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The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently utilized time-discretization numerical schemes for solving the Allen-Cahn equation, with focuses on the Backward Euler, Crank-Nicolson (CN), convex splitting of modified CN, and Diagonally Implicit Runge-Kutta (DIRK) methods. Our stability analysis reveals that the Convex Splitting of the Modified CN scheme exhibits unconditional stability, allowing greater flexibility in time step selection, while the other schemes are conditionally stable. Additionally, our robustness analysis highlights that the Backward Euler method converges to correct physical solutions regardless of initial conditions. In contrast, the other methods studied in this work show sensitivity to initial conditions and may converge to incorrect physical solutions if the initial conditions are not carefully chosen. This study introduces a comprehensive approach to assessing stability and robustness in numerical methods for solving the Allen-Cahn equation, providing a new perspective for evaluating numerical techniques for general nonlinear differential equations.

Recent studies have demonstrated that ultrahigh-$Q$ resonances, which are robust to fabrication imperfections, can be realized by merging multiple bound states in the continuum (BICs) in momentum space. The merging of multiple BICs holds significant promise for practical applications, providing a robust means to attain ultrahigh-$Q$ resonances that greatly enhance light-matter interactions. In this study, we introduce a novel approach to achieve the merging of BICs at the edges of the fourth stop band, which opens at the third-order $\Gamma$ point, in one-dimensional leaky-mode photonic lattices. Photonic band gaps and BICs arise from periodic modulations in lattice parameters. However, near the third-order $\Gamma$ point, out-of-plane radiation arises by the first and second Fourier harmonic components in the lattice parameters. Accidental BICs can emerge at specific $k$ points where an optimal balance exists between these two Fourier harmonic components. We demonstrate that these accidental BICs are topologically stable, and their positions in momentum space can be precisely controlled by adjusting a specific lattice parameter that influences the strength of the first and second Fourier harmonic components. Furthermore, we show that accidental BICs can be merged at the third-order $\Gamma$ point, with or without a symmetry-protected BIC, by finely adjusting this specific lattice parameter while keeping other parameters constant.

Unidirectional light emission from planar photonic structures is highly advantageous for a wide range of optoelectronic applications. Recently, it has been demonstrated that unidirectional guided resonances (UGRs) can be realized by utilizing topological polarization singularities in momentum space. However, the practical application of these topological unidirectional emitters has been limited due to their intricate geometric configurations, requiring special efforts with high-cost fabrication processes. In this study, we show that unidirectional light emission can be achieved in conventional one-dimensional zero-contrast gratings (ZCGs), which can be easily fabricated using current nanofabrication technologies. In ZCGs, the interband coupling between even-like and odd-like waveguide modes leads to the formation of quasi-UGRs, characterized by significantly higher decay rates in either the upward or downward direction compared to the opposite direction. We demonstrate that these quasi-UGRs evolve into genuine UGRs with an gradual increase in grating thickness. Moreover, the emission direction of UGRs can be selectively steered either upward or downward by adjusting the lattice parameters. In addition to quasi-UGRs and UGRs, our study also reveals additional topological phenomena in ZCGs, including exceptional points and quasi-BICs.

Quantum interferometry based on induced-coherence phenomena has demonstrated the possibility of undetected-photon measurements. Perturbation in the optical path of probe photons can be detected by interference signals generated by quantum mechanically correlated twin photons propagating through a different path, possibly at a different wavelength. To the best of our knowledge, this work demonstrates for the first time a hybrid-type induced-coherence interferometer that incorporates a Mach-Zehnder-type interferometer for visible photons and a Michelson-type interferometer for infrared photons, based on double-pass pumped spontaneous parametric down-conversion. This configuration enables infrared optical measurements via the detection of near-visible photons and provides methods for characterizing the quality of measurements by identifying photon pairs of different origins. The results verify that the induced-coherence interference visibility is approximately the same as the heralding efficiencies between twin photons along the relevant spatial modes. Applications to both time-domain and frequency-domain quantum-optical induced-coherence tomography for three-dimensional test structures are demonstrated. The results prove the feasibility of practical undetected-photon sensing and imaging techniques based on the presented structure.

