Matter Model Research Articles

Revisiting Relativistic Electrically Charged Polytropic Spheres

AbstractThe problem of the structure and physical properties of electrically charged static spherically symmetric solutions of the Einstein‐Maxwell system of equations is revisited, where the matter model is a polytropic gas. A relativistic polytrope equation of state (EOS) is considered and the electric charge density is assumed to be proportional to the rest mass density. Families of solutions corresponding to various sets of parameters are constructed and analyzed their stability and compliance with the causality requirement, emphasizing the possibility of obtaining black hole mimickers. Concretely, this study wants to test how much electric charge a given object can hold and how compact it can be. It is concluded that there is a microscopic bound on the charge density to rest mass density ratio coincident with the macroscopic bound regarding the extremal Reissner‐Nordström (ERN) black hole. The macroscopic charge to mass ratio for the object can exceed the corresponding microscopic ratio if the object is non‐extremal. Crucially, the only way to construct a black hole mimicker is by taking a subtle limit in which an electrically counterpoised dust (ECD) solution is attained.

Completeness of atomic structure representations

In this paper, we address the challenge of obtaining a comprehensive and symmetric representation of point particle groups, such as atoms in a molecule, which is crucial in physics and theoretical chemistry. The problem has become even more important with the widespread adoption of machine-learning techniques in science, as it underpins the capacity of models to accurately reproduce physical relationships while being consistent with fundamental symmetries and conservation laws. However, some of the descriptors that are commonly used to represent point clouds— notably those based on discretized correlations of the neighbor density that power most of the existing ML models of matter at the atomic scale—are unable to distinguish between special arrangements of particles in three dimensions. This makes it impossible to machine learn their properties. Atom-density correlations are provably complete in the limit in which they simultaneously describe the mutual relationship between all atoms, which is impractical. We present a novel approach to construct descriptors of finite correlations based on the relative arrangement of particle triplets, which can be employed to create symmetry-adapted models with universal approximation capabilities, and have the resolution of the neighbor discretization as the sole convergence parameter. Our strategy is demonstrated on a class of atomic arrangements that are specifically built to defy a broad class of conventional symmetric descriptors, showing its potential for addressing their limitations.

Emergence of the Gambier equation in cosmology

In this paper, we show how the Gambier equation arises in connection to Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology and a Dark Matter equation of state. Moreover, we provide a correspondence between the Friedmann equations and the Gambier equations that possess the Painlevé property in (2 + 1) dimensions. We also consider special cases of the Gambier G27 equation such as the generalized Pinney equation. For an extended FLRW model with dynamic scalar field as matter model, the Einstein equations correspond to the Milne–Pinney equation which in turn can be mapped to the parametric Gambier equation of second order.

The fabrication and growth mechanism of AlCrFeCoNiCu0.5 HEA thin films by substrate-biased cathodic arc deposition

AlCrFeCoNiCu0.5 thin films were fabricated by cathodic arc deposition under different substrate biases. Detailed characterization of the chemistry and structure of the film, from the substrate interface to the film surface, was achieved by combining high-resolution transmission electron microscopy, X-ray photoelectron spectroscopy, and atomic force microscopy. Computer simulations using the transport of ions in matter model were applied to understand the ion surface interactions that revealed the key mechanism of the film growth. The final compositions of the films are significantly different from that of the target used. A trend of elemental segregation, which was more pronounced with higher ion kinetic energy, was observed. The XPS results reveal the formation of {mathrm{Al}}_{2}{mathrm{O}}_{3} and {mathrm{Cr}}_{2}{mathrm{O}}_{3} on the thin film surface. The grain size is shown to increase with the increasing of the ion kinetic energy. The growth of equiaxed grains contributed to the formation of a flat surface with a relatively low surface roughness as shown by atomic force microscopy.

