arXiv subjects

Jongho Park

Publications and source records attributed to Jongho Park.

At least 55 records · Page 3Linked to original sources

arXiv2024

Magnetic field control over the axialness of Higgs modes in charge-density wave compounds

Understanding how symmetry-breaking processes generate order out of disorder is among the most fundamental problems of nature. The scalar Higgs mode - a massive (quasi-) particle - is a key ingredient in these processes and emerges with the spontaneous breaking of a continuous symmetry. Its related exotic and elusive axial counterpart, a Boson with vector character, can be stabilized through the simultaneous breaking of multiple continuous symmetries. Here, we employ a magnetic field to tune the recently discovered axial Higgs-type charge-density wave amplitude modes in rare-earth tritellurides. We demonstrate a proportionality between the axial Higgs component and the applied field, and a 90$^{\circ}$ phase shift upon changing the direction of the B-field. This indicates that the axial character is directly related to magnetic degrees of freedom. Our approach opens up an in-situ control over the axialness of emergent Higgs modes.

cond-mat.str-el↗

arXiv2024

Wiedemann-Franz Law and Thermoelectric Inequalities: Effective ZT and Single-leg Efficiency Overestimation

We derive a thermoelectric inequality in thermoelectric conversion between the material figure of merit (ZT) and the module effective ZT using the Constant Seebeck-coefficient Approximation combining with the Wiedemann-Franz law. In a P-N leg-pair module, the effective ZT lies between the individual ZT values of the P- and N-legs. In a single-leg module, however, the effective ZT is less than approximately one-third of the leg's ZT. This reduction results from the need for an external wire to complete the circuit, introducing additional thermal and electrical losses. Multi-dimensional numerical analysis shows that, although structural optimization can mitigate these losses, the system efficiency remains limited to below half of the ideal single-leg material efficiency. Our findings explain the single-leg efficiency overestimation and highlight the importance of optimizing the P-N leg-pair module structure. They also underscore the need for thermoelectric leg-compatibility, particularly with respect to Seebeck coefficients.

physics.app-ph↗

arXiv2024

Additive Schwarz methods for fourth-order variational inequalities

Fourth-order variational inequalities are encountered in various scientific and engineering disciplines, including elliptic optimal control problems and plate obstacle problems. In this paper, we consider additive Schwarz methods for solving fourth-order variational inequalities. Based on a unified framework of various finite element methods for fourth-order variational inequalities, we develop one- and two-level additive Schwarz methods. We prove that the two-level method is scalable in the sense that the convergence rate of the method depends on $H/h$ and $H/δ$ only, where $h$ and $H$ are the typical diameters of an element and a subdomain, respectively, and $δ$ measures the overlap among the subdomains. This proof relies on a new nonlinear positivity-preserving coarse interpolation operator, the construction of which was previously unknown. To the best of our knowledge, this analysis represents the first investigation into the scalability of the two-level additive Schwarz method for fourth-order variational inequalities. Our theoretical results are verified by numerical experiments.

math.NA↗

arXiv2024

Discovery of Limb Brightening in the Parsec-scale Jet of NGC 315 through Global Very Long Baseline Interferometry Observations and Its Implications for Jet Models

We report the first observation of the nearby giant radio galaxy NGC 315 using a global VLBI array consisting of 22 radio antennas located across five continents, including high-sensitivity stations, at 22 GHz. Utilizing the extensive $(u,v)$-coverage provided by the array, coupled with the application of a recently developed super-resolution imaging technique based on the regularized maximum likelihood method, we were able to transversely resolve the NGC 315 jet at parsec scales for the first time. Previously known for its central ridge-brightened morphology at similar scales in former VLBI studies, the jet now clearly exhibits a limb-brightened structure. This finding suggests an inherent limb-brightening that was not observable before due to limited angular resolution. Considering that the jet is viewed at an angle of $\sim50^\circ$, the observed limb-brightening is challenging to reconcile with the magnetohydrodynamic models and simulations, which predict that the Doppler-boosted jet edges should dominate over the non-boosted central layer. The conventional jet model that proposes a fast spine and a slow sheath with uniform transverse emissivity may pertain to our observations. However, in this model, the relativistic spine would need to travel at speeds of $Γ\gtrsim6.0-12.9$ along the de-projected jet distance of (2.3-10.8) $\times 10^3$ gravitational radii from the black hole. We propose an alternative scenario that suggests higher emissivity at the jet boundary layer, resulting from more efficient particle acceleration or mass loading onto the jet edges, and consider prospects for future observations with even higher angular resolution.

