Quarterly of Applied Mathematics最新文献

{"title":"Hydrodynamic alignment with pressure II. Multi-species","authors":"J. Lu, E. Tadmor","doi":"10.1090/qam/1639","DOIUrl":"https://doi.org/10.1090/qam/1639","url":null,"abstract":"We study the long-time hydrodynamic behavior of systems of multi-species which arise from agent-based description of alignment dynamics. The interaction between species is governed by an array of symmetric communication kernels. We prove that the crowd of different species flocks towards the mean velocity if (i) cross interactions form a heavy-tailed connected array of kernels, while (ii) self-interactions are governed by kernels with singular heads. The main new aspect here is that flocking behavior holds without closure assumption on the specific form of pressure tensors. Specifically, we prove the long-time flocking behavior for connected arrays of multi-species, with self-interactions governed by entropic pressure laws (see E. Tadmor [Bull. Amer. Math. Soc. (2023), to appear]) and driven by fractional \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-alignment. In particular, it follows that such multi-species hydrodynamics approaches a mono-kinetic description. This generalizes the mono-kinetic, “pressure-less” study by He and Tadmor [Ann. Inst. H. Poincaré C Anal. Non Linéaire 38 (2021), pp. 1031–1053].","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45588342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Riemann problem for a two-phase mixture hyperbolic system with phase function and multi-component equation of state","authors":"M. Hantke, Christoph Matern, G. Warnecke, Hazem Yaghi","doi":"10.1090/qam/1664","DOIUrl":"https://doi.org/10.1090/qam/1664","url":null,"abstract":"In this paper a hyperbolic system of partial differential equations for two-phase mixture flows with \u0000\u0000 \u0000 N\u0000 N\u0000 \u0000\u0000 components is studied. It is derived from a more complicated model involving diffusion and exchange terms. Important features of the model are the assumption of isothermal flow, the use of a phase field function to distinguish the phases and a mixture equation of state involving the phase field function as well as an affine relation between partial densities and partial pressures in the liquid phase. This complicates the analysis. A complete solution of the Riemann initial value problem is given. Some interesting examples are suggested as benchmarks for numerical schemes.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44433071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear stability of liquid Lane-Emden stars","authors":"K. Lam","doi":"10.1090/qam/1677","DOIUrl":"https://doi.org/10.1090/qam/1677","url":null,"abstract":"<p>We establish various qualitative properties of liquid Lane-Emden stars in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R Superscript d\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">R</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>d</mml:mi>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {R}^d</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, including bounds for its density profile <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"rho\">\u0000 <mml:semantics>\u0000 <mml:mi>ρ<!-- ρ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">rho</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and radius <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\">\u0000 <mml:semantics>\u0000 <mml:mi>R</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">R</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Using them we prove that against radial perturbations, the liquid Lane-Emden stars are linearly stable when <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma greater-than-or-equal-to 2 left-parenthesis d minus 1 right-parenthesis slash d\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>γ<!-- γ --></mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>d</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">gamma geq 2(d-1)/d</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>; linearly stable when <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma greater-than 2 left-parenthesis d minus 1 right-parenthesis slash d\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>γ<!-- γ --></mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>d</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">gamma >2(d-1)/d</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> for stars with small relative central density <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"rho left-parenthesis 0 right-parenthesis minus rho left-parenthesis ","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41600692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Oberbeck–Boussinesq system with non-local boundary conditions","authors":"A. Abbatiello, E. Feireisl","doi":"10.1090/qam/1635","DOIUrl":"https://doi.org/10.1090/qam/1635","url":null,"abstract":"<p>We consider the Oberbeck–Boussinesq system with non-local boundary conditions arising as a singular limit of the full Navier–Stokes–Fourier system in the regime of low Mach and low Froude numbers. The existence of strong solutions is shown on a maximal time interval <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-bracket 0 comma upper T Subscript normal m normal a normal x Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">m</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">a</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">x</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">[0, T_{mathrm {max}})</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Moreover, <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T Subscript normal m normal a normal x Baseline equals normal infinity\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">m</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">a</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">x</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">T_{mathrm {max}} = infty</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in the two-dimensional setting.