Dimensional Domain Research Articles

Uniqueness of global weak solutions for the general Ericksen–Leslie system with Ginzburg–Landau penalization in {mathbb {T}}^2

The Ericksen–Leslie system is a fundamental hydrodynamic model that describes the evolution of incompressible liquid crystal flows of nematic type. In this paper, we prove the uniqueness of global weak solutions to the general Ericksen–Leslie system with a Ginzburg–Landau type approximation in a two dimensional periodic domain. The proof is based on some delicate energy estimates for the difference of two weak solutions within a suitable functional framework that is less regular than the usual one at the natural energy level, combined with the Osgood lemma involving a specific double-logarithmic type modulus of continuity. We overcome the essential mathematical difficulties arising from those highly nonlinear terms in the Leslie stress tensor and in particular, the lack of maximum principle for the director equation due to the stretching effect of the fluid on the director field. Our argument makes full use of the coupling structure as well as the dissipative nature of the system, and relies on some techniques from harmonic analysis and paradifferential calculus in the periodic setting.

Sharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution

Finite difference method as a popular numerical method has been widely used to solve fractional diffusion equations. In the general spatial error analyses, an assumption $$u\in C^{4}({\bar{\varOmega }})$$ is needed to preserve $${\mathcal {O}}(h^{2})$$ convergence when using central finite difference scheme to solve fractional sub-diffusion equation with Laplace operator, but this assumption is somewhat strong, where u is the exact solution and h is the mesh size. In this paper, a novel analysis technique is proposed to show that the spatial convergence rate can reach $${\mathcal {O}}(h^{\min (\sigma +\frac{1}{2}-\epsilon ,2)})$$ in both $$l^{2}$$ -norm and $$l^{\infty }$$ -norm in one-dimensional domain when the initial value and source term are both in $${\dot{H}}^{\sigma }(\varOmega )$$ but without any regularity assumption on the exact solution, where $$\sigma \ge 0$$ and $$\epsilon >0$$ being arbitrarily small. After making slight modifications on the scheme, acting on the initial value and source term, the spatial convergence rate can be improved to $${\mathcal {O}}(h^{2})$$ in $$l^{2}$$ -norm and $${\mathcal {O}}(h^{\min (\sigma +\frac{3}{2}-\epsilon ,2)})$$ in $$l^{\infty }$$ -norm. It is worth mentioning that our spatial error analysis is applicable to high dimensional cube domain by using the properties of tensor product. Moreover, two kinds of averaged schemes are provided to approximate the Riemann–Liouville fractional derivative, and $${\mathcal {O}}(\tau ^{2})$$ convergence is obtained for all $$\alpha \in (0,1)$$ . Finally, some numerical experiments verify the effectiveness of the built theory.

Energy storage analysis during melting in presence of metallic fins via numerical method

The performance of the storage unit during the discharging process can be improved with installing extended surfaces and this study aims to show the effect of two arrangements of fins on solidification. The same area of I and V shaped fins indicates that the volume of paraffin will not change with altering the configuration of the system. Unsteady terms were applied via implicit technique and two dimensional domains were simulated via FVM to show the behavior of the system during discharging. The conductivity of utilized paraffin (RT28) has been improved by loading nanoparticles of CuO. Since the fraction of additives is low, it is logical to use homogeneous model formulation to derive the properties of NEPCM. The both cases were compared and outputs showed that the required time for case 1 is 8.93 % lower than that of case 2. With involving I and V shaped fins, the required time of freezing will be 47.26 min and 51.89 min, respectively.

Seasonal dynamics of shoots growth in <i>Forsythia ovata</i> Nakai plants: Rhythmicity of apical and radial growth