Nanoscale subsurface dynamics of solids upon high-intensity femtosecond laser irradiation observed by grazing-incidence x-ray scattering

Observing ultrafast laser-induced structural changes in nanoscale systems is essential for understanding the dynamics of intense light-matter interactions. For laser intensities on the order of 1014W/cm2, highly collisional plasmas are generated at and below the surface. Subsequent transport processes such as heat conduction, electron-ion thermalization, surface ablation, and resolidification occur at picosecond and nanosecond timescales. Imaging methods, e.g., using x-ray free-electron lasers (XFEL), were hitherto unable to measure the depth-resolved subsurface dynamics of laser-solid interactions with appropriate temporal and spatial resolution. Here we demonstrate picosecond grazing-incidence small-angle x-ray scattering (GISAXS) from laser-produced plasmas using XFEL pulses. Using multilayer (ML) samples, both the surface ablation and subsurface density dynamics are measured with nanometer depth resolution. Our experimental data challenges the state-of-the-art modeling of matter under extreme conditions and opens new perspectives for laser material processing and high-energy density science.Received 11 December 2021Accepted 23 May 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.033038Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasHigh intensity laser-plasma interactionsHigh-energy-density plasmasPhysical SystemsPlasma sheaths & surfacesStrongly-coupled plasmasWarm-dense matterTechniquesHydrodynamicsLaser ablationParticle-in-cell methodsX-ray reflectivityX-ray scatteringPlasma PhysicsCondensed Matter, Materials & Applied Physics

Hyperspectral Modeling of Soil Organic Matter Based on Characteristic Wavelength in East China

Soil organic matter (SOM) is a key index of soil fertility. Visible and near-infrared (VNIR, 350–2500 nm) reflectance spectroscopy is an effective method for modeling SOM content. Characteristic wavelength screening and spectral transformation may improve the performance of SOM prediction. This study aimed to explore the optimal combination of characteristic wavelength selection and spectral transformation for hyperspectral modeling of SOM. A total of 219 topsoil (0–20 cm) samples were collected from two soil types in the East China. VNIR reflectance spectra were measured in the laboratory. Firstly, after spectral transformation (inverse-log reflectance (LR), continuum removal (CR) and first-order derivative reflectance (FDR)) of VNIR spectra, characteristic wavelengths were selected by competitive adaptive reweighted sampling (CARS) and uninformative variables elimination (UVE) algorithms. Secondly, the SOM prediction models were constructed based on the partial least squares regression (PLSR), random forest (RF) and support vector regression (SVR) methods using the full spectra and selected wavelengths, respectively. Finally, optimal SOM prediction models were selected for two soil types. The results were as follows: (1) The CARS algorithm screened 40–125 characteristic wavelengths from the full spectra. The UVE algorithm screened 105–884 characteristic wavelengths. (2) For two soil types and full spectra, CARS and UVE improved the SOM modeling precision based on the PLSR and SVR methods. The coefficient of determination (R2) value in the validation of the CARS-PLSR (PLSR model combined with CARS) and CARS-SVR (SVR model combined CARS) models ranged from 0.69 to 0.95, and the relative percent deviation (RPD) value ranged from 1.74 to 4.31. Lin’s concordance correlation coefficient (LCCC) values ranged from 0.83 to 0.97. The UVE-PLSR and UVE-SVR models showed moderate precision. (3) The PLSR and SVR modeling accuracies of Paddy soil were better than those for Shajiang black soil. RF models performed worse for both soil types, with the R2 values of validation ranging from 0.22 to 0.68 and RPD values ranging from 1.01 to 1.60. (4) For Paddy soil, the optimal SOM prediction models (highest R2 and RPD, lowest root mean square error (RMSE)) were CR-CARS-PLSR (R2 and RMSE: 0.97 and 1.21 g/kg in calibration sets, 0.95 and 1.72 g/kg in validation sets, RPD: 4.31) and CR-CARS-SVR (R2 and RMSE: 0.98 and 1.04 g/kg in calibration sets, 0.91 and 2.24 g/kg in validation sets, RPD: 3.37). For Shajiang black soil, the optimal SOM prediction models were LR-CARS-PLSR (R2 and RMSE: 0.95 and 0.93 g/kg in calibration sets, 0.86 and 1.44 g/kg in validation sets, RPD: 2.62) and FDR-CARS-SVR (R2 and RMSE: 0.99 and 0.45 g/kg in calibration sets, 0.83 and 1.58 g/kg in validation sets, RPD: 2.38). The results suggested that the CARS algorithm combined CR and FDR can significantly improve the modeling accuracy of SOM content.

Spatial distribution of soil nutrients and evaluation of cultivated land in Xuwen county.

