Advances in Mathematical Physics最新文献

{"title":"Free Convection Heat Transfer in Composite Enclosures with Porous and Nanofluid Layers","authors":"Abeer Alhashash","doi":"10.1155/2023/2088607","DOIUrl":"https://doi.org/10.1155/2023/2088607","url":null,"abstract":"This work conducts a numerical investigation of convection heat transfer within two composite enclosures. These enclosures consist of porous and nanofluidic layers, where the porous layers are saturated with the same nanofluid. The first enclosure has two porous layers of different sizes and permeabilities, while the second is separated by a single porous layer. As the porous layer thickness approaches zero, both enclosures transition to clear nanofluid enclosures. The study uses the Navier–Stokes equations to govern fluid flow in the nanofluid domain and the Brinkman–Forchheimer extended Darcy model to describe flow within the saturated porous layer. Numerical solutions are obtained using an iterative finite difference method. Key parameters studied include the porous thickness (<span><svg height=\"9.75571pt\" style=\"vertical-align:-1.11981pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 26.707 9.75571\" width=\"26.707pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.24,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,9.204,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.076,0)\"></path></g></svg><span></span><svg height=\"9.75571pt\" style=\"vertical-align:-1.11981pt\" version=\"1.1\" viewbox=\"30.2891838 -8.6359 17.399 9.75571\" width=\"17.399pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,30.339,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,40.107,0)\"><use xlink:href=\"#g117-93\"></use></g></svg><span></span><span><svg height=\"9.75571pt\" style=\"vertical-align:-1.11981pt\" version=\"1.1\" viewbox=\"51.320183799999995 -8.6359 15.739 9.75571\" width=\"15.739pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,51.37,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,57.61,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,60.574,0)\"><use xlink:href=\"#g113-49\"></use></g></svg>),</span></span> the nanoparticle volume fraction (<span><svg height=\"12.3916pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.96212 26.707 12.3916\" width=\"26.707pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,6.24,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,9.204,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.076,0)\"><use xlink:href=\"#g117-93\"></use></g></svg><span></span><svg height=\"12.3916pt\" style=\"vertical-align:-3.42948pt\" version=\"1.1\" viewbox=\"30.2891838 -8.96212 18.609 12.3916\" width=\"18.609pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,30.339,0)\"></path>","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138569867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"QMU Analysis of Flexoelectric Timoshenko Beam by Evidence Theory","authors":"Feng Zhang, Jiajia Zhang, Weiyue Wang, Ruijie Du, Cheng Han, Zijie Qiao","doi":"10.1155/2023/2967408","DOIUrl":"https://doi.org/10.1155/2023/2967408","url":null,"abstract":"In recent years, with the rapid development of nanotechnology, a new type of electromechanical coupling effect similar to the piezoelectric effect, the flexoelectric effect, has gradually come into the public’s view. The flexoelectric beam that is the main structural unit of the flexoelectric signal output has broad application prospects in the next generation of micro- and nanoelectromechanical systems. Therefore, the investigation of flexoelectric materials and structures has important scientific and engineering application significances for the design of flexoelectric devices. In this paper, a model of flexoelectric Timoshenko beam is established, the deflection, rotation angle, and dynamic electrical signal output of the forced vibration are taken as the system response, and the density <span><svg height=\"9.39034pt\" style=\"vertical-align:-3.42943pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 7.13289 9.39034\" width=\"7.13289pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>,</span> shear correction factor <span><svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 6.71534 6.1673\" width=\"6.71534pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>,</span> and frequency ratio <svg height=\"9.49473pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 7.30254 9.49473\" width=\"7.30254pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> are selected as the key performance parameters of the system. The combination of available data and engineers’ experience suggests that there are random and cognitive uncertainties in the parameters. Therefore, the probability distribution of the system performance response is expressed by the likelihood function and belief function through the quantification of margins and uncertainties (QMUs) analysis methodology under the framework of evidence theory, and the system reliability or performance evaluation is measured by the calculated confidence factors. These results provide a theoretical basis for accurate analysis of flexoelectric components and provide guidance for the design of flexoelectric components with excellent performance.