The aim of the study was to establish the type (linear or non-linear) and shape (presence of extremes and trends) of the time dependences of apical and radial growth rates for shoots of two types (branching and formation) in woody plants. The object of the study was an introduced in the Middle Urals ornamental early-flowering shrub species Forsythia ovata Nakai. Seasonal dynamics of morphometric parameters of two types of shoots, which differ in intensity of growth and origin (developing from the apical or dormant buds of the skeletal branch respectively), was examined. Also, there was made an assessment of their relationship with air temperature and precipitation values. Apical and radial growth are accompanied by oscillations of increments. The duration of individual phases of oscillations is about 7 or more days, which makes it possible to attribute this phenomenon to infradian growth rhythms. The weak relationship between the characteristics of the observed oscillations and weather conditions indicates the predominantly endogenous nature of the observed morphogenetic processes. The growth of formation shoots begins 4 weeks later than branching shoots. This delay is apparently related to the time necessary for activation of dormant bud growth. Seasonal dynamics curves of rates and accelerations of the apical and radial shoot’s growth have the shape of previously unobserved oscillations with phases fading in amplitude and changing in duration. The growth ends 1–2 months before the environmental conditions become unfavorable. The oscillations of the growth rate of shoots are apparently associated with the action of two or more differently directed factors, which determine the increase in volume of different segments of the shoot. These factors include the different contribution of cell division and elongation to the change in the geometric dimensions of the apical meristem domains. The main differences in the seasonal dynamics of the apical and radial increments for both types of shoots are: the duration of growth (6–8 and 4 weeks, respectively), the number of extremes, the amplitude and the duration of individual phases of oscillations. Higher amplitudes of the growth rate oscillations in shoots formation compared with branching shoots, cause bigger values of the formation shoots total increments. The dynamic curves of the apical growth rates have two maxima, while those of the radial growth have only one. Each type of growth, despite the delay in the onset of the formation shoots, has the same total duration. The shapes of curves of seasonal changes in speeds and accelerations of shoot growth values are also similar for different types of shoots. These similarities indicate that shoots have the same “programs” of growth regulation, ultimately determined by the genotype. The rhythmic growth of both types of shoots during the season suggests the existence of the relationship in time between the rates of division and growth of cells located in functionally different groups of cells in the apical meristem zone.

Analysis of the Influence of Grid-Connected Photovoltaic Power Stations with Virtual Inertia on Low-Frequency Oscillation of Power System Based on Small Signal and Prony Analysis Methods

With the virtual synchronous generator (VSG) technology gradually becoming an emerging technology for new energy consumption, its introduction has solved the problems of weak support and weak anti-interference of traditional new energy stations. However, the practice shows that the grid-connected characteristics of VSG limit its large-scale utilization, and there is little research on the interaction between VSG and a multi-machine system. In this paper, small signal models and time domain simulation models of each link of a photovoltaic(PV) power station with the PV virtual synchronous generator (PV-VSG) are first conducted, and then the influence of the grid-connected PV power station with the PV-VSG on the low-frequency oscillation of power system and its interaction mechanism with the multi-machine system are qualitatively obtained based on the small signal analysis method and prony analysis method from two dimensions of frequency domain and time domain, respectively. The analysis and simulation show that the PV power station based on VSG technology affects the dynamic characteristics of the system by changing the electromagnetic torque of each synchronous generator. Unreasonable operating conditions and parameter settings will aggravate the phenomenon of low-frequency oscillation of the system. Before the grid connection of PV power station, the operating parameters shall be reasonably set to ensure their safe and stable grid connection.

Shifting ecologies of family language planning: Hungarian Australian families during COVID-19

ABSTRACT This study took a mixed-methods approach to investigate family language planning (FLP) in Hungarian families raising children in Australia. The study aimed to explore the complex factors impacting FLP and how families responded to the rapidly changing social conditions during the outbreak of Covid-19. The pandemic highlighted the shifting spatiotemporal dynamics of the family domain. Therefore, the project sought a holistic insight into the shifting family ecology, incorporating language use patterns, motivations, language maintenance and learning strategies and family well-being. Data were collected through an online survey (N = 80) and parental interviews (N = 13). The findings provide empirical evidence of the translocal and transnational dimensions of intergenerational language maintenance. The paper argues for an ecological approach in FLP, which recognises the complex social, affective and ideological dimensions of the family domain and the translocal aspects of language planning. As the results demonstrate, Hungarian families experienced the impact of Covid-19 in contrastive ways: for some, new opportunities arose to establish the home domain as a dynamic multilingual space; for others, the social isolation further reduced the space afforded to the heritage language. Therefore, agency was crucial for responding to these shifting circumstances.

Non-linear Young equations in the plane and pathwise regularization by noise for the stochastic wave equation

We study pathwise regularization by noise for equations on the plane in the spirit of the framework outlined by Catellier and Gubinelli (Stoch Process Appl 126(8):2323–2366, 2016). To this end, we extend the notion of non-linear Young equations to a two dimensional domain and prove existence and uniqueness of such equations. This concept is then used in order to prove regularization by noise for stochastic equations on the plane. The statement of regularization by noise is formulated in terms of the regularity of the local time associated to the perturbing stochastic field. For this, we provide two quantified example: a fractional Brownian sheet and the sum of two one-parameter fractional Brownian motions. As a further illustration of our regularization results, we also prove well-posedness of a 1D non-linear wave equation with a noisy boundary given by fractional Brownian motions. A discussion of open problems and further investigations is provided.

