base our model on observationally-supported assumptions that accretion rates are higher and disk lifetimes are shorter around more massive stars, we can produce a synthetic giant planet population with closely aligned properties to the observed distribution. We also find that in this scenario, the runaway gas accretion occurs at a larger orbital distance and earlier times as the stellar mass increases.

In this work, we develop a new orbital optimization approach, perturbative Super-CI (Super-CIPT), for the two-component complete active space self-consistent field (2C-CASSCF) method. By variationally optimizing spinor orbitals and consistently incorporating spin--orbit coupling (SOC) at the orbital level, the 2C-CASSCF method enables a simultaneous treatment of relativistic effects and static correlation. The Super-CIPT approach demonstrates robust convergence behavior and is applicable to systems under strong SOC. The inclusion of Gaunt or Breit term via the atomic mean field approximation yields the most accurate results, with errors dropping below 2% for halogens. We systematically assess the performance of 2C-CASSCF on spin-orbit splittings (SOSs) of selected p-block elements. Results show that 2C-CASSCF outperforms conventional one-component (1C) CASSCF. This work establishes 2C-CASSCF with Super-CIPT as a reliable and efficient approach for multireference relativistic quantum chemistry.

These are expanded notes of a seminar held in Columbia university during the Spring and Fall of 2024 about the theory of analytic stacks of Clausen and Scholze, with a focus in the theory of solid mathematics. The seminar is inspired from the Lecture Series of Analytic Stacks of Clausen and Scholze during the winter semester of 2023. All the theory of light condensed mathematics, analytic stacks and the proof of Serre duality must be attributed to Clausen and Scholze, any mistake or misconception is totally due to the author. The only original work in these notes is the discussion of smooth, étale and finite presentation morphisms of solid Huber rings in Section 7.

We propose new concepts for experiments in which intense high energy photon or muon beams are employed parasitically to detect scattering by cosmic heavy weakly interacting dark matter (DM) particles. We show that the scattering cross-sections are sizeable enough to potentially observe beam scattering on heavy dark matter particles at high beam intensities for typically inferred near-Earth DM densities of $ρ_χ\sim0.3~GeV/cm^3$. The predicted effect is particularly large in the case of a proposed muon collider Higgs factory, especially in the heavy (and poorly constrained) DM scenarios of WIMPZilla's. Current photon facilities such as at Jefferson Laboratory are predicted to require intensity and energy upgrades to reach detectable rates.

Recent advances in Information Retrieval have established transformer-based cross-encoders as a keystone in IR. Recent studies have focused on knowledge distillation and showed that, with the right strategy, traditional cross-encoders could reach the level of effectiveness of LLM re-rankers. Yet, comparisons with previous training strategies, including distillation from strong cross-encoder teachers, remain unclear. In addition, few studies cover a similar range of backbone encoders, while substantial improvements have been made in this area since BERT. This lack of comprehensive studies in controlled environments makes it difficult to identify robust design choices. In this work, we reproduce \citet{schlattRankDistiLLMClosingEffectiveness2025} LLM-based distillation strategy and compare it to \citet{hofstatterImprovingEfficientNeural2020} approach based on an ensemble of cross-encoder teachers, as well as other supervised objectives, to fine-tune a large range of cross-encoders, from the original BERT and its follow-ups RoBERTa, ELECTRA and DeBERTa-v3, to the more recent ModernBERT. We evaluate all models on both in-domain (TREC-DL and MS~MARCO dev) and out-of-domain datasets (BEIR, LoTTE, and Robust04). Our results show that objectives emphasizing relative comparisons -- pairwise MarginMSE and listwise InfoNCE -- consistently outperform pointwise baselines across all backbones and evaluation settings, and that objective choice can yield gains comparable to scaling the backbone architecture.

Consider an SI process on a graph $G$ where each S--I connection becomes I--I at rate $λ$. Here S and I stand for ``susceptible'' and ``infected'' respectively. The evoSI model is a modification of the SI model in which S--I edges are broken at rate $ρ$ and the ``S'' connects to a randomly chosen vertex. It is proven in Durrett and Yao [2022, Electron. J. Probab.] that, for the supercritical evoSI process on the configuration model, there exists a quantity $Δ$ depending on the first three moments of the degree distribution such that the sign of $Δ$ governs the continuity of the phase transition of the final epidemic size near the critical infection rate $λ_c$. In this paper, we consider the critical evoSI model on the configuration model, i.e., $λ=λ_c$. We show that, if $Δ>0$, then the probability of a major outbreak starting from a single infected individual is $Cn^{-1/3}(1+o(1))$ for some explicit constant $C>0$, where $n$ is the size of the graph. On the contrary, if $Δ<0$, then this probability is $o(n^{-1/3})$. The case $Δ<0$ is reminiscent of the critical {\ER} graphs, where the probability for the size of the largest component to be of order $n$ decays exponentially in $n$.