While many FSCIL studies have been undertaken, achieving satisfactory performance, especially during incremental sessions, has remained challenging. One prominent challenge is that the encoder, trained with an ample base session training set, often underperforms in incremental sessions. In this study, we introduce a novel training framework for FSCIL, capitalizing on the generalizability of the Contrastive Language-Image Pre-training (CLIP) model to unseen classes. We achieve this by formulating image-object-specific (IOS) classifiers for the input images. Here, an IOS classifier refers to one that targets specific attributes (like wings or wheels) of class objects rather than the image's background. To create these IOS classifiers, we encode a bias prompt into the classifiers using our specially designed module, which harnesses key-prompt pairs to pinpoint the IOS features of classes in each session. From an FSCIL standpoint, our framework is structured to retain previous knowledge and swiftly adapt to new sessions without forgetting or overfitting. This considers the updatability of modules in each session and some tricks empirically found for fast convergence. Our approach consistently demonstrates superior performance compared to state-of-the-art methods across the miniImageNet, CIFAR100, and CUB200 datasets. Further, we provide additional experiments to validate our learned model's ability to achieve IOS classifiers. We also conduct ablation studies to analyze the impact of each module within the architecture., Comment: 8 pages, 4 figures, 4 tables

This paper proposes a system capable of recognizing a speaker's utterance-level emotion through multimodal cues in a video. The system seamlessly integrates multiple AI models to first extract and pre-process multimodal information from the raw video input. Next, an end-to-end MER model sequentially predicts the speaker's emotions at the utterance level. Additionally, users can interactively demonstrate the system through the implemented interface., Comment: Interspeech 2023

Bound states in the continuum (BICs) theoretically have the ability to confine electromagnetic waves in limited regions with infinite radiative quality ($Q$) factors. However, in practical experiments, resonances can only exhibit finite $Q$ factors due to unwanted scattering losses caused by fabrication imperfections. Recently, it has been shown that ultrahigh-$Q$ guided-mode resonances (GMRs), which are robust to fabrication imperfections, can be realized by merging multiple BICs in momentum space. In this study, we analytically and numerically investigate the merging and band transition of accidental BICs in planar photonic lattices. Accidental BICs can merge at the edges of the second stop band, either with or without a symmetry-protected BIC. We show that as the thickness of the photonic lattice gradually increases, the merged state of BICs transitions from the upper to the lower band edge. Using coupled-mode analysis, we present the analytical merging thickness at which multiple accidental BICs merge at the second-order $\Gamma$ point. Our coupled-mode analysis could be beneficial for achieving ultrahigh-$Q$ GMRs in various photonic lattices composed of materials with different dielectric constants.

The use of nonlinear PDEs has led to significant advancements in various fields, such as physics, biology, ecology, and quantum mechanics. However, finding multiple solutions for nonlinear PDEs can be a challenging task, especially when suitable initial guesses are difficult to obtain. In this paper, we introduce a novel approach called the Companion-Based Multilevel finite element method (CBMFEM), which can efficiently and accurately generate multiple initial guesses for solving nonlinear elliptic semi-linear equations with polynomial nonlinear terms using finite element methods with conforming elements. We provide a theoretical analysis of the error estimate of finite element methods using an appropriate notion of isolated solutions, for the nonlinear elliptic equation with multiple solutions and present numerical results obtained using CBMFEM which are consistent with the theoretical analysis.

Barcode magnetic nanowires typically comprise a multilayer magnetic structure in a single body with more than one segment type. Interestingly, owing to selective functionalization and novel interactions between the layers, barcode magnetic nanowires have attracted significant attention, particularly in the field of bioengineering. However, an analysis of their magnetic properties at the individual nanowire level remains challenging. With this background, herein, we investigated the characterization of magnetic nanowires at room temperature under ambient conditions based on magnetic images obtained via wide-field quantum microscopy with nitrogen-vacancy centers in diamond. Consequently, we could extract critical magnetic properties, such as the saturation magnetization and coercivity, of single nanowires by comparing the experimental results with those of micromagnetic simulations. This study opens up the possibility for a versatile characterization method suited to individual magnetic nanowires., Comment: main text (20 pages, 5 figures), supplementary materials (9 pages, 8 figures)

We study the problem of detecting the community structure from the generalized stochastic block model (GSBM). Based on the analysis of the Stieljtes transform of the empirical spectral distribution, we prove a BBP-type transition for the largest eigenvalue of the GSBM. For specific models such as a hidden community model and an unbalanced stochastic model, we provide precise formulas for the two largest eigenvalues, establishing the gap in the BBP-type transition., Comment: 18 pages, 4 figures

