arXiv subjects

Arnab Roy

Publications and source records attributed to Arnab Roy.

At least 37 records · Page 2Linked to original sources

arXiv2026

On Hamming-Lipschitz Type Stability of the Subdominant (Minmax) Ultrametric: Theory and Simple Proofs

The subdominant (minmax) ultrametric is a canonical tree-structured summary of a dissimilarity matrix, arising equivalently as the ultrametric induced by single-linkage clustering. While its classical stability theory is usually formulated in $\ell_\infty$ or Gromov--Hausdorff terms, such bounds are poorly suited to sparse perturbations that alter only a few pairwise distances. We develop an $\ell_0$-type stability theory for this operator. Our analysis shows that sparse edits propagate only through the minimum spanning tree (MST): a pairwise ultrametric value can change only if its tree path crosses an edited edge or a cut newly exposed by an edited off-tree edge. This yields a sharp per-edit exposed-cut score and a tree-only global envelope, leading to Hamming--Lipschitz bounds on the number of ultrametric entries that can change. We also prove sharpness results showing that this dependence on tree geometry is unavoidable: under strict cut separation the tree-edge bound is attained exactly, and for off-tree edits there are explicit families in which one edited distance changes $Θ(n^2)$ ultrametric entries. In addition, we prove a conditional near-additivity principle for multiple edits under certified large per-edit changed regions and negligible aggregate overlap. Experiments on deep-embedding graphs show that the resulting structural scores provide useful vulnerability diagnostics for hierarchical representations.

cs.LG↗

arXiv2026

Strong well-posedness for a stochastic fluid-rigid body system via stochastic maximal regularity

We develop a rigorous analytical framework for a coupled stochastic fluid-rigid body system in $\mathbb{R}^3$. The model describes the motion of a rigid ball immersed in an incompressible Newtonian fluid subjected to both additive noise in the fluid and body equations and transport-type noise in the fluid equation. We establish local strong well-posedness of the resulting system by combining stochastic maximal $\mathrm{L}^p$-regularity theory with a decoupling approach for the associated fluid-structure operator. A key step is to prove the boundedness of the $\mathcal{H}^\infty$-calculus for this operator. In addition, we provide blow-up criteria for the maximal existence time of solutions. To our knowledge, this is the first rigorous treatment of strong solutions of stochastic fluid-structure interactions.

math.AP↗

arXiv2026

Strong time-periodic solutions for a multilayered fluid-structure interaction system with nonlinear coupling

We investigate a time-periodic fully three-dimensional fluid-structure interaction system in which the Navier-Stokes equations for an incompressible viscous fluid are coupled with a multilayered elastic structure composed of a damped thin linear plate and a thick viscoelastic layer. The coupling is nonlinear, meaning that it is on a moving interface that is not known a priori, rendering the problem a moving-domain problem. We prove the existence of strong time-periodic solutions. The proof relies on a fixed point argument, combining sharp nonlinear estimates with a detailed analysis of the linearized system. The linearized problem is analyzed by employing the Arendt-Bu theorem on maximal periodic $\mathrm{L}^p$-regularity, which requires several new analytical ingredients including a refined lifting procedure, a decoupling strategy establishing $\mathcal{R}$-sectoriality of the coupled operator, a careful treatment of the thick structural layer, and a spectral analysis adapted to the multilayered setting. This provides the first strong time-periodic existence result for multilayered fluid-structure interaction systems, and the methods are expended to extend more broadly to nonlinear coupled PDEs on moving domains with periodic forcing.

math.AP↗

arXiv2026

Monojet and direct detection constraints on real scalar dark matter: EFT and a simple UV completion