We propose a focused weighted-average least squares (FWALS) estimator that addresses the computational burden of focused model averaging. By semi-orthogonalizing auxiliary regressors, the weighting problem is reduced from $2^{k_2}$ sub-models to at most $k_2$ regressor-wise weights, yielding a tractable sub-optimal procedure. Under local-to-zero conditions, we derive the limiting distribution of FWALS for smooth focused functions and provide a plug-in AMSE criterion for data-driven weight selection. Simulations show that FWALS closely matches the focused information criterion (FIC) benchmark and delivers stable performance when focused function is designed for impulse response function. Prior-based WALS can be competitive in some settings, but its performance depends on the signal regime and the design of focused parameter. Overall, FWALS offers a practical and robust alternative with substantial computational savings.

The influence of gravity on the drag force acting on a projectile impacting granular media is investigated experimentally via embedded inertial measurement unit (IMU) sensor and numerically through discrete element method (DEM) simulations. As gravity approaches zero, inertial drag dominates, yielding qualitatively different scaling laws and cavity dynamics. Analogous to fluid dynamics, we define a dimensionless granular drag coefficient $C_{\rm gd}$, which is found to stay largely at a constant $\sim 1.2$ in microgravity while an additional term inversely proportional to impact velocity arises in the presence of gravity. The constant term can be understood from momentum transfer along the penetration direction while the additional term suggests the influence of internal stress built-up due to gravity. Similar discrepancy is also found for the initial peak of the drag force. This analogy provides novel insights into the nature of granular drag in microgravity and sheds light on future space missions.

This thesis presents an extensive analysis of the behavior of topological solitons when one or more of their internal modes are activated. The first part of this manuscript is devoted to the study of the simplest topological solitons in (1+1) dimensions: kinks. Specifically, we investigate how these solutions emit radiation when one of their internal modes is initially excited, within the framework of the double $ϕ^4$ model. The simplest kink solution in this theory exhibits a complex internal mode structure that depends on a coupling constant appearing in the potential governing the dynamics. We will show how the amplitude and frequency of the emitted radiation are affected by changes in this coupling constant. We also examine the dynamics of wobbling kink/antikink scattering when the kinks possess more than one internal mode. To this end, we study kink/antikink collisions in the context of the simplest kink solution arising in the MSTB model. This analysis sheds light on the resonant energy exchange mechanism, allowing energy transfer between internal modes and the translational mode. The second part of this thesis focuses on excited vortex solutions in (2+1) dimensions. We begin with a detailed study of the internal mode structure associated with vortex solutions in the Abelian-Higgs model. We demonstrate how the problem can be significantly simplified by choosing an appropriate angular dependence for the eigenfunctions. Furthermore, we investigate the radiation emitted by a vortex when its internal mode is initially activated. To achieve this, we extend the analytical techniques used in (1+1) dimensions to field theories defined in two spatial dimensions. This enables us to compute the radiation amplitude, its frequency, and the decay of the internal mode amplitude due to energy loss via radiation. All analytical results are contrasted with data from numerical simulations.

Resource allocation is a key factor in multiuser (MU) multiple-input multiple-output (MIMO) wireless systems to provide high quality of service to all user equipments (UEs). In congested scenarios, UE scheduling enables UEs to be distributed over time, frequency, or space in order to mitigate inter-UE interference. Many existing UE scheduling methods rely on greedy algorithms, which fail at treating the resource-allocation problem globally. In this work, we propose a UE scheduling framework for MU-MIMO wireless systems that approximately solves a nonconvex optimization problem that treats scheduling globally. Our UE scheduling framework determines subsets of UEs that should transmit simultaneously in a given resource slot and is flexible in the sense that it (i) supports a variety of objective functions (e.g., post-equalization mean squared error, capacity, and achievable sum rate) and (ii) enables precise control over the minimum and maximum number of resources the UEs should occupy. We demonstrate the efficacy of our UE scheduling framework for millimeter-wave massive MU-MIMO and sub-6-GHz cell-free massive MU-MIMO systems, and we show that it outperforms existing scheduling algorithms while approaching the performance of an exhaustive search.