Clinician perception of pathological narcissism in females: a vignette-based study.

The DSM-5 reports that up to 75% of those diagnosed with Narcissistic Personality Disorder (NPD) are males, which denotes that narcissism is a clinical phenomenon that operates differently in men and women. Vulnerable narcissism, which tends to be more prevalent in females and is currently under-appreciated in the DSM-5, may be diagnosed as other "vulnerable" disorders (e.g., Borderline Personality Disorder; BPD). The current study investigated gender differences in clinicians' perceptions of narcissistic pathology. Adopting an online vignette-based study, clinicians (N = 108; 79 females) read clinical case vignettes of hypothetical patients and provided diagnostic ratings of existing personality disorders. Clinicians' diagnostic ratings of NPD were concurrent with the vignette containing grandiose narcissism symptoms, irrespective of patient gender. However, when presented with a vulnerable narcissism vignette, clinicians were significantly more likely to attribute a BPD diagnosis in female patients, compared to male patients. Clinicians with a psychodynamic approach and more experience in practice were also more likely to label vulnerable narcissism symptoms as NPD, compared to those with a CBT approach and less experience in practice. The clinical implications of these results support the shift toward assessing personality dysfunction based on dimensional trait domains.

Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors

Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in three dimensional domains in which the boundary normal vector is included in the frame on the boundary. To do this we identify an isomorphism between a given tetrahedral frame and a symmetric, traceless third order tensor under a particular nonlinear constraint. We then define a Ginzburg-Landau-type functional which penalizes the associated nonlinear constraint. Using gradient descent, one retrieves a globally defined limiting tensor outside of a singular set. The tetrahedral frame can then be recovered from this tensor by a determinant maximization method, developed in this work. The resulting numerically generated frame fields are smooth outside of one dimensional filaments that join together at triple junctions.

Optimisation of the Aerodynamic Shape of a Monorail Suspended Unibus

The aerodynamic optimisation of the shape of a monorail suspended unibus of string transport has been described within the study on the influence of geometric and structural elements on aerodynamic characteristics. The estimate was carried out through a comparative analysis of the features of two shapes of a model with a further change and recalculation of the model being finalised. The comparison was focused on the drag force and the shape drag coefficient. The calculations used a gas dynamics model based on the Reynolds equations using the Menter SST-k-ω (shear stress transport) turbulence model. To solve the equations to find the design functions, an upwind second-order discretisation scheme was used applying the «pressure–velocity» refinement procedure in the framework of SIMPLE algorithm of Patankar–Spalding with the ANSYS Computational Fluid Dynamics Software. The dimensions of the computational domain were chosen considering the geometric dimensions of the 3D model of the shape. Boundary conditions were identified in the solver. The simulation was carried out for the case of motion of a vehicle at a constant speed. The calculations have shown the importance and influence of the geometry of the transition sections of the vehicle body, the mandatory use of wheel fairings and the advantages of the S-shaped tail. The proposed design optimisation made it possible to reduce the drag force and coefficient by 16,9 %. The studies have resulted in selection of the optimal vehicle model which has the lowest aerodynamic drag coefficient, which made it possible to improve the energy efficiency of the system and its environmental friendliness, and consequently, the profit potential of the transportation process.

Development of a cerebral aneurysm segmentation method to prevent sentinel hemorrhage

Image segmentation being the first step is always crucial for brain aneurysm treatment planning; it is also crucial during the procedure. A robust brain aneurysm segmentation has the potential to prevent the blood leakage, also known as sentinel hemorrhage. Here, we present a method combining a multiresolution and a statistical approach in two dimensional domain to segment cerebral aneurysm in which the Contourlet transform (CT) extracts the image features, while the Hidden Markov Random Field with Expectation Maximization (HMRF-EM) segments the image, based on the spatial contextual constraints. The proposed algorithm is tested on Three-Dimensional Rotational Angiography (3DRA) datasets; the average values of segmentation accuracy, DSC, FPR, FNR, specificity, and sensitivity, are found to be 99.72%, 93.52%, 0.07%, 5.23%, 94.77%, and 99.96%, respectively.

