Small Values Research Articles

The Evolution of Photospheric Magnetic Fields at the Footpoints of Reconnected Structures in the Solar Atmosphere

Magnetic reconnection is believed to play an important role in the release and conversion of energy among magnetized plasma systems. So far, we have been unable to understand under what conditions magnetic reconnection can take place. Based on observations from the New Vacuum Solar Telescope and the Solar Dynamics Observatory (SDO), we study 16 magnetic reconnection events, and each event has a clear X-type configuration consisting of two sets of atmospheric structures. We focus on 38 footpoints that are relevant to these structures and can be clearly determined. By using SDO/Helioseismic and Magnetic Imager line-of-sight magnetograms, we track the field evolution of these footpoints. Prior to the occurrence of magnetic reconnection, the associated fields at the footpoints underwent convergence and shear motions, and thus became enhanced and complex. During the converging period, the rates of increase of the mean magnetic flux densities (MFDs) at these footpoints are 0.03–0.25 hr−1. While the unsigned mean MFDs are 70–300 G, magnetic reconnection in the solar atmosphere takes place. Subsequently, the photospheric fields of these footpoints diffuse and weaken, with rates of decrease of the MFDs from 0.03 to 0.18 hr−1. These results suggest that, due to the photospheric dynamical evolution at the footpoints, the footpoint MFDs increase from a small value to a large one, and the corresponding atmospheric magnetic fields become complicated and nonpotential; then reconnection happens and it releases the accumulated magnetic field energy. Our study supports the conjecture that magnetic reconnection releases free magnetic energy stored in the nonpotential fields.

Characteristics of Inferior Myocardial Infarction With a Special Electrocardiographic Pattern (Aslanger) in Metabolic Syndrome

To evaluate the features of ST-segment elevation myocardial infarction with the Aslanger pattern in comparison with traditional forms of inferior myocardial infarction in metabolic syndrome. This study included 30 patients with inferior myocardial infarction in the presence of metabolic syndrome: 9 patients with the Aslanger electrocardiographic pattern (group 1, age 59.7 [58.4; 63.1] years) and the rest with one of the traditional forms (control group, 59.9 [57.2; 63.8] years, matched by all criteria of metabolic syndrome). All patients underwent primary percutaneous intervention with assessment of the angiographic picture. The magnitude of ST-segment elevation was measured in lead III at the J point and following 0.06 seconds, and the optimal threshold value of this indicator was determined for a new picture of myocardial infarction. The infarct-related artery in the Aslanger pattern was more often the circumflex artery (p=0.0099), and coronary thrombosis was characterized by a lower TIMI thrombus grade (p=0.014). SYNTAX values for the Aslanger pattern and for the traditional picture of inferior infarction with ST elevation in lead II≥III were higher than for a similar picture with ST elevation in lead III>II. The level of cTnI at admission (p=0.013) and after 24 hours (p=0.0017), the platelet count (p=0.0011) and mean volume (p=0.0047) in group 1 had smaller values than with traditional inferior infarction. The ST elevation at J point and at J+0.06 s point for lead III with the Aslanger pattern was significantly lower than values of such shift in lead III>II and lead II≥III with traditional inferior infarction (p<0.001). An elevation value ≤1.5 mm at J point +0.06 s was a predictor of infarction with the Aslanger pattern. Constructing the ROC curve made it possible to determine that with the Aslanger pattern, the best cutoff value for this index is 2 mm. Myocardial infarction with the Aslanger pattern as compared with traditional lower infarction in metabolic syndrome is characterized by specific individual angiographic signs, lower ST segment elevation, cTnI level, and thrombotic disorders.

Timescales Associated with the Evolution of Reactive Scalar Gradient in Premixed Turbulent Combustion: A Direct Numerical Simulation Analysis

The fractional change in the reaction progress variable gradient depends on the flow normal straining within the flame and also upon the corresponding normal gradients of the reaction rate and its molecular diffusion transport. The statistical behaviours of the normal strain rate and the contributions arising from the normal gradients of the reaction rate and molecular diffusion rate within the flame were analysed by means of a Direct Numerical Simulation (DNS) database of statistically planar turbulent premixed flames ranging from the wrinkled/corrugated flamelets regime to the thin reaction zones regime. The interaction of flame-normal straining with the flame-normal gradient of molecular diffusion rate was found to govern the reactive scalar gradient transport in the preheat zone, where comparable timescales for turbulent straining and molecular diffusion are obtained for small values of Karlovitz numbers. However, the molecular diffusion timescale turns out to be smaller than the turbulent straining timescale for high values of Karlovitz numbers. By contrast, the reaction and hot product zones of the flame remain mostly unaffected by turbulence, and the reactive scalar gradient transport in this zone is determined by the interaction between the flame-normal gradients of molecular diffusion and chemical reaction rates.