astro-ph.HE↗

arXiv2024

On the linear convergence of additive Schwarz methods for the $p$-Laplacian

We consider additive Schwarz methods for boundary value problems involving the $p$-Laplacian. While existing theoretical estimates suggest a sublinear convergence rate for these methods, empirical evidence from numerical experiments demonstrates a linear convergence rate. In this paper, we narrow the gap between these theoretical and empirical results by presenting a novel convergence analysis. Firstly, we present a new convergence theory for additive Schwarz methods written in terms of a quasi-norm. This quasi-norm exhibits behavior akin to the Bregman distance of the convex energy functional associated with the problem. Secondly, we provide a quasi-norm version of the Poincar'{e}--Friedrichs inequality, which plays a crucial role in deriving a quasi-norm stable decomposition for a two-level domain decomposition setting. By utilizing these key elements, we establish the asymptotic linear convergence of additive Schwarz methods for the $p$-Laplacian.

math.NA↗

arXiv2024

First Order Stochastic Optimization with Oblivious Noise

We initiate the study of stochastic optimization with oblivious noise, broadly generalizing the standard heavy-tailed noise setup. In our setting, in addition to random observation noise, the stochastic gradient may be subject to independent oblivious noise, which may not have bounded moments and is not necessarily centered. Specifically, we assume access to a noisy oracle for the stochastic gradient of $f$ at $x$, which returns a vector $\nabla f(γ, x) + ξ$, where $γ$ is the bounded variance observation noise and $ξ$ is the oblivious noise that is independent of $γ$ and $x$. The only assumption we make on the oblivious noise $ξ$ is that $\mathbf{Pr}[ξ= 0] \ge α$ for some $α\in (0, 1)$. In this setting, it is not information-theoretically possible to recover a single solution close to the target when the fraction of inliers $α$ is less than $1/2$. Our main result is an efficient list-decodable learner that recovers a small list of candidates, at least one of which is close to the true solution. On the other hand, if $α= 1-ε$, where $0< ε< 1/2$ is sufficiently small constant, the algorithm recovers a single solution. Along the way, we develop a rejection-sampling-based algorithm to perform noisy location estimation, which may be of independent interest.

cs.DS↗

arXiv2024

Mapping the distribution of the magnetic field strength along the NGC 315 jet

We study magnetic field strengths along the jet in NGC~315. First, we estimated the angular velocity of rotation in the jet magnetosphere by comparing the measured velocity profile of NGC~315 with the magneto-hydrodynamic jet model of proposed by Tomimatsu and Takahashi. Similar to the case of M87, we find that the model can reproduce the logarithmic feature of the velocity profile and suggest a slowly rotating black hole magnetosphere for NGC~315. By substituting the estimated $Ω_{F}$ into the jet power predicted by the Blandford-Znajek mechanism, we estimate the magnetic field strength near the event horizon of the central black hole as $5\times 10^{3}~{\rm G}\lesssim B_{H}\lesssim 2\times 10^{4}~{\rm G}$. We then estimate magnetic-field strengths along the jet by comparing the spectral index distribution obtained from VLBI observations with a synchrotron-emitting jet model. Then we constrain the magnetic field strength at a de-projected distance $z$ from the black hole to be in the range $0.06~{\rm G}\lesssim B(z)\lesssim 0.9~{\rm G}$ for $5.2 \times 10^{3}~r_{g}\lesssim z \lesssim 4.9 \times 10^{4}~r_{g}$, where $r_{g}$ represents the gravitational radius. By combining the obtained field strengths at the event horizon and the downstream section of the jet, we find that the accretion flow at the jet base is consistent with a magnetically arrested disk (MAD). We discuss a comparison of the jet power and the magnetic flux anchored to the event horizon in NGC~315 and M87.