In this paper, we introduce a new benchmark dataset for the challenging writing in the air (WiTA) task -- an elaborate task bridging vision and NLP. WiTA implements an intuitive and natural writing method with finger movement for human-computer interaction (HCI). Our WiTA dataset will facilitate the development of data-driven WiTA systems which thus far have displayed unsatisfactory performance -- due to lack of dataset as well as traditional statistical models they have adopted. Our dataset consists of five sub-datasets in two languages (Korean and English) and amounts to 209,926 video instances from 122 participants. We capture finger movement for WiTA with RGB cameras to ensure wide accessibility and cost-efficiency. Next, we propose spatio-temporal residual network architectures inspired by 3D ResNet. These models perform unconstrained text recognition from finger movement, guarantee a real-time operation by processing 435 and 697 decoding frames-per-second for Korean and English, respectively, and will serve as an evaluation standard. Our dataset and the source codes are available at https://github.com/Uehwan/WiTA., Comment: 10 pages, 6 figures, 6 tables

In conventional diffraction theory, a subwavelength period is considered a prerequisite to achieve interesting resonance-assisted physical phenomena, such as bound states in the continuum and diverse zero-order spectral responses with $100\%$ diffraction efficiency. Here, we present modified diffraction equations that provide mechanisms to control light diffraction beyond the subwavelength limit. We show that resonant diffraction phenomena are governed by the superposition of scattering processes, owing to higher Fourier harmonic components. By appropriately engineering the Fourier harmonic components in the grating parameters, unwanted diffraction orders can be suppressed. Moreover, bound states in the continuum and highly efficient zero-order spectral responses can be achieved beyond the subwavelength limit. The concept of engineering Fourier harmonic components in periodic modulations provides new mechanisms to overcome the diffraction limit.

We present a challenging dataset, ChangeSim, aimed at online scene change detection (SCD) and more. The data is collected in photo-realistic simulation environments with the presence of environmental non-targeted variations, such as air turbidity and light condition changes, as well as targeted object changes in industrial indoor environments. By collecting data in simulations, multi-modal sensor data and precise ground truth labels are obtainable such as the RGB image, depth image, semantic segmentation, change segmentation, camera poses, and 3D reconstructions. While the previous online SCD datasets evaluate models given well-aligned image pairs, ChangeSim also provides raw unpaired sequences that present an opportunity to develop an online SCD model in an end-to-end manner, considering both pairing and detection. Experiments show that even the latest pair-based SCD models suffer from the bottleneck of the pairing process, and it gets worse when the environment contains the non-targeted variations. Our dataset is available at http://sammica.github.io/ChangeSim/., Comment: Accepted to IROS 2021

Bound states in the continuum (BICs) and Fano resonances in planar photonic lattices, including metasurfaces and photonic crystal slabs, have been studied extensively in recent years. Typically, the BICs and Fano resonances are associated with the second stop bands open at the second-order Gamma ($\Gamma$) point. This paper address the fundamental properties of the fourth stop band accompanied by BICs at the third-order $\Gamma$ point in one-dimensional (1D) leaky-mode photonic lattices. At the fourth stop band, one band edge mode suffers radiation loss, thereby generating a Fano resonance, while the other band edge mode becomes a nonleaky BIC. The fourth stop band is controlled primarily by the Bragg processes associated with the first, second, and fourth Fourier harmonic components of the periodic dielectric constant modulation. The interplay between these three major processes closes the fourth band gap and induces a band flip whereby the leaky and BIC edges transit across the fourth band gap. At the fourth stop band, a new type of BIC is formed owing to the destructive interplay between the first and second Fourier harmonics. When the fourth band gap closes with strongly enhanced $Q$ factors, Dirac cone dispersions can appear at the third-order $\Gamma$ point. Our results demonstrate a method for manipulating electromagnetic waves by utilizing the high-$Q$ Bloch modes at the fourth stop band.

A perfect metal film with a periodic arrangement of cut-through slits, an anisotropic metallic metamaterial film, mimics a dielectric slab and supports guided electromagnetic waves in the direction perpendicular to the slits. Here, we introduce metallic metasurface superlattices that include multiple slits in a period, and demonstrate that the superlattices support the Fano resonances and bound states in the continuum. The number of Fano resonances and bound states depend on the number of slits in a period of superlattices. The metallic metasurface superlattices provide new mechanisms to manipulate electromagnetic waves, ranging from microwave to far-infrared wavelengths, where a conventional metal can be considered as a perfect electric conductor.