Probabilistic Forecast of Multiphase Transport Under Viscous and Buoyancy Forces in Heterogeneous Porous Media

AbstractWe develop a probabilistic approach to map parametric uncertainty to output state uncertainty in first‐order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two‐phase transport in heterogeneous porous media in the presence of a stochastic velocity field. The uncertainty in the velocity field can arise from incomplete descriptions of either porosity field, injection flux, or both. This uncertainty leads to spatiotemporal uncertainty in the saturation field. Given information about spatial/temporal statistics of spatially correlated heterogeneity, we leverage the method of distributions to derive deterministic equations that govern the evolution of pointwise cumulative distribution functions (CDFs) of saturation for a vertical reservoir, while handling the manipulation of multiple shocks arising due to buoyancy forces. Unlike the Buckley‐Leverett equation, the equation describing the fine‐grained CDF is linear in space and time. Ensemble averaging of the fine‐grained CDF results in the CDF of saturation. Thus, we give routes to circumventing the computational cost of Monte Carlo simulations (MCS), while obtaining a pointwise description of the saturation field. We conduct a set of numerical experiments for one‐dimensional transport, and compare the obtained saturation CDFs, against those obtained using MCS as our reference solution, and the statistical moment equation method. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties, that is, standard deviation and correlation length of the underlying random fields, whereas the corresponding low‐order statistical moment equations significantly deviate from the MCS results, except for very small values of standard deviation and correlation length.

Ergodicity Breaking Under Confinement in Cold-Atom Quantum Simulators

The quantum simulation of gauge theories on synthetic quantum matter devices has gained a lot of traction in the last decade, making possible the observation of a range of exotic quantum many-body phenomena. In this work, we consider the spin-1/2 quantum link formulation of 1+1D quantum electrodynamics with a topological θ-angle, which can be used to tune a confinement-deconfinement transition. Exactly mapping this system onto a PXP model with mass and staggered magnetization terms, we show an intriguing interplay between confinement and the ergodicity-breaking paradigms of quantum many-body scarring and Hilbert-space fragmentation. We map out the rich dynamical phase diagram of this model, finding an ergodic phase at small values of the mass μ and confining potential χ, an emergent integrable phase for large μ, and a fragmented phase for large values of both parameters. We also show that the latter hosts resonances that lead to a vast array of effective models. We propose experimental probes of our findings, which can be directly accessed in current cold-atom setups.

Structural damage identification with output-only strain measurements and swarm intelligence algorithms: a comparative study

The identification of structural damage with the unavailability of input excitations is highly desired but challenging since structural dynamic responses are affected by the coupling effect of structural parameters and external excitations. To deal with this issue, in this paper, an output-only damage identification strategy based on swarm intelligence algorithms and correlation functions of strain responses is proposed to identify structures subjected to single or multiple unknown white noise excitations. In the proposed strategy, four different population-based optimization algorithms—particle swarm optimization, the butterfly optimization algorithm, the tree seed algorithm, and a micro search Jaya (MS-Jaya)—are employed and compared. The micro search mechanism is integrated into a basic Jaya algorithm to improve its computational efficiency and accuracy by eliminating some damage variables with small values for the identified best solution after several iterations. The objective function is established based on the proposed auto/cross-correlation function of strain responses and a penalty function. The effectiveness of the proposed method is verified with numerical studies on a simply supported beam structure and a steel grid benchmark structure under ambient excitation. In addition, the effect of the reference point, number of sensors, and arrangement of strain gauges on the performance of the proposed method are discussed in detail. The investigated results demonstrate that the proposed approach can accurately detect, locate, and quantify structural damage with limited sensors and 20% noise-polluted strain responses. In particular, the proposed MS-Jaya algorithm presents a more superior capacity in solving the optimization-based damage identification problem than the other three algorithms.