Precision tests of the Standard Model (SM) currently show a deficit in first-row Cabibbo-Kobayashi-Maskawa (CKM) unitarity. In this talk, we discuss progress towards a correlated analysis of the lattice-QCD inputs needed to test this relation with kaon data using highly improved staggered quarks (HISQ) on the MILC $N_{f}=2+1+1$ configurations. We present the status of a new analysis of light-meson decay constant data where chiral-continuum fits are guided by staggered chiral perturbation theory (SChPT). The goal of SChPT is twofold: it allows us to use data not only at physical pion mass but also at unphysical masses. Moreover, it provides values of ChPT low energy constants (LECs) as well as their correlations. We also present a reanalysis of our previous kaon semileptonic form factor calculation, aiming to estimate correlations between the form factor and light-meson decay constants. We discuss the new methodology, new data included, and present some preliminary results.

We review some of the interesting consequences that tilts, warps, and eccentricities can introduce into the dynamics, thermodynamics, and observational appearance of accreting systems, with an emphasis on disks around black holes and compact stars. We begin with a review of the two types of precession that are associated with eccentric and tilted orbits in general relativity and Newtonian gravity. We then discuss the types of accretion systems that may manifest tilted or eccentric disks. In separate sections we discuss first tilted and then eccentric disks, each section covering relevant and interesting observational, theoretical, and numerical results. Next, we explore potential connections between the phenomenology of quasi-periodic oscillations and either tilted or eccentric disks. Finally, we present some concluding thoughts and discuss future directions this research might take.

We have studied the anti-ferromagnetic Kitaev model on a honeycomb lattice under the Zeeman field, using an extensive Majorana mean-field analysis. When the magnetic field is along a specific Cartesian axis, we find that the emergent fields exhibit direction-dependent stabilization up to a certain critical strength of the external field. For a conical magnetic field, the characteristics of the emergent intermediate state are elusive. Our mean-field analysis reveals the existence of two distinct phases in the intermediate region. First, the system enters a disordered phase, where emergent-field densities converge to random values, and the Chern number is ill-defined. The magnitude of magnetization also fluctuates and remains less than unity, indicating a strong quantum effect. In the second phase, emergent-field densities attain vanishingly small values. In this phase, the magnetization components fluctuate heavily, but the magnitude of the magnetization vectors becomes unity, indicating highly degenerate classical ground states. We perform exact diagonalization calculations that qualitatively support some of the mean-field results. We extend our study to the anisotropic limit of the Kitaev coupling parameters. When the couplings are beyond the triangular inequality, the pure Kitaev model is known to host a topologically trivial gapped quantum spin liquid. We find that, for intermediate strengths of a conical magnetic field, topology shows a reentrant behavior.

Quantum Computing promises to solve complex combinatorial optimization problems more efficiently than classical methods, with the Quantum Approximate Optimization Algorithm (QAOA) being a leading candidate. Recent fixed-parameter variations of QAOA eliminate costly run-time optimization, but determining their optimal initialization as well as the number of required layers (p) for a target solution remains a critical, unsolved challenge. In this work, we propose a novel approach using a Graph Neural Network (GNN) to predict QAOA performance: Based on a graph representation of the problem, the GNN forecasts the probability of the optimal solution in the resulting distribution across different parameter initializations and layer depths for a wide variety of combinatorial optimization problems. We demonstrate that the GNN accurately predicts QAOA performance within a 10% margin of the true values. Furthermore, the model exhibits strong generalization capabilities across unseen problem classes, larger problem sizes, and higher layer counts. Our approach allows to identify viable problem instances for QAOA and to select an adequate parameter initialization strategy with minimal layer depth, without the need of costly parameter optimization.

The equations of linearized viscoelastodynamics in Kelvin-Voigt rheology are rigorously derived from a nonlinear model that satisfies the time-dependent frame indifference in the sense of Antman. Besides showing the convergence of corresponding solutions of both systems, we also prove the convergence of time-discrete solutions on various scales and of continuous solutions of nonlinear problems to linearized ones.

Tools shape our mind. This is why it is important to have extensible and flexible tools for developers to adapt to their needs. Reasoning about programs in the abstract -- by imagining what objects should look like -- can make it harder to grasp the underlying model. In Smalltalk environments like Pharo, developers work closely with their objects, gaining immediate feedback -- not guessing how they will look like but directly interacting with them. This article presents some tools developers use in Pharo: Inspector custom views for defining specific views and navigation for objects, Microcommits for reverting changes without the need to commit and pull, Xtreme TDD that allows developers to code in the debugger, On the Fly Rewriting Deprecations that support API evolution through automated rewriting of deprecated calls, and Object-Centric Breakpoints -- when a problem cannot be efficiently solved with a dummy trace, developers can use break points that will only halt for a given instance. By showcasing these features that evolved alongside Smalltalk, we invite reflection on how other IDEs could rethink some of their features and improve developers' workflows.