It is of great significance to promote the quantitative research of soil science and the implementation of precision agriculture. On this basis, taking Xuwen County as the research object, this paper comprehensively analyzed the soil characteristics of cultivated land in Xuwen County and clarify the soil nutrient content and spatial distribution characteristics of cultivated land in Xuwen County, this paper comprehensively applied the methods of geostatistics, geographic information system (GIS) and fuzzy mathematics, and referred to the cultivated land quality grade standard (GB/T 33469-2016), to analyze the soil characteristics and evaluate the soil fertility of this region. The results show that the optimal interpolation model of soil pH and available phosphorus (AP) is a Gaussian model, and the optimal interpolation model of soil organic matter (SOM), available nitrogen (AN) and available potassium (AK) is a J-Bessel model. In addition, the spatial correlation of AK is weak, whereas pH, SOM, AN and AP show moderate spatial correlation. The proportion of excellent, good, average, medium and poor comprehensive fertility index are 26.00%, 32.67%, 19.33%, 19.00% and 3.00%, respectively. The overall level of soil fertility in Xuwen County is above the average, and the fertility quality presents an obvious trend of high in the South and low in the North. Areas that above average fertility are mainly distributed in Maichen Town, Qujie Town, Nanshan Town and Chengbei Town. The results can provide theoretical basis for improving the utilization rate of chemical fertilizer, fine management of cultivated land and ecological environment in this region, which can help in decision-making of precision fertilization.

Fault detection of overhead contact systems based on multi-view Faster R-CNN

Overhead contact systems are important power supply equipments for electrified railway locomotives. If there are faults in the equipment, it will threaten the safety of train operation. Dropper faults and foreign matter are two common types of Overhead contact systems faults, the fault regions of which occupy a relatively small area in the whole image, so it is difficult to detect the faults accurately by capturing detailed features using original Faster R-CNN. To solve the above problem, an improved Faster R-CNN based on convolutional neural networks, named multi-view Faster R-CNN, is proposed in order to extract more details of the fault regions by combining deep and shallow feature maps. Experiments on the images collected from the Lanzhou-Xinjiang Railway line show that the feature fusion can significantly enhance the mean average precision. The precision of our model on the test set was 89.53%, increasing by 3.5%, 9.65%, and 5.8% compared with YOLOv3, SSD, and Faster R-CNN, and the detection accuracies of our model for unforced droppers and foreign matter were 88.17% and 90.60%, respectively, under a recall rate of almost 1.0. Because the multi-view feature fusion model in our method can flexibly detect faults with various sizes, it has an important application value in the fault detection of an overhead contact system.

A BP Neural Network Algorithm for Multimedia Data Monitoring of Air Particulate Matter.

In order to study a BP neural network algorithm for air particulate matter data monitoring, firstly, the monitoring data collected by particle sensor using the light scattering method are proposed. Then, based on the improved BP neural network method, the mapping relationship between the actual measured value of the sensor, weather and other influencing factors, and the standard value of the monitoring station is established, and the calibration model of air particulate matter is realized. Finally, through theoretical analysis and experimental comparison, the results show that the model based on BP neural network algorithm has good accuracy and generalization ability in the evaluation of air particulate index, which makes it possible to scientifically and accurately refine the evaluation and management of urban air particulate index. The experimental results show that the air particle calibration model based on the light scattering method and improved BP neural network algorithm is practical and effective.

Measuring the stability of fundamental constants with a network of clocks

The detection of variations of fundamental constants of the Standard Model would provide us with compelling evidence of new physics, and could lift the veil on the nature of dark matter and dark energy. In this work, we discuss how a network of atomic and molecular clocks can be used to look for such variations with unprecedented sensitivity over a wide range of time scales. This is precisely the goal of the recently launched QSNET project: A network of clocks for measuring the stability of fundamental constants. QSNET will include state-of-the-art atomic clocks, but will also develop next-generation molecular and highly charged ion clocks with enhanced sensitivity to variations of fundamental constants. We describe the technological and scientific aims of QSNET and evaluate its expected performance. We show that in the range of parameters probed by QSNET, either we will discover new physics, or we will impose new constraints on violations of fundamental symmetries and a range of theories beyond the Standard Model, including dark matter and dark energy models.

Metrics on End-Periodic Manifolds as Models for Dark Matter

In this paper we will detail an approach to generate metrics and matter models on end-periodic manifolds, which are used extensively in the study of the exotic smooth structures of R4. After an overview of the technique, we will present two specific examples, discuss the associated matter models by solving the Einstein equations, and determine the physical viability by examining the energy conditions. We compare the resulting model directly with existing models of matter distributions in extragalactic systems, to highlight the viability of utilizing exotic smooth structures to understand the existence and distribution of dark matter.