Research Slices

Educational Design Research (EDeR) methodologists argue that iteration is a core component of EDeR. Iteration is currently defined as a process of gathering more information through actions, such as testing, and using that information to improve the design. In this paper, we seek to tighten the definition of iteration to help EDeR teams conduct iterations more effectively. We argue that EDeR teams should organize their research in slices that deliver small but real value to end users while informing the design research. EDeR should pick slices that are: (a) minimal and focused, (b) deployed in a real context, (c) valuable to the end users, and (d) informative to the research. Slicing helps EDeR teams increase ecological validity when they test because it allows testing which is within real-world educational contexts or with the stakeholders who will use and be impacted by the design. Increasing ecological validity of testing is particularly important because EDeR projects tackle highly complex real-world problems with many unknown elements and relational complexity—this means it is challenging to predict what designs will have the desired impact without real-world deployment. Effective iteration through organizing research in slices helps EDeR teams to better support stakeholder goals, develop more impactful theory, and have greater and earlier impact upon education.

Design Method for Freeform Off-Axis Three-Mirror Anastigmat Optical Systems with a Large Field of View and Low Error Sensitivity

A freeform off-axis three-mirror anastigmat (TMA) optical system with a large field of view (FOV) can obtain target image information with a larger spatial range and more spatial details, which is a development trend within the realm of space optics. The optical aberration increases exponentially with the FOV, resulting in a significant increase in error sensitivity for large-FOV optical systems. To address this issue, a method for designing optical systems with a large FOV and low error sensitivity is proposed. The FOV is gradually expanded from a small initial value in equal-length increments until it reaches the full FOV. At each step, the error sensitivity is recalculated and controlled to a lesser extent than in the previous step. In this design process, the freeform surface is used to correct the aberration and obtain low error sensitivity. An optical system with a focal length of 1000 mm and an F-number of 10 is used as an example, and the FOV is enlarged from 5° × 1° to 20° × 4°. The design results show that the modulation transfer function (MTF) of the optical system can reach 0.45@50 lp/mm, and the average wavefront aberration is 0.029λ. After four rounds of FOV expansion and error sensitivity optimization, the error sensitivity is reduced by 37.27% compared to the initial system, which verifies the correctness and practicality of the method.

High electric‐field‐induced strain of SnO2‐modified PLSBZT ceramic for actuator applications

AbstractIn this study, piezoelectric and ferroelectric properties of the Pb0.931La0.006Sr0.03Ba0.03(Zr0.535Ti0.465)O3–xwt%SnO2 (PLSBZT–xwt%SnO2) with x = 0–0.6 were investigated comprehensively. When the content of SnO2 was 0.55 wt%, the sample achieved optimum properties obtaining a high Curie temperature (259°C) and a large strain (0.203% at 20 kV/cm). In particular, the sample's maximum strain (Smax) remained stable with a variation of less than 4% between −20 and 120°C. Moreover, the PLSBZT–0.55 wt%SnO2 ceramic not only presented a small εr value of 1662, enabling the actuator to respond quickly, but also had a high value of g33 (35.8 × 10−3 V/m/N). These results implied that SnO2‐modified PLSBZT ceramics have significant potential for actuator applications owing to their high Curie temperature, large electric‐field‐induced strain, fast response, and good strain–temperature stability.

Designing high-performance polyaniline @MoS2@AC hybrid electrode for electrochemical–based Next-generation battery-supercapacitor hybrid energy storage device and hydrogen evolution reaction

Polyaniline (PANI), a conducting polymer, has attracted the attention of researchers as a potential candidate due to its higher capacitance and outstanding electrochemical reversibility. In this research, we used the hydrothermal approach to synthesize MoS2@PANI hybrid electrode material that may overcome the low cyclic stability of PANI. The composite material MoS2/PANI (with M/P-25/75 wt%) demonstrated a specific capacity (Qs) with the amount 1087.5 C g−1 or 1812.5 F/g, much more advanced than reference samples due to the hybrid structural integrity and enhancement of the specific surface area of MoS2 and PANI interaction through electrostatic repulsion and hydrogen bonding. The asymmetric device (MoS2/PANI-25/75wt%//AC) demonstrated an extraordinary value of a Qs of 361 C g−1 over pure PANI. This novel supercapattery device showed a supreme high energy density of 65.33 Wh kg−1 and a power density of 1668.83 W/kg. Further, the hybrid electrode is used for the hydrogen evolution reactions and obtained the value of over potential is 43 mV. A small value of the Tafel slope of 39 mV/dec is observed with high stability. The improved energy storage capabilities of MoS2/PANI hybrid electrodes with multiple applications provide a new paragon to design unusual and fast multi-functional devices.