astro-ph.HE↗

arXiv2024

Two-level overlapping Schwarz preconditioners with universal coarse spaces for $2m$th-order elliptic problems

We propose a novel universal construction of two-level overlapping Schwarz preconditioners for $2m$th-order elliptic boundary value problems, where $m$ is a positive integer. The word "universal" here signifies that the coarse space construction can be applied to any finite element discretization for any $m$ that satisfies some common assumptions. We present numerical results for conforming, nonconforming, and discontinuous Galerkin-type finite element discretizations for high-order problems to demonstrate the scalability of the proposed two-level overlapping Schwarz preconditioners.

math.NA↗

arXiv2024

Evolution of the Termination Region of the Parsec-Scale Jet of 3C 84 Over the Past 20 Years

We present the kinematics of the parsec-scale jet in 3C 84 from 2003 November to 2022 June observed with the Very Long Baseline Array (VLBA) at 43 GHz. We find that the C3 component, a bright feature at the termination region of the jet component ejected from the core in 2003, has maintained a nearly constant apparent velocity of 0.259 +/- 0.003c over the period covered by observations. We observe the emergence of four new subcomponents from C3, each exhibiting apparent speeds higher than that of C3. Notably, the last two subcomponents exhibit apparent superluminal motion, with the fastest component showing an apparent speed of 1.22 +/- 0.14c. Our analysis suggests that a change in viewing angle alone cannot account for the fast apparent speeds of the new subcomponents, indicating that they are intrinsically faster than C3. We identify jet precession (or reorientation), a jet-cloud collision, and magnetic reconnection as possible physical mechanisms responsible for the ejection of the new subcomponents.

astro-ph.HE↗

arXiv2024

Jet Collimation and Acceleration in the Flat Spectrum Radio Quasar 1928+738

Using time-resolved multifrequency Very Long Baseline Array data and new KaVA (KVN and VERA Array) observations, we study the structure and kinematics of the jet of the flat spectrum radio quasar (FSRQ) 1928+738. We find two distinct jet geometries as function of distance from the central black hole, with the inner jet having a parabolic shape, indicating collimation, and the outer jet having a conical shape, indicating free expansion of the jet plasma. Jet component speeds display a gradual outward acceleration up to a bulk Lorentz factor $Γ_{\rm max} \approx10$, followed by a deceleration further downstream. The location of the acceleration zone matches the region where the jet collimation occurs; this is the first direct observation of an acceleration and collimation zone (ACZ) in an FSRQ. The ACZ terminates approximately at a distance of 5.6$\times 10^6$ gravitational radii, which is in good agreement with the sphere of gravitational influence of the supermassive black hole, implying that the physical extent of the ACZ is controlled by the black hole gravity. Our results suggest that confinement by an external medium is responsible for the jet collimation and that the jet is accelerated by converting Poynting flux energy to kinetic energy.

