We provide analytical solutions to the problems of a circular bending of a beam in plane strain and the torsion of a non-circular cross-section beam, the beams obeying a second-gradient elasticity law proposed by the ...We provide analytical solutions to the problems of a circular bending of a beam in plane strain and the torsion of a non-circular cross-section beam, the beams obeying a second-gradient elasticity law proposed by the author, following a previous suggestion of delrlsola et al. （2009）. The motivation was to find benchmark analytical solutions that can serve to grasp the physical foundations of second gradient elasticity laws for heterogeneous materials. The analytical solution of the circular beam problem presents the additional advantage to establish some nice properties on the unknown second gradient elastic moduli introduced by Enakoutsa （2014） model and the classical elasticity constants for both incompressible and compressible heterogeneous elastic materials. A framework to find the elastic moduli of the new model is also proposed.展开更多
The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fl...The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fluid layer contained between two free boundaries. A linear stability analysis and a normal mode analysis method are carried out to study the onset convection. For stationary convection, various parameters such as the medium permeability, the solute gradients, the non-buoyancy magnetization, and the micropolar parameters （i.e., the coupling parameter, the spin diffusion parameter, and the micropolar heat conduction parameter） are analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for a sufficiently large value of the buoyancy magnetization parameter M1. The principle of exchange of stabilities is found to be true for the micropolar fluid heated from below in the absence of the micropolar viscous effect, the microinertia, and the solute gradients. The micropolar viscous effect, the microinertia, and the solute gradient introduce oscillatory modes, which are non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained.展开更多
§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if...§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if p>2 or singular if 1<p<2. A vector function u=(u1, u2, …, um) defined in ΩT=Ω×[0, T] is called a solution of the system (1.1) if展开更多
Triboelectrification is the transfer of electrical chargebetween surfaces during contact. When the contact is purely normal(i.e., no sliding), the term contact electrification is often used. It wasproposed in 2019 by ...Triboelectrification is the transfer of electrical chargebetween surfaces during contact. When the contact is purely normal(i.e., no sliding), the term contact electrification is often used. It wasproposed in 2019 by Laurence Marks and co-workers (Phys. Rev. Lett.,123, 116103) that flexoelectricity (i.e., strain gradient-inducedpolarization) might be a key driver of triboelectricity at least ininsulators. They explained how to determine flexoelectric surfacepotentials for Hertzian sphere-on-flat contacts and calculatedappreciable values when the typical small size of surface asperities wasconsidered. However, the theory developed so far is only valid whentwo contacting surfaces are in the loading stage where transferredcharges are restricted within the contact area. However, nearly allexperimental measurements of surface charge and potential are madeat the end of the unloading stage when two surfaces are completelyseparated. Here, we develop a Hertzian (sphere-on-flat) flexoelectric non-adhesive contact electrification model that accounts forthe Hertzian contact in both the loading and unloading stages. The impetus for the model is the fact that flexoelectric polarizationclearly decreases monotonically during unloading. For this reason, we find that the residual surface charges and potential (after acomplete separation of two mating surfaces) are considerably altered if unloading is considered. Their magnitudes are muchreduced, and their profiles take on a very different shape. The trends of increasing surface charge and potential magnitudes withincreasing normal load are in agreement with experiments. The next major step will require the addition of adhesion to theloading–unloading model as this can be expected to further alter the evolution of strain gradients during the loading andunloading stages.展开更多
文摘We provide analytical solutions to the problems of a circular bending of a beam in plane strain and the torsion of a non-circular cross-section beam, the beams obeying a second-gradient elasticity law proposed by the author, following a previous suggestion of delrlsola et al. （2009）. The motivation was to find benchmark analytical solutions that can serve to grasp the physical foundations of second gradient elasticity laws for heterogeneous materials. The analytical solution of the circular beam problem presents the additional advantage to establish some nice properties on the unknown second gradient elastic moduli introduced by Enakoutsa （2014） model and the classical elasticity constants for both incompressible and compressible heterogeneous elastic materials. A framework to find the elastic moduli of the new model is also proposed.
文摘The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fluid layer contained between two free boundaries. A linear stability analysis and a normal mode analysis method are carried out to study the onset convection. For stationary convection, various parameters such as the medium permeability, the solute gradients, the non-buoyancy magnetization, and the micropolar parameters （i.e., the coupling parameter, the spin diffusion parameter, and the micropolar heat conduction parameter） are analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for a sufficiently large value of the buoyancy magnetization parameter M1. The principle of exchange of stabilities is found to be true for the micropolar fluid heated from below in the absence of the micropolar viscous effect, the microinertia, and the solute gradients. The micropolar viscous effect, the microinertia, and the solute gradient introduce oscillatory modes, which are non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained.
文摘§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if p>2 or singular if 1<p<2. A vector function u=(u1, u2, …, um) defined in ΩT=Ω×[0, T] is called a solution of the system (1.1) if
基金support of the UK Engineering and Physical Sciences Research Council(EPSRC)for supporting the work through Grant No.EP/V003380/1(“Next Generation Energy Autonomous Textile Fabrics based on Triboelectric Nanogenerators”)the National Natural Science Foundation of China(No.52105179)+1 种基金the Fundamental Research Funds for the Central Universities(No.JZ2025HGTG0298)the Novo Nordisk Foundation Challenge Programme in Energy Materials with Biological Applications(EMGUT)Grant No.NNF22OC0072961。
文摘Triboelectrification is the transfer of electrical chargebetween surfaces during contact. When the contact is purely normal(i.e., no sliding), the term contact electrification is often used. It wasproposed in 2019 by Laurence Marks and co-workers (Phys. Rev. Lett.,123, 116103) that flexoelectricity (i.e., strain gradient-inducedpolarization) might be a key driver of triboelectricity at least ininsulators. They explained how to determine flexoelectric surfacepotentials for Hertzian sphere-on-flat contacts and calculatedappreciable values when the typical small size of surface asperities wasconsidered. However, the theory developed so far is only valid whentwo contacting surfaces are in the loading stage where transferredcharges are restricted within the contact area. However, nearly allexperimental measurements of surface charge and potential are madeat the end of the unloading stage when two surfaces are completelyseparated. Here, we develop a Hertzian (sphere-on-flat) flexoelectric non-adhesive contact electrification model that accounts forthe Hertzian contact in both the loading and unloading stages. The impetus for the model is the fact that flexoelectric polarizationclearly decreases monotonically during unloading. For this reason, we find that the residual surface charges and potential (after acomplete separation of two mating surfaces) are considerably altered if unloading is considered. Their magnitudes are muchreduced, and their profiles take on a very different shape. The trends of increasing surface charge and potential magnitudes withincreasing normal load are in agreement with experiments. The next major step will require the addition of adhesion to theloading–unloading model as this can be expected to further alter the evolution of strain gradients during the loading andunloading stages.