In the present paper we consider anisotropic cosmological vacuum solutions in (4+1) dimensional general quadratic gravity. In particular, we present a solution with 3 equal and 1 different Hubble parameters, and study its stability. We show that for a certain range of coupling constants this solution is stable. This means that initially totally anisotropic 4-dim Universe can evolve naturally to a product of 3-dim isotropic subspace and 1-dim space. By numerical integration of equations of motion we construct bassin of attraction of this solution which covers part of the initial conditions space with non-zero measure.

We investigate the weak Banach--Saks property in the setting of Hölder spaces over metric spaces. We show that, for every infinite metric space $(M,d)$ and every $α\in (0,1]$, the Hölder space $C^α(M)$ fails to have the weak Banach--Saks property.

This paper develops a nonlinear grid-forming (GFM) controller with provable voltage-formation guarantees, with over-current limiting enforced via a control-barrier-function (CBF)-based safety filter. The nominal controller follows a droop-based inner-outer architecture, in which voltage references and frequency are generated by droop laws, an outer-loop voltage controller produces current references using backstepping (BS), and an inner-loop current controller synthesizes the terminal voltage. The grid voltage is treated as an unknown bounded disturbance, without requiring knowledge of its bound, and the controller design does not rely on any network parameters beyond the point of common coupling (PCC). To robustify voltage formation against the grid voltage, a deadzone-adapted disturbance suppression (DADS) framework is incorporated, yielding practical voltage regulation characterized by asymptotic convergence of the PCC voltage errors to an assignably small and known residual set. Furthermore, the closed-loop system is proven to be globally well posed, with all physical and adaptive states bounded and voltage error transients (due to initial conditions) decaying exponentially at an assignable rate. On top of the nominal controller, hard over-current protection is achieved through a minimally invasive CBF-based safety filter that enforces strict current limits via a single-constraint quadratic program. The safety filter is compatible with any locally Lipschitz nominal controller. Rigorous analysis establishes forward invariance of the safe-current set and boundedness of all states under current limiting. Numerical results demonstrate improved transient performance and faster recovery during current-limiting events when the proposed DADS-BS controller is used as the nominal control law, compared with conventional PI-based GFM control.

We describe the application of a scalable algorithm for interpolating solution data in the overlapping mesh region of two solvers. This feature is essential to obtain a globally consistent solution for in-situ coupled atmospheric wave simulation. We provide timings and discuss a real-world application run.

Solidification, coupled with melt flow, plays a critical role in determining the microstructure and properties of materials in several manufacturing processes. Phase-field models coupled with the Navier-Stokes equations are widely used to model and simulate these dynamics. However, most existing models neglect essential thermodynamic couplings, particularly the capillary (Korteweg) stress in the momentum equation. This stress, which arises from the coupling between the phase field and the melt flow, accounts for thermal capillary effects during non-isothermal solidification. Neglecting it leads to models inconsistent with non-equilibrium thermodynamics and incapable of capturing capillarity-driven melt flow. In this work, we present a thermodynamically consistent, non-isothermal phase-field model for solidification coupled with melt flow, incorporating cross-coupling terms and explicitly including the Korteweg stress in the momentum equation. Model validation is performed for solidification-only cases, followed by simulations of dendritic growth under melt flow. The results show that thermal capillary effects induce flow near the interface, influencing dendrite tip velocity and morphology. Simulations under forced convection further demonstrate asymmetric dendrite growth due to the imposed flow field. Additionally, we numerically demonstrate the influence of viscosity interpolation schemes on enforcing the no-slip boundary condition in phase-field models with melt flow.

Alloying offers an effective way to improve the functionality of transition metal dichalcogenides (TMDCs) in both fundamental research and optoelectronic applications, as it allows for engineering their electronic and optical properties. This study investigates the optoelectronic properties of CVD-synthesized alloy MoSSe, which exhibits an inherent out-of-plane dipole moment, arising from asymmetry in S and Se atoms on either side of the Mo layer, as confirmed by piezoelectric force microscopy, polarization-resolved second harmonic generation studies and theoretical first-principles calculations. Time-resolved photoluminescence measurements reveal an extended exciton radiative recombination lifetime in MoSSe, attributed to electron-hole wavefunction separation by the dipole moment, which improves photodetection by facilitating enhanced electron-hole separation before recombination. The device demonstrates significant responsivity over broad spectral range. By employing the photogating effect, the device response can be switched from slow to fast modes. These findings are further supported by illumination intensity-dependent photoluminescence and Raman measurements, underscoring the potential of polar TMDCs in future optoelectronic devices.