When two nonorthogonal resonances are coupled to the same radiation channel, avoided crossing arises and a bound state in the continuum (BIC) appears in parametric space. This paper presents numerical and analytical results on the properties of avoided crossing and BIC due to the coupled guided-mode resonances in one-dimensional leaky-mode photonic lattices with slab geometry. In symmetric photonic lattices with up-down mirror symmetry, Friedrich-Wintgen BICs with infinite lifetime are accompanied by avoided crossings due to the coupling between two guided modes with the same transverse parity. In asymmetric photonic lattices with broken up-down mirror symmetry, quasi-BICs with finite lifetime appear with avoided crossings because radiating waves from different modes cannot be completely eliminated. We also show that unidirectional-BICs are accompanied by avoided crossings due to guided-mode resonances with different transverse parities in asymmetric photonic lattices. The Q factor of a unidirectional-BIC is finite, but its radiation power in the upward or downward direction is significantly smaller than that in the opposite direction. Our results may be helpful in engineering BICs and avoided crossings in diverse photonic systems that support leaky modes.

Conventional photonic lattices, such as metamaterials and photonic crystals, exhibit various interesting physical properties that are attributed to periodic modulations in lattice parameters. In this study, we introduce novel types of photonic lattices, namely Fourier-component-engineered metasurfaces, that do not possess the first Fourier harmonic component in the lattice parameters. We demonstrate that these metasurfaces support the continuous high-$Q$ bound states near second stop bands. The concept of engineering Fourier harmonic components in periodic modulations provides a new method to manipulate electromagnetic waves in artificial periodic structures.

Along a single strand of micro-capillary optical waveguide, we achieved an efficient transfer of the light momentum onto the liquid contained there within, successfully atomizing it into nanoscale droplets. A hollow optical fiber (HOF), with a ring core and central air hole, was used to optically drive jetting of non-conducting transparent liquid of sub-pico liter volume, out of a surface-treated facet orifice, producing droplets ranging from nano to micrometer scale. These droplets were carried over the propagating light field forming a spherical cone, which were then deposited on a silica substrate in a Gaussian spatial distribution. The deposited patterns and sizes of individual droplets were characterized as a function of the laser power, irradiation time, and distance between the HOF and a substrate. This HOF based laser driven atomization technique obviates imperative electrode or aerial pressure requirements in prior methods, opening a new pathway to drastically scale down the form-factor of liquid jetting devices, and has a high potential to in-situ atomization and delivery of bio-medical non-conducting liquids in a microscopic environment, which was not possible in prior arts.

Leaky-mode photonic lattices exhibit intricate resonance effects originating in quasi-guided lateral Bloch modes. Key spectral properties are associated with phase-matched modes at the second (leaky) stop band. One band edge mode suffers radiation loss generating leaky-mode resonance whereas the other band edge mode becomes a bound state in the continuum (BIC). Here, we present analytical and numerical results on the formation and properties of the leaky stop band. We show that the frequency of the leaky-mode resonance band edge, and correspondingly the BIC edge, is determined by superposition of Bragg processes chiefly generated by the first two Fourier harmonics of the spatial modulation. We derive conditions for the band closure and band flip wherein the leaky edge and the bound-state edge transit across the band gap. Our work elucidates fundamental aspects of periodic photonic films and has high relevance to the burgeoning field of metamaterials., Comment: 11 pages, 5 figures

In this paper, we study an interference avoidance scenario in the presence of a smart interferer which can rapidly observe the transmit power of a backscatter wireless sensor network (WSN) and effectively interrupt backscatter signals. We consider a power control with a sub-channel allocation to avoid interference attacks and a time-switching ratio for backscattering and RF energy harvesting in backscatter WSNs. We formulate the problem based on a Stackelberg game theory and compute the optimal transmit power, time-switching ratio, and sub-channel allocation parameter to maximize a utility function against the smart interference. We propose two algorithms for the utility maximization using Lagrangian dual decomposition for the backscatter WSN and the smart interference to prove the existence of the Stackelberg equilibrium. Numerical results show that the proposed algorithms effectively maximize the utility, compared to that of the algorithm based on the Nash game, so as to overcome smart interference in backscatter communications., Comment: 13 pages

The Large Area Picosecond PhotoDetector (LAPPD) Collaboration was formed in 2009 to develop large-area photodetectors capable of time resolutions measured in pico-seconds, with accompanying sub-millimeter spatial resolution. During the next three and one-half years the Collaboration developed the LAPPD design of 20 x 20 cm modules with gains greater than $10^7$ and non-uniformity less than $15\%$, time resolution less than 50 psec for single photons and spatial resolution of 700~microns in both lateral dimensions. We describe the R\&D performed to develop large-area micro-channel plate glass substrates, resistive and secondary-emitting coatings, large-area bialkali photocathodes, and RF-capable hermetic packaging. In addition, the Collaboration developed the necessary electronics for large systems capable of precise timing, built up from a custom low-power 15-GigaSample/sec waveform sampling 6-channel integrated circuit and supported by a two-level modular data acquisition system based on Field-Programmable Gate Arrays for local control, data-sparcification, and triggering. We discuss the formation, organization, and technical successes and short-comings of the Collaboration. The Collaboration ended in December 2012 with a transition from R\&D to commercialization.