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of Soret and Dufour on Unsteady Magneto-Convective Transport through a Vertical Perforated Sheet with Chemical Reaction","authors":"Md. Mosharrof Hossain, Md. Hasanuzzaman, A. Rahim Laskar, Ashish Barmon","doi":"10.1155/2023/6648797","DOIUrl":"https://doi.org/10.1155/2023/6648797","url":null,"abstract":"An investigation of the effects of Soret and Dufour on an unsteady MHD convective transmission over a vertical porous sheet with chemical reaction was introduced throughout this study. The model that formed nonlinear governing equations is transformed by applying the similarity analysis with the help of the finite difference method. The numerical resolutions of the fluid characteristics like velocity, concentration, and temperature are explained graphically. This research also presented the mass transmission rate, heat transmission rate, and the local skin friction coefficient, which are explained in tabular form. The results give the fluid motion and temperature improvement for growing values of the Dofour effect. Also, the fluid velocity and concentration improve for elevated amounts of the Soret effect. The local skin friction improves by around 66% whereas the mass transmission rate lessens by around 247% with the growing Soret number (0.5–2.0).","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Modulation Instability Analysis and Analytical Solutions of the Nonlinear Gross−Pitaevskii Model with Conformable Operator and Riemann Wave Equations via Recently Developed Scheme","authors":"Wei Gao, Haci Mehmet Baskonus","doi":"10.1155/2023/4132763","DOIUrl":"https://doi.org/10.1155/2023/4132763","url":null,"abstract":"In this manuscript, we focus on the application of recently developed analytical scheme, namely, the rational sine-Gordon expansion method (SGEM). Some new exact solutions of Riemann wave system and the nonlinear Gross−Pitaevskii equation (GPE) by using this method are extracted. This method is based on the general properties of the SGEM which uses the fundamental properties of trigonometric functions. Many novel analytical solutions such as dark, bright, mixed dark–bright, hyperbolic, and periodic wave solutions are successfully extracted. Physical meanings of solutions are simulated by the various figures in 2D and 3D along with the contour graphs. Strain conditions of the existence are also reported in detail. Finally, modulation instability analysis of the nonlinear GPE is studied in detail.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect","authors":"Hang Zhang, Yujuan Jiao, Jinmiao Yang","doi":"10.1155/2023/8942147","DOIUrl":"https://doi.org/10.1155/2023/8942147","url":null,"abstract":"In this paper, we are concerned with traveling wave solutions for two preys–one predator system with switching effect. First, we discuss that there is no traveling wave solution for this system by using linearization method. Second, applying super-sub solution method we establish the existence of semitraveling wave solutions with the minimal speed explicitly defined. Moreover, using the method of Lyapunov function and LaSalle’s invariance principle, under certain conditions, we obtain that the semitraveling wave solutions connect the only positive equilibrium point at infinity, are actually traveling wave solutions. Finally, the numerical experiments support the validity of our theoretical results.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation","authors":"Nebi Yılmaz, Erhan Pişkin, Ercan Çelik","doi":"10.1155/2023/8866861","DOIUrl":"https://doi.org/10.1155/2023/8866861","url":null,"abstract":"In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo–Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents <svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 19.8424 12.7178\" width=\"19.8424pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,7.71,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,12.208,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,15.172,0)\"></path></g></svg> and <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 18.5114 12.7178\" width=\"18.5114pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.383,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.881,0)\"><use xlink:href=\"#g113-46\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.845,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>.</span> Finally, we prove a finite-time blow-up result for negative initial energy.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flow Dynamics of Eyring–Powell Nanofluid on Porous Stretching Cylinder under Magnetic Field and Viscous Dissipation Effects","authors":"Ebba Hindebu Rikitu","doi":"10.1155/2023/9996048","DOIUrl":"https://doi.org/10.1155/2023/9996048","url":null,"abstract":"The current paper scrutinized the flow dynamics of Eyring–Powell nanofluid on porous stretching cylinder under the effects of magnetic field and viscous dissipation by employing Cattaneo–Christov theory. In order to study impacts of thermophoretic force and Brownian motion, the two-phase (Buongiorno) model is considered. As a consequence, very nonlinear PDEs that govern flow problem were formulated, transformed into ODEs via relevant similarity variables, as well as tackled by utilizing R-K-45 integration scheme along with the shooting technique in the MATLAB R2018a software. Consequently, the numerical simulations reveal that Eyring–Powell fluid, curvature, velocity ratio parameters have the propensity to raise nanofluid velocity. Nanofluid temperature shows an increasing pattern with magnetic, curvature, dissipative heating, and thermophoresis parameters. Besides, Prandtl number, Eyring–Powell fluid, velocity ratio, thermal relaxation time, and porous parameters indicate the declining impact against the nanofluid temperature. Hence, the porous medium reasonably and successfully managed nanofluid temperature as well as the overall thermal system in terms of system cooling. The concentration profile gets fall down with escalating values of Schmidt number, magnetic, curvature, dissipative heating, thermophoresis, Brownian motion, and solutal relaxation time parameters. Moreover, coefficient of the skin