We consider constraints that can be placed on certain invisible scalar particles through monojet studies at the LHC and compare them with those from direct detection experiments when interpreted as dark matter. Whereas direct detection constraints are typically more restrictive, we identify regions of parameter space where monojet studies provide important complementary bounds. We carry out our analysis using both a $ϕ$SMEFT for real scalar particle pairs coupled to standard-model fields through operators of up to dimension six, and a simple UV completion with vector-like quarks, with both the scalars and the vector-like quarks being odd under a $\mathbb{Z}_2$ symmetry, while the SM particles are even. The vector-like quarks can only decay into a jet and an invisible scalar, and we recast the current ATLAS monojet data to constrain their parameter space. Comparison of the two descriptions yields some insight into interpreting dark matter constraints obtained with EFTs.

hep-ph↗

arXiv2026

Existence of weak solutions for incompressible fluid-Koiter shell interactions with Navier slip boundary condition

We study a three-dimensional fluid-structure interaction problem describing the motion of an incompressible, viscous fluid coupled with a deformable elastic shell of Koiter type that forms part of the fluid boundary. The fluid motion is governed by the incompressible Navier--Stokes equations posed on a time-dependent domain, while the shell evolution is described by a nonlinear elastic model. At the fluid-structure interface, we impose Navier slip boundary conditions, allowing for tangential slip penalized by friction. Our main result establishes the global-in-time existence of weak solutions up to the first possible self-intersection of the shell, for arbitrarily large initial data with finite energy. The analysis is carried out in a fully three-dimensional setting and addresses the major mathematical challenges arising from the moving domain, the geometric nonlinearity of the shell, and the reduced regularization induced by the slip boundary condition. The proof relies on a careful construction of suitable approximation schemes, novel compactness arguments adapted to the slip framework, and a new extension operator for divergence-free test functions compatible with the fluid-shell coupling. As a further contribution, we provide a direct approach to the strong convergence of second-order spatial derivatives of the shell displacement, which allows us to treat nonlinear Koiter shell models within the same framework.

math.AP↗

arXiv2025

Steady Self-Propelled Motion of a Rigid Body in a Viscous Fluid with Navier-Slip Boundary Conditions

We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the fluid occupies an exterior domain and the propulsion mechanism is modeled through nonhomogeneous Navier-slip boundary conditions at the fluid-body interface. Such conditions provide a realistic description of propulsion in microfluidic and rough-surface regimes, where partial slip effects are significant. Under suitable smallness assumptions on the boundary flux and on the normal component of the prescribed surface velocity, we establish the existence of weak steady solutions to the coupled fluid-structure system. A key analytical ingredient is the derivation of a Korn-type inequality adapted to exterior domains with rigid-body motion and Navier-slip interfaces, which yields uniform control of both the fluid velocity and the translational and rotational velocities of the body. Beyond existence, we provide a necessary and sufficient condition under which a prescribed slip velocity on the body surface induces nontrivial translational or rotational motion of the rigid body. This is achieved through the introduction of a finite-dimensional thrust space, defined via auxiliary exterior Stokes problems with Navier boundary conditions, which captures the effective contribution of boundary-driven flows to the rigid-body motion. Our results clarify how boundary effects generate propulsion and extend the classical Dirichlet-based theory to the Navier-slip setting.

math.AP↗

arXiv2025

Dynamics of the general $Q$-tensor model interacting with a rigid body

In this article, the fluid-rigid body interaction problem of nematic liquid crystals described by the general Beris-Edwards $Q$-tensor model is studied. It is proved first that the total energy of this problem decreases in time. The associated mathematical problem is a quasilinear mixed-order system with moving boundary. After the transformation to a fixed domain, a monolithic approach based on the added mass operator and lifting arguments is employed to establish the maximal $L^p$-regularity of the linearized problem in an anisotropic ground space. This paves the way for the local strong well-posedness for large data and global strong well-posedness for small data of the interaction problem.

math.AP↗

arXiv2025

High-$\rm{p_T}$ LHC constraints on SMEFT operators affecting rare kaon and hyperon decays