Asymmetric Electrode Influence upon Ferroelectric Switching Dynamics in Ag/PVDF‐HFP/ITO Capacitor Structures

Asymmetric electrode (Ag and indium tin oxide (ITO)) influence upon ferroelectric switching dynamics in polyvinylidene fluoride-hexafluoropropylene (PVDF-HFP) thin films across Ag/PVDF-HFP/ITO capacitor structures is systematically investigated. Grazing incidence X-Ray diffraction (GI–XRD), atomic force microscopy (AFM), and UV–visible spectroscopy are utilized to comprehend the structural and microstructural characteristics of PVDF–HFP thin films upon ITO interface. Low voltage rectified and asymmetric current–voltage (I–V) curves reveal the varied barrier potential due to the asymmetric electrodes. Typical squared hysteresis loops along with uniform domain growth model are verified from quasi-static and dynamic ferroelectric loop measurements. Further, from low-frequency (10 and 15 mHz) quasi-static and dynamic (100–1000 Hz) triangular pulses, the switching time, domain dimension with respect to frequency, and amplitude of the electric field are separately evaluated and noted that smaller switching times when electron traverses from Ag to ITO electrode.

Classification of Working Memory Loads via Assessing Broken Detailed Balance of EEG-fNIRS Neurovascular Coupling Measures.

Human brain breaks the detailed balance to drive a variety of cognitive functions, such as memory. Recently, a promising classification framework of working memory loads has been proposed based on functional magnetic resonance imaging (fMRI) data with relative entropy (RE) measurement to quantify the broken detailed balance of human brain. However, there are limitations in previousely developed methods. First, single-modality fMRI can only detect the cerebral hemodynamics but not the neuronal activity, lacking detailed information of the neurovascular coupling process in the brain. Second, the RE measurement utilized to quantify the broken detailed balance may be biased and have no finite upper bound, limiting its application in high dimensional signal domains. In this study, a neurovascular coupling strategy based on concurrent electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) recordings was proposed to take both the cerebral hemedynamics and neuronal activity into consideration in assessing broken detailed balance of the brain. Furthermore, the generalized relative entropy (GRE) was employed to reduce the bias associated with the conventional RE measure. Our results demonstrated that the proposed framework showed higher classification accuracy (82.48%) to identify different levels of working memory loads than conventional methods. In addition, our results revealed that the broken detailed balance was significantly stronger when subjects performed cognitively demanding tasks (P<0.05) and was highly correlated with the neurovascular coupling models derived from the EEG θ and α bands, respectively. In conclusion, our findings provide an advanced framework to accurately classify various levels of working memory with the broken detailed balance of human brain and can be extended to explore the underlying broken detailed balance related to other cognitive behaviors and diseases.

Prediction of ship domain on coastal waters by using AIS data

Ship domain is crucial for collision risk assessments and may vary depending on the navigation area. In this study, an empirical ship domain model for coastal waters is proposed. The proposed ship domain model is planned to reveal the ship domain model for an area where no traffic separation scheme exists. In the study, dodecagon ship domain for different type and size of vessels was created. One-year (11 month) of vessel encounters were analyzed and ship domain boundaries are prepared by considering different safety criteria. The passages of the vessel from forward, aft, port, and starboard were also statistically analyzed and the changes in ship domain dimensions according to the ship type and size are revealed. This model shows the vessels behavior regardless of traffic separation rules.

Field emitter electrostatics: Efficient improved simulation technique for highly precise calculation of field enhancement factors

When solving the Laplace equation numerically via computer simulation, in order to determine the field values at the surface of a shape model that represents a field emitter, it is necessary to define a simulation box and, within this, a simulation domain. This domain must not be so small that the box boundaries have an undesirable influence on the predicted field values. A recent paper discussed the situation of cylindrically symmetric emitter models that stand on one of a pair of well-separated parallel plates. This geometry can be simulated by using two-dimensional domains. For a cylindrical simulation box, formulas have previously been presented that define the minimum domain dimensions (MDD) (height and radius) needed to evaluate the apex value of the field enhancement factor for this type of model, with an error-magnitude never larger than a “tolerance” εtol. This MDD criterion helps to avoid inadvertent errors and oversized domains. The present article discusses (in greater depth than previously) a significant improvement in the MDD method; this improvement has been called the MDD extrapolation technique (MDDET). By carrying out two simulations with relatively small MDD values, it is possible to achieve a level of precision comparable with the results of carrying out a single simulation using a much larger simulation domain. For some simulations, this could result in significant savings of memory requirements and computing time. Following a brief restatement of the original MDD method, the MDDET method is illustrated by applying it to the hemiellipsoid-on-plane and hemisphere-on-cylindrical-post emitter shape models.