Vertex operators for imaginary [formula omitted] subalgebras of the Monster Lie algebra

The Monster Lie algebra m is a quotient of the physical space of the vertex algebra V=V♮⊗V1,1, where V♮ is the Moonshine module vertex operator algebra of Frenkel, Lepowsky, and Meurman, and V1,1 is the vertex algebra corresponding to the rank 2 even unimodular lattice II1,1. We construct vertex algebra elements that project to bases for subalgebras of m isomorphic to gl2, corresponding to each imaginary simple root, denoted (1,j) for j>0. Our method requires the existence of pairs of primary vectors in V♮ satisfying some natural conditions, which we prove. We show that the action of the Monster finite simple group M on the subspace of primary vectors in V♮ induces an M-action on the set of gl2 subalgebras corresponding to a fixed imaginary simple root. We use the generating function for dimensions of subspaces of primary vectors of V♮ to prove that this action is non-trivial for small values of j.

An elementary proof of the amplitude’s exponential decrease in damped oscillations

A damped oscillation is characterized by the diminishing amplitude of an oscillating system resulting from the dissipation of energy. A crucial example of damped oscillations involves a block of mass attached to the end of a linear spring, experiencing a damping force proportional to the object’s velocity and acting in opposition to the direction of its motion. For small values of the damping constant, the amplitude decreases exponentially over time. Typically, this behavior is introduced at the secondary education level without providing a justification. In this paper, a new approach tailored for the secondary education level is introduced to explain the aforementioned exponential decrease without relying on advanced mathematical tools. In addition, utilizing this analysis simplifies the demonstration of why the exponential decrease in amplitude is applicable only for small damping forces. It is also worth noting that the methods used to derive this result can be applied in various areas, including the derivation of the equation that connects the root mean square value of the AC sinusoidal current to its maximum value.

Small time asymptotics of the entropy of the heat kernel on a Riemannian manifold

We give an asymptotic expansion of the relative entropy between the heat kernel qZ(t,z,w) of a compact Riemannian manifold Z and the normalized Riemannian volume for small values of t and for a fixed element z∈Z. We prove that coefficients in the expansion can be expressed as universal polynomials in the components of the curvature tensor and its covariant derivatives at z, when they are expressed in terms of normal coordinates. We describe a method to compute the coefficients, and we use the method to compute the first three coefficients. The asymptotic expansion is necessary for an unsupervised machine-learning algorithm called the Diffusion Variational Autoencoder.

Modulating adhesion strength in multi-ferroic composite materials: Insights from adhesive contact with arbitrary profile indenters

Adhesion control is a critical aspect of various applications, from industrial adhesion devices to the locomotion of insects on ceilings and walls. Multi-ferroic materials, which encompass mechanical, electrical, and magnetic properties, offer approaches for reversible adhesion control. This study presents a comprehensive theoretical framework for adhesive contact in multi-ferroic composite materials when subjected to axisymmetric rigid indenters with arbitrary profiles. We analytically derive the physical fields for various contact models, including Hertz contact, Johnson–Kendall–Roberts (JKR), and Maugis–Dugdale (MD) adhesive models. The obtained energy release rates indicate that the electric and magnetic potentials can modulate adhesion strength. The Griffith energy balance relation is employed to derive the indentation forces and penetration depths, which can be extended to a range of common indenters. Notably, the classical approximations fail when using small spherical indenters, but the study provides valid alternatives. The influence of amplitude and wavelength on contact behavior is explored, with greater effects observed for larger or smaller values. For cosine-shaped indenters, equivalence to flat-ended cylindrical punches is established under specific conditions. The study also reveals that the power indices for power-law-shaped indenters change the influence of electric and magnetic potentials on pull-off forces. These findings provide a theoretical fundament associated with the biomimetic and artificial adhesive systems and the modern testing techniques.

Perseid: A Secondary Indexing Mechanism for LSM-Based Storage Systems

LSM-based storage systems are widely used for superior write performance on block devices. However, they currently fail to efficiently support secondary indexing, since a secondary index query operation usually needs to retrieve multiple small values, which scatter in multiple LSM components. In this work, we revisit secondary indexing in LSM-based storage systems with byte-addressable persistent memory (PM). Existing PM-based indexes are not directly competent for efficient secondary indexing. We propose Perseid , an efficient PM-based secondary indexing mechanism for LSM-based storage systems, which takes into account both characteristics of PM and secondary indexing. Perseid consists of (1) a specifically designed secondary index structure that achieves high-performance insertion and query, (2) a lightweight hybrid PM-DRAM and hash-based validation approach to filter out obsolete values with subtle overhead, and (3) two adapted optimizations on primary table searching issued from secondary indexes to accelerate non-index-only queries. Our evaluation shows that Perseid outperforms existing PM-based indexes by 3–7× and achieves about two orders of magnitude performance of state-of-the-art LSM-based secondary indexing techniques even if on PM instead of disks.