We consider the constraints on new physics affecting rare kaon and hyperon decay as parametrized by a low energy effective theory that can be obtained from high-$\rm p_T$ observables at LHC. To this end, we match the relevant low energy Wilson coefficients onto those in SMEFT at dimension six and compute their contributions to charged dilepton, monolepton, monojets, and $\rm VH$ searches by ATLAS and CMS. Constraints from rare kaon decays are generally more restrictive, with the ones arising from high-$\rm p_T$ measurements complementing them along directions in parameter space to which the former are not sensitive. We also illustrate the effect of a high luminosity LHC run in reducing the viable parameter regions.

hep-ph↗

arXiv2025

The Lagrangian approach to the compressible primitive equations

This article develops the hydrostatic Lagrangian approach to the compressible primitive equations. A fundamental aspect in the analysis is the investigation of the compressible hydrostatic Lamé and Stokes operators. Local strong well-posedness for large data and global strong well-posedness for small data are established under various assumptions on the pressure law, both in the presence and absence of gravity.

math.AP↗

arXiv2025

Collision/No-collision results of a solid body with its container in a 3D compressible viscous fluid

We consider a bounded domain $Ω\subset\mathbb R^3$ and a rigid body $\mathcal{S}(t)\subsetΩ$ moving inside a viscous compressible Newtonian fluid. We exploit the roughness of the body to show that the solid collides its container in finite time. We investigate the case when the boundary of the body is of $C^{1,α}$-regularity and show that collision can happen for some suitable range of $α$. We also discuss some no-collision results for the smooth body case.

math.AP↗

arXiv2025

Fluid-Structure Interaction with Porous Media: The Beaver-Joseph condition in the strong sense

This article considers fluid structure interaction describing the motion of a fluid contained in a porous medium. The fluid is modelled by Navier-Stokes equations and the coupling between fluid and the porous medium is described by the classical Beaver-Joseph or the Beaver-Joseph-Saffman interface condition. In contrast to previous work these conditions are investigated for the first time in the strong sense and it is shown that the coupled system admits a unique, global strong solution in critical spaces provided the data are small enough. Furthermore, a Serrin-type blow-up criterium is developed and higher regularity estimates at the interface are established, which say that the solution is even analytic provided the forces are so.

math.AP↗

arXiv2025

$Σ^{+}\to p\ell^{+}\ell^{-}$ decays within the standard model and beyond

Motivated by the LHCb measurement of the hyperon decay mode $Σ^+\to pμ^+μ^-$ and prospects for improvement, we revisit the estimates for the rate and muon forward-backward asymmetry within the standard model and beyond. The standard model prediction has a fourfold ambiguity, and we suggest ways to resolve it with other measurements, including possible studies of $Σ^+\to p e^+e^-$ in the BESIII and LHCb experiments. We use the recent BESIII measurements of $Σ^+\to p γ$ and $Σ^+\to Nπ$ to reduce the uncertainty in the long-distance contribution to $Σ^+\to pμ^+μ^-$. Beyond the standard model, we consider a general effective Hamiltonian at low energy with ten operators whose Wilson coefficients parametrize the new physics. We derive expressions for the $Σ^+\to pμ^+μ^-$ rate and the associated muon forward-backward asymmetry in terms of these coefficients. Finally, we present the constraints on these Wilson coefficients that result from both kaon and hyperon decays and emphasize their complementarity.

hep-ph↗

arXiv2024

Compressible fluids and elastic plates in 2D: A conditional no-contact theorem

We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The displacement of the latter evolves according to a beam equation. Both are coupled through kinematic boundary conditions and the balance of forces. We prove that for any weak solution to the coupled system, which satisfies certain additional regularity requirements, no contact occurs between the elastic wall and the bottom of the fluid cavity. This applies to both isentropic and heat-conducting fluids. As a special case of our general theory we extend the unconditional result from Grandmont and Hillairet (Arch. Ration. Mech. Anal. 220, 1283--1333, 2016) on incompressible fluids from visco-elastic to perfectly elastic plates.