OVQE: Omniscient Network for Compressed Video Quality Enhancement

How to use information from temporal, spatial, and frequency domain dimensions is crucial for the quality enhancement of compressed video. The state-of-the-art methods generally design powerful networks to fuse the spatiotemporal information of the videos. But the spatiotemporal information of the entire video is not fully utilized and effectively fused, resulting in the learned context information that is not closely related to the target frame. In addition, various compressed videos have varying degrees of frequency domain information loss. The previous methods ignored the non-uniform distortion of compressed video in different frequency domains and did not design unique algorithms for different frequency domains, so the real texture details of the video could not be restored. In this paper, we propose an omniscient network, which learns video spatiotemporal and omni-frequency information more effectively. The omniscient network consists of two novel components: a Spatio-Temporal Feature Fusion (STFF) module and an Omni-Frequency Adaptive Enhancement (OFAE) block. The former aims to capture spatiotemporal information in adjacent frames, while the latter aims to adaptively recover different frequency domains of compressed video. The information is designed to be bidirectionally propagated in a grid manner such that the omni-enhanced results can be applied. Extensive experiments show that our method outperforms the state-of-the-art method in terms of objective metrics, subjective visual effects, and model complexity.

Global existence and large time behaviour for the pressureless Euler–Naver–Stokes system in ℝ3

We investigate the global Cauchy problem for a two–phase flow model consisting of the pressureless Euler equations coupled with the isentropic compressible Navier–Stokes equations through a drag forcing term. This model was first derived by Choi–Kwon [J. Differential Equations, 261(1) (2016), pp. 654–711] by taking the hydrodynamic limit of the Vlasov/compressible Navier–Stokes equations. Under the assumption that the initial perturbation is sufficiently small, Choi–Kwon [J. Differential Equations, 261(1) (2016), pp. 654–711] established the global well–posedness and large time behaviour for the three dimensional periodic domain $\mathbb {T}^3$. However, up to now, the global well–posedness and large time behaviour for the three dimensional Cauchy problem still remain unsolved. In this paper, we resolve this problem by proving the global existence and optimal decay rates of classic solutions for the three dimensional Cauchy problem when the initial data is near its equilibrium. One of key observations here is that to overcome the difficulties arising from the absence of pressure in the Euler equations, we make full use of the drag forcing term and the dissipative structure of the Navier–Stokes equations to closure the energy estimates of the variables for the pressureless Euler equations.

Dynamical behavior of cancer cell densities in two dimensional domain by the representation theory of solitons

This article analyzes the mathematical model which is described by the nonlinear partial differential equation governing the density of cancer cells at any position (x,y) in the open bounded subset of the plane at any time t. This is a two-dimensional model that describes the dynamics of cancer cells under radiotherapy and its comparison with the one in the absence of radiation effects. The ϕ6-model expansion method has been used to find the exact solutions of the underlying problem. The simulation of obtained results have also been argued.

Global space-time Trefftz DG schemes for the time-dependent linear wave equation

In this paper we are concerned with Trefftz discretizations of the time-dependent linear wave equation in anisotropic media in arbitrary space dimensional domains $\Omega \subset \mathbb{R}^d~ (d\in \mathbb{N})$. We propose two variants of the Trefftz DG method, define novel plane wave basis functions based on rigorous choices of scaling transformations and coordinate transformations, and prove that the corresponding approximate solutions possess optimal-order error estimates with respect to the meshwidth $h$ and the condition number of the coefficient matrices, respectively. Besides, we propose the global Trefftz DG method combined with local DG methods to solve the time-dependent linear nonhomogeneous wave equation in anisotropic media. In particular, the error analysis holds for the (nonhomogeneous) Dirichlet, Neumann, and mixed boundary conditions from the original PDEs. Furthermore, a strategy to discretize the model in heterogeneous media is proposed. The numerical results verify the validity of the theoretical results, and show that the resulting approximate solutions possess high accuracy.

A Fast Temporal Second Order Difference Scheme for the Fractional Sub-Diffusion Equations on One Dimensional Space Unbounded Domain

A Fast Temporal Second Order Difference Scheme for the Fractional Sub-Diffusion Equations on One Dimensional Space Unbounded Domain