Wetting and Spreading Behavior of Axisymmetric Compound Droplets on Curved Solid Walls Using Conservative Phase Field Lattice Boltzmann Method.

Compound droplets have received increasing attention due to their applications in many several areas, including medicine and materials. Previous works mostly focused on compound droplets on planar surfaces and, as such, the effects of curved walls have not been studied thoroughly. In this paper, the influence of the properties of curved solid wall (including the shape, curvature, and contact angle) on the wetting behavior of compound droplets is explored. The axisymmetric lattice Boltzmann method, based on the conservative phase field formulation for ternary fluids, was used to numerically study the wetting and spreading of a compound droplet of the Janus type on various curved solid walls at large density ratios, focusing on whether the separation of compound droplets occurs. Several types of wall geometries were considered, including a planar wall, a concave wall with constant curvature, and a convex wall with fixed or variable curvature (specifically, a prolate or oblate spheroid). The effects of surface wettability, interfacial angles, and the density ratio (of droplet to ambient fluid) on the wetting process were also explored. In general, it was found that, under otherwise identical conditions, droplet separation tends to happen more likely on more hydrophilic walls, under larger interfacial angles (measured inside the droplet), and at larger density ratios. On convex walls, a larger radius of curvature of the surface near the droplet was found to be helpful to split the Janus droplet. On concave walls, as the radius of curvature increases from a small value, the possibility to observe droplet separation first increases and then decreases. Several phase diagrams on whether droplet separation occurs during the spreading process were produced for different kinds of walls to illustrate the influences of various factors.

Estimation of the Charge Mobility of Phenanthroline derivatives with the view of Density Functional Theory: Reorganization Energy and Charge Transfer Integral are in play

Molecular arrangement and noncovalent interactions in organic materials greatly influence the charge mobility in organic light-emitting diodes (OLEDs), organic photovoltaics (OPVs), and organic field-effect transistors (OFETs). In the light of the this argument, we examined the electronic properties of the phenanthroline derivatives by considering the charge mobility with the combination of density functional theory and Marcus Charge Transfer Theory. The drift electron mobility of the molecule 1 and 2 were determined to 21.13 cm2 V-1 s-1 and 18.00 cm2 V-1 s-1, respectively through J type π⋯π stacking interactions created by small perpendicular distances between the adjacent rings. The effective charge pathways of the molecules were generated with strong π⋯π stacking interactions consolidated by noncovalent interactions in their solid phases. The electron reorganization energy for both molecules were determined smaller than that of holes which means they have n-type semiconductor properties. The charge transfer integrals were calculated with the optimization of molecules’ dimer configurations that the theoretical results demonstrate the charge transfer integral depends on the distance between the stacking rings. High charge transfer integral and small reorganization energy give the high charge mobility fort he semiconductor molecules. Beside the mobility, energy band gap, ionization potential, electron and hole injection barriers of the molecules were interpreted to further understand their electronic properties. Due to the small LUMO values which provide n-type molecule and small electron injection barrier. From the our work both molecules can be effective n type organic semiconductor devices with the high mobility and can be modified for more efficient charge transport in phenanthroline derivatives.

Assessment of Interaural Attenuation in Infants and Young Children Using Bone-Conducted Auditory Brainstem Response.