math.AP↗

arXiv2024

zkLogin: Privacy-Preserving Blockchain Authentication with Existing Credentials

For many users, a private key based wallet serves as the primary entry point to blockchains. Commonly recommended wallet authentication methods, such as mnemonics or hardware wallets, can be cumbersome. This difficulty in user onboarding has significantly hindered the adoption of blockchain-based applications. We develop zkLogin, a novel technique that leverages identity tokens issued by popular platforms (any OpenID Connect enabled platform e.g., Google, Facebook, etc.) to authenticate transactions. At the heart of zkLogin lies a signature scheme allowing the signer to sign using their existing OpenID accounts and nothing else. This improves the user experience significantly as users do not need to remember a new secret and can reuse their existing accounts. zkLogin provides strong security and privacy guarantees. Unlike prior works, zkLogin's security relies solely on the underlying platform's authentication mechanism without the need for any additional trusted parties (e.g., trusted hardware or oracles). As the name suggests, zkLogin leverages zero-knowledge proofs (ZKP) to ensure that the sensitive link between a user's off-chain and on-chain identities is hidden, even from the platform itself. zkLogin enables a number of important applications outside blockchains. It allows billions of users to produce \textit{verifiable digital content leveraging their existing digital identities}, e.g., email address. For example, a journalist can use zkLogin to sign a news article with their email address, allowing verification of the article's authorship by any party. We have implemented and deployed zkLogin on the Sui blockchain as an additional alternative to traditional digital signature-based addresses.

cs.CR↗

arXiv2024

Constraining Asymmetric Dark Matter using Colliders and Direct Detection

We reappraise the viability of asymmetric dark matter (ADM) realized as a Dirac fermion coupling dominantly to the Standard Model fermions. Treating the interactions of such a DM particle with quarks/leptons in an effective-interactions framework, we derive updated constraints using mono-jet searches from the Large Hadron Collider (LHC) and mono-photon searches at the Large Electron-Positron (LEP) collider. We carefully model the detectors used in these experiments, which is found to have significant impact. The constraint of efficient annihilation of the symmetric part of the ADM, as well as other observational constraints are synthesized to produce a global picture. Consistent with previous work, we find that ADM with mass in the range $1-100$ GeV is strongly constrained, thus ruling out its best motivated mass range. However, we find that leptophilic ADM remains allowed for $\gtrsim 10$ GeV DM, including bounds from colliders, direct detection, and stellar heating. We forecast that the Future Circular Collider for electron-positron collisions (FCC-ee) will improve sensitivity to DM-lepton interactions by almost an order of magnitude.

hep-ph↗

arXiv2024

On the collective effect of a large system of heavy particles immersed in a Newtonian fluid

We consider the motion of a large number of heavy particles in a Newtonian fluid occupying a bounded spatial domain. When we say "heavy", we mean a particle with a mass density that approaches infinity at an appropriate rate as its radius vanishes. We show that the collective effect of heavy particles on the fluid motion is similar to the Brinkman perturbation of the Navier-Stokes system identified in the homogenization process.

math.AP↗

arXiv2024

Interaction of liquid crystals with a rigid body

This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global strong solution for initial data close to constant equilibria. The proof of the global strong solution relies on a new splitting method for the director in a mean value zero and average part.

math.AP↗

arXiv2024

On the effect of a large cloud of rigid particles on the motion of an incompressible non--Newtonian fluid

We show that the collective effect of $N$ rigid bodies $(\mathcal{S}_{n,N})_{n=1}^N$ of diameters $(r_{n,N})_{n=1}^N$ immersed in an incompressible non--Newtonian fluid is negligible in the asymptotic limit $N \to \infty$ as long as their total packing volume $\sum_{n=1}^N r_{n,N}^d$, $d=2,3$ tends to zero exponentially -- $\sum_{n=1}^N r_{n,N}^d \approx A^{-N}$ -- for a certain constant $A > 1$. The result is rather surprising and in a sharp contrast with the associated homogenization problem, where the same number of obstacles can completely stop the fluid motion in the case of shear thickening viscosity. A large class of non--Newtonian fluids is included, for which the viscous stress is a subdifferential of a convex potential.

math.AP↗