Scotogenic neutrino masses with gauged matter parity and gauge coupling unification

Building up on previous work we propose a Dark Matter (DM) model with gauged matter parity and dynamical gauge coupling unification, driven by the same physics responsible for scotogenic neutrino mass generation. Our construction is based on the extended gauge group SU(3)c ⊗ SU(3)L ⊗ U(1)X ⊗ U(1)N, whose spontaneous breaking leaves a residual conserved matter parity, MP, stabilizing the DM particle candidates of the model. The key role is played by Majorana SU(3)L-octet leptons, allowing the successful gauge coupling unification and a one-loop scotogenic neutrino mass generation. Theoretical consistency allows for a plethora of new particles at the ≲ mathcal{O} (10) TeV scale, hence accessible to future collider and low-energy experiments.

Disentangling land model uncertainty via Matrix-based Ensemble Model Inter-comparison Platform (MEMIP)

BackgroundLarge uncertainty in modeling land carbon (C) uptake heavily impedes the accurate prediction of the global C budget. Identifying the uncertainty sources among models is crucial for model improvement yet has been difficult due to multiple feedbacks within Earth System Models (ESMs). Here we present a Matrix-based Ensemble Model Inter-comparison Platform (MEMIP) under a unified model traceability framework to evaluate multiple soil organic carbon (SOC) models. Using the MEMIP, we analyzed how the vertically resolved soil biogeochemistry structure influences SOC prediction in two soil organic matter (SOM) models. By comparing the model outputs from the C-only and CN modes, the SOC differences contributed by individual processes and N feedback between vegetation and soil were explicitly disentangled.ResultsResults showed that the multi-layer models with a vertically resolved structure predicted significantly higher SOC than the single layer models over the historical simulation (1900–2000). The SOC difference between the multi-layer models was remarkably higher than between the single-layer models. Traceability analysis indicated that over 80% of the SOC increase in the multi-layer models was contributed by the incorporation of depth-related processes, while SOC differences were similarly contributed by the processes and N feedback between models with the same soil depth representation.ConclusionsThe output suggested that feedback is a non-negligible contributor to the inter-model difference of SOC prediction, especially between models with similar process representation. Further analysis with TRENDY v7 and more extensive MEMIP outputs illustrated the potential important role of multi-layer structure to enlarge the current ensemble spread and the necessity of more detail model decomposition to fully disentangle inter-model differences. We stressed the importance of analyzing ensemble outputs from the fundamental model structures, and holding a holistic view in understanding the ensemble uncertainty.

Elementary Preservice Teachers’ Perceptions of Assessment Tasks that Measure Content Knowledge for Teaching about Matter

ABSTRACT Developing knowledge about science instruction is critical for preservice teachers. This study explores how 79 elementary preservice teachers perceive the relevance and importance of assessment task scenarios designed to elicit information about content knowledge for teaching (CKT) about matter and its interactions—a foundational topic for teaching physical science. Participants completed practice-based assessment tasks that described teaching scenarios about elementary science teaching and that addressed five matter topics: properties of matter, changes in matter, the model of matter, materials, and conservation of matter. We aimed to explore how relevant preservice teachers felt these task scenarios were to their teaching experience and how important knowing how to answer these tasks was for the work of elementary teachers. Findings suggest that preservice teachers tended to recognize the centrality of these task scenarios for the work typically done in elementary classrooms, even if they do not report having firsthand experience with the content and practices represented in the scenarios. Moreover, participants tended to provide a general rationale about why these scenarios were important for the work of teaching science, but a limited number of responses made explicit connections between a task scenario and the specific instructional practice related to elementary teachers’ work. This study poses implications for the use of CKT tasks in elementary education programs.

Constraining ultra light dark matter with the Galactic nuclear star cluster

ABSTRACT We use the Milky Way’s nuclear star cluster (NSC) to test the existence of a dark matter ‘soliton core’, as predicted in ultra-light dark matter (ULDM) models. Since the soliton core size is proportional to $m_{\rm DM}^{-1}$, while the core density grows as $m_{\rm DM}^{2}$, the NSC (dominant stellar component within ∼3 pc) is sensitive to a specific window in the dark matter particle mass, mDM. We apply a spherical isotropic Jeans model to fit the NSC line-of-sight velocity dispersion data, assuming priors on the precisely measured Milky Way’s supermassive black hole (SMBH) mass and the well-measured NSC density profile. We find that the current observational data reject the existence of a soliton core for a single ULDM particle with mass in the range 10−20.4 eV ≲ mDM ≲ 10−18.5 eV, assuming that the soliton core structure is not affected by the Milky Way’s SMBH. We test our methodology on mock data, confirming that we are sensitive to the same range in ULDM mass as for the real data. Dynamical modelling of a larger region of the Galactic centre, including the nuclear stellar disc, promises tighter constraints over a broader range of mDM. We will consider this in future work.