We measured the absolute frequency of the optical clock transition 1S0 (F = 1/2) - 3P0 (F = 1/2) of 171Yb atoms confined in a one-dimensional optical lattice and it was determined to be 518 295 836 590 863.5(8.1) Hz. The frequency was measured against Terrestrial Time (TT; the SI second on the geoid) by using an optical frequency comb of which the frequency was phase-locked to an H-maser as a flywheel oscillator traceable to TT. The magic wavelength was also measured as 394 798.48(79) GHz. The results are in good agreement with two previous measurements of other institutes within the specified uncertainty of this work., Comment: 11 pages, 10 figures, 1 Table

Radiative decay from the excited $^1P_1$ state to metastable $^3P_2$ and $^3P_0$ states is expected to limit attainable trapped atomic population in a magneto-optic trap of ytterbium (Yb) atoms. In experiments we have carried out with optical repumping of $^3P_{0,2}$ states to $^3P_1$, we observe enhancement of trapped atoms yield in the excited $^1P_1$ state. The individual decay rate to each metastable state is measured and the results show an excellent agreement with the theoretical values., Comment: 5 pages, 5 figures

We analyze bound states of an electron in the field of a positively charged nanoshell. We find that the binding and excitation energies of the system decrease when the radius of the nanoshell increases. We also show that the ground and the first excited states of this system have remarkably the same properties of the highly excited Rydberg states of a hydrogen-like atom i.e. a high sensitivity to the external perturbations and long radiative lifetimes., Comment: 16 pages

We propose a super-resolution quantum lithography scheme based on coherent population trapping in lambda-type atoms coupled to temporally-cascaded standing-wave driving fields. By realizing effective multiplication of optical intensity profiles on an atomic state density distribution, the scheme enables an arbitrarily high degree of resolution enhancement without modifying the atomic level structure of the photographic medium or the light source configuration. It is also shown that the visibility of the super-resolution patterns is preserved under a significant atomic state decoherence rate., Comment: 13 pages, 4 figures; Added a figure and references, revised the Abstract and the text to better emphasize the major points

The usability test team examined design problems that limit the ability of instructors at the Indiana University to use data entry forms on the School of Education Web site. The forms permit instructors to publish information about themselves and about courses they teach on the School of Education Web site. Faculty and graduate student instructors were asked to perform typical tasks with the Web forms under observation. Participants were asked to describe what they were thinking and feeling as they attempted to perform the task. From these observations, several key design problems were identified that prevented or frustrated the participants. Solutions are recommended to eliminate these problems. The paper concludes that the designers of this Web site should address the following problems in future versions of the site. First, the recommended procedure for adding an HTML-formatted syllabus to the School of Education Web site fails to produce satisfactory results. Designers should find tools that produce reliable results, or eliminate this option. The School of Education may need to make organizational changes such as employing specialists to assist instructors in preparing electronic versions if this feature is desired. Second, the Personal Information page causes problems for uses due to its length and complexity. At a minimum, the form should be separated into two pages, one for required information and one for optional information. In addition, the designers should make sure that all multi-line text fields handle carriage returns properly. Third, the designers should add navigational elements to the Web forms that provide users with indications of what steps they have completed and what steps they still need to complete. (Author/AEF)

We investigate the time evolution of atomic population in a two-level atom driven by a monochromatic radiation field, taking spontaneous emission into account. The Rabi oscillation exhibits amplitude damping in time caused by spontaneous emission. We show that the semiclassical master equation leads in general to an overestimation of the damping rate and that a correct quantitative description of the damped Rabi oscillation can thus be obtained only with a full quantum mechanical theory., Comment: 5 pages, 5 figures

Asians are now the fastest growing ethnic group in the United States. And although disproportionately more likely to live in Western states, some are settling in nontraditional host communities. Focusing on one such instance in southeast Georgia, the present ethnographic case study considers a poultry processing plant's decision to recruit dozens of South Koreans. Starting in 2006, Korean immigrants began working at Claxton Poultry in Evans County, Georgia. This study looks at the factors motivating the workers to leave Korea and the host community's motives for seeking their labor. Education plays a critical role in the findings.