astro-ph.HE↗

arXiv2024

Can Mamba Learn How to Learn? A Comparative Study on In-Context Learning Tasks

State-space models (SSMs), such as Mamba (Gu & Dao, 2023), have been proposed as alternatives to Transformer networks in language modeling, by incorporating gating, convolutions, and input-dependent token selection to mitigate the quadratic cost of multi-head attention. Although SSMs exhibit competitive performance, their in-context learning (ICL) capabilities, a remarkable emergent property of modern language models that enables task execution without parameter optimization, remain underexplored compared to Transformers. In this study, we evaluate the ICL performance of SSMs, focusing on Mamba, against Transformer models across various tasks. Our results show that SSMs perform comparably to Transformers in standard regression ICL tasks, while outperforming them in tasks like sparse parity learning. However, SSMs fall short in tasks involving non-standard retrieval functionality. To address these limitations, we introduce a hybrid model, MambaFormer, that combines Mamba with attention blocks, surpassing individual models in tasks where they struggle independently. Our findings suggest that hybrid architectures offer promising avenues for enhancing ICL in language models.

cs.LG↗

arXiv2024

A neuron-wise subspace correction method for the finite neuron method

In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace Correction Method (NPSC) for the finite neuron method that approximates numerical solutions of partial differential equations (PDEs) using neural network functions. Despite extremely extensive research activities in applying neural networks for numerical PDEs, there is still a serious lack of effective training algorithms that can achieve adequate accuracy, even for one-dimensional problems. Based on recent results on the spectral properties of linear layers and landscape analysis for single neuron problems, we develop a special type of subspace correction method that optimizes the linear layer and each neuron in the nonlinear layer separately. An optimal preconditioner that resolves the ill-conditioning of the linear layer is presented for one-dimensional problems, so that the linear layer is trained in a uniform number of iterations with respect to the number of neurons. In each single neuron problem, a good local minimum that avoids flat energy regions is found by a superlinearly convergent algorithm. Numerical experiments on function approximation problems and PDEs demonstrate better performance of the proposed method than other gradient-based methods.

math.NA↗

arXiv2024

Additive Schwarz methods for semilinear elliptic problems with convex energy functionals: Convergence rate independent of nonlinearity

We investigate additive Schwarz methods for semilinear elliptic problems with convex energy functionals, which have wide scientific applications. A key observation is that the convergence rates of both one- and two-level additive Schwarz methods have bounds independent of the nonlinear term in the problem. That is, the convergence rates do not deteriorate by the presence of nonlinearity, so that solving a semilinear problem requires no more iterations than a linear problem. Moreover, the two-level method is scalable in the sense that the convergence rate of the method depends on $H/h$ and $H/δ$ only, where $h$ and $H$ are the typical diameters of an element and a subdomain, respectively, and $δ$ measures the overlap among the subdomains. Numerical results are provided to support our theoretical findings.

math.NA↗

arXiv2024

DualFL: A Duality-based Federated Learning Algorithm with Communication Acceleration in the General Convex Regime

We propose a new training algorithm, named DualFL (Dualized Federated Learning), for solving distributed optimization problems in federated learning. DualFL achieves communication acceleration for very general convex cost functions, thereby providing a solution to an open theoretical problem in federated learning concerning cost functions that may not be smooth nor strongly convex. We provide a detailed analysis for the local iteration complexity of DualFL to ensure the overall computational efficiency of DualFL. Furthermore, we introduce a completely new approach for the convergence analysis of federated learning based on a dual formulation. This new technique enables concise and elegant analysis, which contrasts the complex calculations used in existing literature on convergence of federated learning algorithms.

cs.LG↗

arXiv2023

Observational Evidence to Support a Dense Ambient Medium Shaping the Jet in 3C 84