Essentials of a Theory for How Brain Structure Contributes to the Substance of Consciousness

Neuroscience and physics have progressed far enough that the explanatory gap between models of matter and the substance of perceptual experience is tantalizingly close to being bridged, at least insofar as consciousness is produced by the brain. This paper aims to describe the basics of how signals are transmitted within neurons via electromagnetic energy fluctuations, how EM fields emergent from these energy flows manifest as the subconscious and an experience of willed agency, as well as how the quantum principles which both EM radiation and atomic structure abide combine them to form percepts from electromagnetic matter. This might be the most promising option yet for fashioning a physical paradigm that theorizes consciousness.

ГРАВИТАЦИЯ: теоретическая модель

A theoretical model of the formation of gravity and such dialectical categories as time, speed of light and intranuclear superdense matter, directly related to it, are presented. Categories are forms of knowledge reflection about the universal laws of the objective world, its unity, interaction and development of its components. Gravity is the main creative derivative of the potential energy of the Universe. This is a product of the process of interference of quantum wave fluctuations of potential energy and coherent wave oscillations of the quark-gluon energy mechanism of atomic nuclei. The consequence of the most complex microwave interaction between the potential energy consumed by nuclei and the internal energy of atomic nuclei are ultrashort waves, representing electromagnetic γ-radiation (γ-quantum, photon, corpuscle). In areas of increased concentration of wave energy, when the anomalous threshold oscillation frequency of 734 Hz is reached, the interaction of locally manifested wave processes of quantum fluctuation and interference can form elementary particles with a dense mass, increased energy charge and other characteristics characteristic of baryonic matter. The frequency of 734 Hz, indistinguishable by man, corresponds to the time interval of 0.00136 seconds and the supposed boundary of the pulsating material Universe. Electromagnetic and gravitational radiations are actively formed on it, entropy and products of other energy processes corresponding to the bifurcation boundary of evolution decrease or increase. The relevance of the research lies in the expediency of systematics, structuring, systematization of fundamental knowledge about matter, its "origins" to clarify the methodological principles and the significance of the "original" energy evolution in natural science. The object of the research is gravity - one of the most important methodological categories in the form of fundamental time. The subject of the research is the fundamental properties of gravity, which ensure the existence and evolution of the matter of the Metagalaxy. The purpose of the research is virtual forms of the existence and evolution of gravity, and the main task to be solved is to clarify the significance of the wave quantum fluctuation of energy. The methodological tool for solving the problem is the numerous fundamental structural levels of the organization of the matter of the Universe, indicating its polygenic energy essence and evolutionary nature. The concept of a system of scientifically based, interconnected and logically linked scientific views based on many years of experience in small-medium-scale predictive studies in the oldest mining region of Russia - Eastern Transbaikalia. Encyclopedic natural-science knowledge of the matter of the Universe, fundamental hierarchical structures of its matter, cause-and-effect relationships of the functioning of energy systems, theoretical and practical models of the Earth's matter, as well as knowledge of the objective perception of the world, its laws and phenomena by collecting, computer processing of empirical data to solve the problem are used. . It is taken into account that dialectical materialism beyond the "visibility" (length) of light (optical) and electron waves is gradually being replaced by theoretical (philosophical) materialism based on the laws of logic and fractal. Gravity combines space and time into a single energy category called the Universe