In hearing assessment, the term interaural attenuation (IAA) is used to quantify the reduction in test signal intensity as it crosses from the side of the test ear to the nontest ear. In the auditory brainstem response (ABR) testing of infants and young children, the size of the IAA of bone-conducted (BC) stimuli is essential for the appropriate use of masking, which is needed for the accurate measurement of BC ABR thresholds. This study aimed to assess the IAA for BC ABR testing using 0.5 to 4 kHz narrowband (NB) CE-chirp LS stimuli in infants and toddlers with normal hearing from birth to three years of age and to examine the effects of age and frequency on IAA. A total of 55 infants and toddlers with normal hearing participated in the study. They were categorized into three age groups: the young group (n = 31, infants from birth to 3 mo), middle-aged group (n = 13, infants aged 3-12 mo), and older group (n = 11, toddlers aged 12-36 mo). The participants underwent BC ABR threshold measurements for NB CE-chirp LS stimuli at 0.5 to 4 kHz. For each participant, one ear was randomly defined as the "test ear" and the other as the "nontest ear." BC ABR thresholds were measured under two conditions. In both conditions, traces were recorded from the channel ipsilateral to the test ear, whereas masking was delivered to the nontest ear. In condition A, the bone oscillator was placed on the mastoid of the test ear, whereas in condition B, the bone oscillator was placed on the mastoid contralateral to the test ear. The difference between the thresholds obtained under conditions A and B was calculated to assess IAA. The means of IAA (and range) in the young age group for the frequencies 0.5, 1, 2, and 4 kHz were 5.38 (0-15) dB, 11.67 (0-30) dB, 21.15 (10-40) dB, and 23.53 (15-35) dB, respectively. Significant effects were observed for both age and frequency on BC IAA. BC IAA levels decreased with age from birth to 36 mo. In all age groups, smaller values were observed at lower frequencies and increased values were observed at higher frequencies. BC IAA levels were both age and frequency dependent. The study found that the BC IAA values for lower stimulus frequencies were smaller than previously assumed, even in infants younger than 3 mo. These results suggest that masking should be applied in BC ABR threshold assessments for NB CE-chirp LS stimuli at 0.5, 1, and 2 kHz, even in young infants. Masking may not be necessary for testing at 4 kHz if a clear response is obtained at 15 dB normal-hearing level (nHL) in infants younger than 3 mo.

Relative variation between γ coordinate and the potential of the Bohr Hamiltonian producing X(4) from Z(4)

In this paper, four degree of freedom γ-rigid solutions of the Bohr Hamiltonian at γ 0 = π/6 are obtained. The relative variation between γ and the potential of the Hamiltonian is employed to retrieve X(4) from Z(4). γ is varied in the interval 0 ≤ γ 0 ≤ π/6 while the potential minimum, β 0, is varied in the interval 0 ≤ β 0 ≤ ∞ . Very small value of β 0 yields Z(4) while a large value of β 0 produces X(4) and SU(3) is realized at β 0 ≈ ∞ . The solutions at γ 0 = 0 correspond to X(4) while the solutions at γ 0 = π/6 yield Z(4): a dynamic link between Z(4) and X(4) critical point symmetries (CPSs) has been provided. The fact that γ and β 0 of the potential play the same role in the dynamical link between Z(4) and X(4) shows that β 0 also measures the departure from axial symmetry to other shapes as γ does. In the experimental realization of the model, the conformation of 192Pt and 194Pt isotopes to the present Z(4) model shows that the present model can be employed in the description of triaxial rotors and γ-soft isotopes. 194Pt is shown to be the best choice for triaxial rigid rotor candidacy. 130Xe, a critical point isotope, which belongs to the class of γ-soft nuclei, reproduces this present model very well in all the states. Consequently, this present model can serve as a critical point model. 40,0 − β 0 distribution for Z(4) and X(4) candidate isotopes shows a significant interval between the two models where the T(4) CPS lies.

Recent advances in all-optical half-subtractor and full-subtractor based on photonic crystal platforms

Abstract A half-subtractor is a digital circuit that subtracts two inputs and displays the result in two outputs. Photonic crystals (PhCs) are used in optical circuits, including encoders, multiplexers, adders, subtractors, timers, counters, etc. This paper reviews and compares some of the all-optical half-subtractors and full-subtractors based on PhCs reported to date. We study physical parameters, including the arrangement of dielectric rods, rod radius, lattice constant, structure area, background material, and resonator type and illustrate the structure with a small size is suitable for integration in a photonic chip. Another crucial factor is the optical power difference between the two logic states of 0 and 1. A large difference between these two values increases the contrast ratio and reduces the detection error in the output. Delay time as a key parameter specifies that the input signal will leave the desired output after a few femtoseconds. Linear structures have the lowest delay time, fall time, and rise time among compared structures. But on the other hand, non-linear structures have the highest amount of contrast ratio. In the recent papers, relatively favorable delay times are obtained, equal to 0.06, 0.1, and 0.85 ps, respectively. Also, the fall times are a small value and are equal to 0.05, 0.1, and 0.25 ps, respectively, and the rise times are equal to 0.1, 0.5, and 0.7 ps, respectively. Also, the contrast ratio values are high and acceptable which are equal to 25.88, 18.80, and 18.40, respectively.