friction gets rise for larger values of Eyring–Powell fluid, magnetic and curvature parameters however porous medium and velocity ratio parameters reveal the opposite trends on it. The magnetic, curvature, Eyring–Powell fluid, velocity ratio, and dissipative heating parameters indicate increasing impacts on both Nusselt <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 17.9373 8.8423\" width=\"17.9373pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,10.78,0)\"></path></g></svg> and Sherwood <svg height=\"9.49473pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 12.9918 9.49473\" width=\"12.9918pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.136,0)\"></path></g></svg> numbers even though both <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 17.9373 8.8423\" width=\"17.9373pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-79\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.78,0)\"><use xlink:href=\"#g113-118\"></use></g></svg> and <svg height=\"9.49473pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 12.9918 9.49473\" width=\"12.9918pt\" xmlns=\"http://www.w3.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sharp Threshold of Global Existence and Mass Concentration for the Schrödinger–Hartree Equation with Anisotropic Harmonic Confinement","authors":"Min Gong, Hui Jian","doi":"10.1155/2023/4316819","DOIUrl":"https://doi.org/10.1155/2023/4316819","url":null,"abstract":"This article is concerned with the initial-value problem of a Schrödinger–Hartree equation in the presence of anisotropic partial/whole harmonic confinement. First, we get a sharp threshold for global existence and finite time blow-up on the ground state mass in the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -critical case. Then, some new cross-invariant manifolds and variational problems are constructed to study blow-up versus global well-posedness criterion in the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -critical and <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -supercritical cases. Finally, we research the mass concentration phenomenon of blow-up solutions and the dynamics of the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -minimal blow-up solutions in the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"> <msup> <mi>L</mi> <mn>2</mn> </msup> </math> -critical case. The main ingredients of the proofs are the variational characterisation of the ground state, a suitably refined compactness lemma, and scaling techniques. Our conclusions extend and compensate for some previous results.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135808863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some Conditions of Non-Blow-Up of Generalized Inviscid Surface Quasigeostrophic Equation","authors":"Linrui Li, Mingli Hong, Lin Zheng","doi":"10.1155/2023/4420217","DOIUrl":"https://doi.org/10.1155/2023/4420217","url":null,"abstract":"In this paper, we survey some non-blow-up results for the following generalized modified inviscid surface quasigeostrophic equation (GSQG) <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <mfenced open=\"{\" close=\"\"> <mrow> <mtable class=\"smallmatrix\"> <mtr> <mtd columnalign=\"left\"> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mi>u</mi> <mo>·</mo> <mo>∇</mo> <mi>θ</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd columnalign=\"left\"> <mi>u</mi> <mo>=</mo> <msup> <mrow> <mo>∇</mo> </mrow> <mrow> <mo>⊥</mo> </mrow> </msup> <mi>ψ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd columnalign=\"left\"> <mo>−</mo> <msup> <mrow> <mi>Λ</mi> </mrow> <mrow> <mi>β</mi> </mrow> </msup> <mi>ψ</mi> <mo>=</mo> <mi>θ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd columnalign=\"left\"> <mi>θ</mi> <mfenced open=\"(\" close=\")\"> <mrow> <mi>x</mi> <mo>,</mo> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mfenced open=\"(\" close=\")\"> <mrow> <mi>x</mi> </mrow> </mfenced> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mfenced> </math> . This is a generalized surface quasigeostrophic equation (GSQG) with the velocity field <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"> <mi>u</mi> </math> related to the scalar <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"> <mi>θ</mi> </math> by <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"> <mi>u</mi> <mo>=</mo> <mo>−</mo> <msup> <mrow> <mo>∇</mo> </mrow> <mrow> <mo>⊥</mo> </mrow> </msup> <msup> <mrow> <mi>Λ</mi> </mrow> <mrow> <mo>−</mo> <mi>β</mi> </mrow> </msup> <mi>θ</mi> </math> , where <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"> <mn>1</mn> <mo>≤</mo> <mi>β</mi> <mo>≤</mo> <mn>2</mn> </math> . We prove that there is no finite-time singularity if the level set of generalized quasigeostrophic equation does not have a hyperbolic saddle, and the angle of opening of the saddle can go to zero at most as an exponential decay. Moreover, we give some conditions that rule out the formation of sharp fronts for generalized inviscid surface quasigeostrophic equation, and we obtain some estimates on the formation of semiuniform fronts. These results greatly weaken the geometrical assumptions which rule out the collapse of a simple hyperbolic saddle in finite time.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136104291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Retracted: The Statistical Analysis of Multidimensional Psychological Characteristics and User Feedback Willingness","authors":"Advances in Mathematical Physics","doi":"10.1155/2023/9837132","DOIUrl":"https://doi.org/10.1155/2023/9837132","url":null,"abstract":"<jats:p />","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135824482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}