ПОТЕНЦИАЛЬНАЯ ЭНЕРГИЯ - КАТЕГОРИЯ ПРОСТРАНСТВА

A theoretical model of potential energy is presented as a world space filled with “dormant” energy waves of low oscillation frequency, diverse in configuration. It has been established that the interaction of locally manifested wave processes of quantum fluctuations, interference and diffraction in areas of increased energy concentration upon reaching the anomalous threshold oscillation frequency of 734 Hz forms elementary particles with a denser mass, increased energy charge and other characteristics characteristic of baryonic matter. The relevance of the research is observed in the expediency of systematics, structuring fundamental knowledge about matter, its “sources” to clarify the methodological principles and the significance of the evolution of “original” energy in natural science. The object of the research is potential energy, which is one of the most important methodological categories in the form of space. The subject of the research is the fundamental properties of potential energy, which ensure the existence and evolution of the matter of the Metagalaxy. The purpose of the study is virtual forms of the existence and evolution of energy, and the main task to be solved is to clarify the significance of the wave quantum fluctuation of energy. The methodological tool for solving the problem is the numerous fundamental structural levels of the organization of the matter of the Universe, indicating its polygenic energy essence and evolutionary nature. The concept of a system of scientifically based, interconnected and logically linked scientific views based on many years of experience in small-medium-scale predictive studies in the oldest mining region of Russia - Eastern Transbaikalia. Encyclopedic natural-science knowledge of the matter of the Universe, fundamental hierarchical structures of its matter, cause-and-effect relationships of the functioning of energy systems, theoretical and practical models of the Earth's matter, as well as knowledge of the objective perception of the world, its laws and phenomena by collecting, computer processing of empirical data to solve the problem are used. . It is taken into account that dialectical materialism beyond the “visibility” (length) of light (optical) and electron waves is gradually being replaced by theoretical (philosophical) materialism based on the laws of logic and fractal. Physically invisible all-penetrating potential energy is consumed by all material particles, all inorganic and organic bodies, without this “spatially nourishing” energy, physical existence is excluded.

Vector dark matter production from catalyzed annihilation

We provide a simple model of vector dark matter (DM) which can realize the recently proposed freeze-out mechanism with catalyzed annihilation. In our setup, a vector DM field Xμ and a catalyst field Cμ is unified by an SU(2)D gauge symmetry. These gauge fields acquire their masses via spontaneously symmetry breaking triggered by a doublet and a real triplet scalar fields. The catalyst particle is automatically lighter than the DM since it only acquires mass from the vacuum expectation value of the doublet scalar. We also introduce a dimension-5 operator to generate a kinetic mixing term between Cμ and the U(1)Y gauge field Bμ. This mixing term is naturally small due to a suppression with a high UV completion scale, and thus it allows the catalyst to decay after the DM freeze-out. We derive the annihilation cross sections of processes X* + X → 2C and 3C → X* + X and solve the Boltzmann equations for both the DM and the catalyst. We develop the analytical approximate solutions of the equations and find them matching the numerical solutions well. Constraints from relic abundance and indirect detection of DM are considered. We find that the DM with a mass mX ≳ 4.5 TeV survives in the case of a long-living catalyst. On the other hand, if the catalyst decays during the catalyzed annihilation era, then the bound can be released. We also discuss two paradigms which can maintain the kinetic equilibrium of DM until the DM freeze-out. In both cases, the freeze-out temperature of DM is an order of magnitude higher than the original model.

Cancellation mechanism of dark matter direct detection in Higgs-portal and vector-portal models

We present two alternative proofs for the cancellation mechanism in the U(1) symmetric pseudo-Nambu-Goldstone-Boson Dark Matter (pNGB DM) model. They help us to have a better understanding of the mechanism from multi-angle, and inspire us to propose some interesting generalizations. In the first proof, we revisit the non-linear representation method and rephrase the argument with the interaction eigenstates. In this picture, the phase mode (DM) can only have a trilinear interaction with a derivative-squared acting on the radial mode when the DM is on-shell. Thus, the DM-quark scattering generated by a mass mixing between the radial mode and the Higgs boson vanishes in the limit of zero-momentum transfer. Using the same method, we can easily generalize the model to an SO(N) model with general soft-breaking structures. In particular, we study the soft-breaking cubic terms and identify those terms which preserve the cancellation mechanism for the DM candidate. In our discussion of the second method, we find that the cancellation relies on the special structure of mass terms and interactions of the mediators. This condition can be straightforwardly generalized to the vector-portal models. We provide two examples of the vector-portal case where the first one is an SU(2)L × U(1)Y × U(1)X model and the second one is an SU(2)L × U(1)Y × U(1)B−L × U(1)X model. In the first model the vector mediators are the Zμ boson and a new U(1)X gauge boson Xν, while in the second model the mediators are the U(1)B−L and U(1)X gauge bosons. The cancellation mechanism works in both models when there are no generic kinetic mixing terms for the gauge bosons. Once the generic kinetic mixing terms are included, the first model requires a fine-tuning of the mixing parameter to avoid the stringent direct detection bound, while the second model can naturally circumvent it.