Highly collimated relativistic jets are a defining feature of certain active galactic nuclei (AGN), yet their formation mechanism remains elusive. Previous observations and theoretical models have proposed that the ambient medium surrounding the jets could exert pressure, playing a crucial role in shaping the jets. However, direct observational confirmation of such a medium has been lacking. In this study, we present very long baseline interferometric (VLBI) observations of 3C 84 (NGC 1275), located at the center of the Perseus Cluster. Through monitoring observations with the Very Long Baseline Array (VLBA) at 43 GHz, a jet knot was detected to have been ejected from the sub-parsec scale core in the late 2010s. Intriguingly, this knot propagated in a direction significantly offset from the parsec-scale jet direction. To delve deeper into the matter, we employ follow-up VLBA 43 GHz observations, tracing the knot's trajectory until the end of 2022. We discovered that the knot abruptly changed its trajectory in the early 2020s, realigning itself with the parsec-scale jet direction. Additionally, we present results from an observation of 3C 84 with the Global VLBI Alliance (GVA) at 22 GHz, conducted near the monitoring period. By jointly analyzing the GVA 22 GHz image with a VLBA 43 GHz image observed about one week apart, we generated a spectral index map, revealing an inverted spectrum region near the edge of the jet where the knot experienced deflection. These findings suggest the presence of a dense, cold ambient medium characterized by an electron density exceeding $\sim10^5\ {\rm cm^{-3}}$, which guides the jet's propagation on parsec scales and significantly contributes to the overall shaping of the jet.

astro-ph.HE↗

arXiv2023

Singular Hall response from a correlated ferromagnetic flat nodal-line semimetal

Topological quantum phases have been largely understood in weakly correlated systems, which have identified various quantum phenomena such as spin Hall effect, protected transport of helical fermions, and topological superconductivity. Robust ferromagnetic order in correlated topological materials particularly attracts attention, as it can provide a versatile platform for novel quantum devices. Here, we report singular Hall response arising from a unique band structure of flat topological nodal lines in combination with electron correlation in an itinerant, van der Waals ferromagnetic semimetal, Fe3GaTe2, with a high Curie temperature of Tc=360 K. High anomalous Hall conductivity violating the conventional scaling, resistivity upturn at low temperature, and a large Sommerfeld coefficient are observed in Fe3GaTe2, which implies heavy fermion features in this ferromagnetic topological material. Our circular dichroism in angle-resolved photoemission spectroscopy and theoretical calculations support the original electronic features in the material. Thus, low-dimensional Fe3GaTe2 with electronic correlation, topology, and room-temperature ferromagnetic order appears to be a promising candidate for robust quantum devices.

cond-mat.str-el↗

arXiv2023

Melting of unidirectional charge density waves across twin domain boundaries in GdTe$_{3}$

Solids undergoing a transition from order to disorder experience the proliferation of topological defects. The melting process generates transient quantum states. However, their dynamical nature with femtosecond lifetime hinders exploration with atomic precision. Here, we suggest an alternative approach to the dynamical melting process by focusing on the interface created by competing degenerate quantum states. We use a scanning tunneling microscope (STM) to visualize the unidirectional charge density wave (CDW) and its spatial progression ("static melting") across a twin domain boundary (TDB) in the layered material GdTe$_{3}$. Combining STM with a spatial lock-in technique, we reveal that the order parameter amplitude attenuates with the formation of dislocations and thus two different unidirectional CDWs coexist near the TDB, reducing the CDW anisotropy. Notably, we discover a correlation between this anisotropy and the CDW gap. Our study provides valuable insight into the behavior of topological defects and transient quantum states.

cond-mat.str-el↗

arXiv2023

Balanced Group Convolution: An Improved Group Convolution Based on Approximability Estimates

The performance of neural networks has been significantly improved by increasing the number of channels in convolutional layers. However, this increase in performance comes with a higher computational cost, resulting in numerous studies focused on reducing it. One promising approach to address this issue is group convolution, which effectively reduces the computational cost by grouping channels. However, to the best of our knowledge, there has been no theoretical analysis on how well the group convolution approximates the standard convolution. In this paper, we mathematically analyze the approximation of the group convolution to the standard convolution with respect to the number of groups. Furthermore, we propose a novel variant of the group convolution called balanced group convolution, which shows a higher approximation with a small additional computational cost. We provide experimental results that validate our theoretical findings and demonstrate the superior performance of the balanced group convolution over other variants of group convolution.

cs.LG↗