</p>","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42223331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two-dimensional non-self-similar Riemann solutions for a thin film model of a perfectly soluble anti-surfactant solution","authors":"R. Barthwal, T. Raja Sekhar","doi":"10.1090/qam/1625","DOIUrl":"https://doi.org/10.1090/qam/1625","url":null,"abstract":"In this article, we construct non-self-similar Riemann solutions for a two-dimensional quasilinear hyperbolic system of conservation laws which describes the fluid flow in a thin film for a perfectly soluble anti-surfactant solution. The initial Riemann data consists of two different constant states separated by a smooth curve in \u0000\u0000 \u0000 \u0000 x\u0000 −\u0000 y\u0000 \u0000 x-y\u0000 \u0000\u0000 plane, so without using self-similarity transformation and dimension reduction, we establish solutions for five different cases. Further, we consider interaction of all possible nonlinear waves by taking initial discontinuity curve as a parabola to develop the structure of global entropy solutions explicitly.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48021412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On stability for semilinear generalized Rayleigh-Stokes equation involving delays","authors":"Do Lan, P. Tuan","doi":"10.1090/qam/1624","DOIUrl":"https://doi.org/10.1090/qam/1624","url":null,"abstract":"We consider a functional semilinear Rayleigh-Stokes equation involving fractional derivative. Our aim is to analyze some circumstances, in those the global solvability, and asymptotic behavior of solutions are addressed. By establishing a Halanay type inequality, we show the dissipativity and asymptotic stability of solutions to our problem. In addition, we prove the existence of a compact set of decay solutions by using local estimates and fixed point arguments.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42594948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Diagnostic Insight of Dental Pulp Testing Methods in Pediatric Dentistry.","authors":"Andreea Igna, Doina Mircioagă, Marius Boariu, Ștefan-Ioan Stratul","doi":"10.3390/medicina58050665","DOIUrl":"10.3390/medicina58050665","url":null,"abstract":"<p><p>The accurate diagnosis of pulpal pathology in pediatric dentistry is essential for the success of vital pulp therapy. Pulp testing is often a challenging task due to understanding and cooperation issues of pediatric patients, as well as the particularities of pulpal physiology encountered in primary and immature permanent teeth. Sensibility tests, although still widely used by dental practitioners, are no longer recommended by pediatric specialists mainly due to their subjective nature. Vitality pulp tests have gained popularity in the last decade in light of some encouraging results of clinical studies. However, their use is not a routine practice yet. This paper is a literature review aimed to guide dental practitioners towards selecting the appropriate pulp testing method for their pediatric cases. It provides an overview on a multitude of pulp testing methods and an update in recommendations for primary and immature permanent teeth.</p>","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":"36 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9145630/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82641833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Upscaling of a reaction-diffusion-convection problem with exploding non-linear drift","authors":"Vishnu Raveendran, E. Cirillo, A. Muntean","doi":"10.1090/qam/1622","DOIUrl":"https://doi.org/10.1090/qam/1622","url":null,"abstract":"We study a reaction-diffusion-convection problem with non-linear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. Because of the imposed large drift scaling, this non-linearity is expected to explode in the limit of a vanishing scaling parameter. As main working techniques, we employ two-scale formal homogenization asymptotics with drift to derive the corresponding upscaled model equations as well as the structure of the effective transport tensors. Finally, we use Schauder’s fixed point theorem as well as monotonicity arguments to study the weak solvability of the upscaled model posed in an unbounded domain. This study wants to contribute with theoretical understanding needed when designing thin composite materials that are resistant to high velocity impacts.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43745816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Error estimates for pressure-driven Hele-Shaw flow","authors":"J. Fabricius, Salvador Manjate, P. Wall","doi":"10.1090/qam/1619","DOIUrl":"https://doi.org/10.1090/qam/1619","url":null,"abstract":"","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41618691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differential equations of quantum mechanics","authors":"I. Sigal","doi":"10.1090/qam/1611","DOIUrl":"https://doi.org/10.1090/qam/1611","url":null,"abstract":"We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48567205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}