On the self-similar solution to the Euler equations for an incompressible fluid in three dimensions

The equations for a self-similar solution to an inviscid incompressible fluid are mapped into an integral equation that hopefully can be solved by iteration. It is argued that the exponents of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering a kernel given by a 3D integral for a swirling flow, likely within reach of present-day computational power. Because of the slow decay of the similarity solution at large distances, its kinetic energy diverges, and some mathematical results excluding non-trivial solutions of the Euler equations in the self-similar case do not apply.     

Synthesis of Pure Silica MWW Zeolite in Fluoride Medium by Using an Imidazolium-Based Long Dication

As the spacer length in 1,2-dimethylimidazolium-based dications increases beyond a specific point (six methylene units), they fail in structure-directing towards STW zeolites in any synthetic conditions. These dications can instead produce, under fluoride concentrated conditions, either *BEA [in the case of the eight-methylene-unit structure-directing agent (SDA)] or MWW (ten methylene units) zeolites. For any length of the dication, the default zeolite (MTW) is a relatively dense zeolite containing a unidimensional channel, whereas the zeolite demanding most specificity (STW, *BEA or MWW) is more porous, affording a larger concentration of the dication to be occluded. This work provides the first reported fluoride synthesis of pure silica MWW zeolites. Charge balance of the organic dications in this zeolite was achieved by combining “structural” silanolates, regular “connectivity defects” and occluded fluoride. Molecular mechanics calculations showed a perfect fit of the decamethylenebis(dimethylimidazolium) dication in the sinusoidal intralayer pore system of MWW. The calculations showed also that the dication is able to stabilize the interlayer space without disturbing the hydrogen-bonding system that holds the layers together in the as-made material. The ¹⁹F magic-angle spinning (MAS) NMR presented two distinct resonances at −71 and −83 ppm, which, on the basis of DFT calculations, we tentatively assigned to fluoride occluded in [4⁶6²] and [4¹5²6²] cages of the MWW structure, respectively. The same DFT study determines a different chemical shift of one methyl ¹³C nuclear magnetic resonance according to the imidazolium ring residing in the sinusoidal channels or in the large cup cavities, thus explaining an experimentally observed splitting of that resonance.     

Geometric derivation of the microscopic stress: A covariant central force decomposition

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.     

受限空间油气爆燃火焰形态

通过受限空间油气爆燃可视化实验发现，在不同初始油气体积分数下，爆燃火焰呈现出不同的表观特征，据此提出了受限空间油气爆燃的3种火焰形态，即光滑球形火焰、褶皱球形火焰和卷曲絮状火焰。分析了3种火焰形态的形成机理，并通过实验观测与理论分析，给出了区分3种火焰形态的临界条件。结合实验中采集到的关键参数，总结了不同的火焰形态下受限空间油气爆燃的反应产物、最大压力、升压速率、反应时间、火焰强度等关键参数的特征与变化规律。     

Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

Barriers to Internal Rotation and Conformational Behaviour of the MESO and D,L Isomers of Pt(II) Complexes with Antitumour Activity

Abstract

The conformational behaviour of a series of ring substituted (ortho-Cl, F and meta or para OH) Pt(II) complexes of general formula [(1,2-hydroxyphenyl)ethylenediamine]PtL₂ [L ? Cl, 1] has been studied by molecular mechanics (MM) methods. Preferred orientations of the phenyl rings, which are important for the complexes′ biological activity, were obtained by calculations of rotational energies about C_sp3?C_ar bonds for all theoretically possible isomers and conformers, meso-λ (R,S/S,R-λ), meso-δ (R,S/S,R-δ), d,l-δ (S,S/R,R-λ) and d,l-λ (S,S/R, R-δ). The influence of the ring substituents and the conformation type on the positions of the energy minima and barriers to rotations about C_sp3?C_ar and C_ar-O(H) bonds were investigated in detail. Theoretical predictions were compared with the experimental results where appropriate.     

Effect of thickness and boundary conditions on the behavior of viscoelastic layers in sliding contact with wavy profiles

In this work, the sliding contact of viscoelastic layers of finite thickness on rigid sinusoidal substrates is investigated within the framework of Green's functions approach. The periodic Green's functions are determined by means of a novel formalism, which can be applied, in general, to either 2D and 3D viscoelastic periodic contacts, regardless of the contact geometry and boundary conditions.Specifically, two different configurations are considered here: a free layer with a uniform pressure applied on the top, and a layer rigidly confined on the upper boundary. It is shown that the thickness affects the contact behavior differently, depending on the boundary conditions. In particular, the confined layer exhibits increasing contact stiffness when the thickness is reduced, leading to higher loads for complete contact to occur. The free layer, instead, becomes more and more compliant as thickness is reduced.We find that, in partial contact, the layer thickness and the boundary conditions significantly affect the frictional behavior. In fact, at low contact penetrations, the confined layer shows higher friction coefficients compared to the free layer case; whereas, the scenario is reversed at large contact penetrations. Furthermore, for confined layers, the sliding speed related to the friction coefficient peak is shifted as the contact penetration increases. However, once full contact is established, the friction coefficient shows a unique behavior regardless of the layer thickness and boundary conditions.     

Fullerenes as mass sensors: A numerical investigation

This paper investigates the novel development of a mass sensitive nanosensor based on the use of individual spherical fullerenes. The main advantage of the mass sensing ability of spherical fullerenes in comparison with other nanomaterials such as carbon nanotubes (CNTs) or graphene nanoribbons (GNRs) is the fact that they present almost perfect geometric symmetry and thus a unique vibrational behavior which is independent from the location of the externally added nanoparticle. The study is conducted by the use of a computationally effective numerical scheme based on the adoption of appropriate three dimensional line spring elements as well as point mass elements to simulate the atomistic structure of fullerenes and interatomic interactions appearing between carbon atoms. The free vibration of C₂₀, C₆₀, C₈₀ and C₁₈₀ molecules is analyzed without and with an external nanoparticle of specific mass attached on their structure to calculate the arisen change in their natural frequencies and corresponding shape modes. A parametric study concerning the magnitude and location of the added mass is performed in order to evaluate the mass sensing ability of the fullerenes under consideration.     

First mushroom-shaped adhesive microstructure: A review

This letter reviews the adhesive and frictional properties of the first mushroom-shaped adhesive microstructure (MSAMS), which has come a long way from inspiration by the attachment devices evolved in beetles to a large-scale industrial production. It was shown to have an that about twice higher pull-off force compared to a smooth control made from the same material measured on smooth substrates. Pull-off forces measured underwater are even higher than those in air. Moreover, it retained adhesive performance over thousands of attachment cycles and initial adhesive capability could be recovered by washing after being contaminated. In shearing, MSAMS exhibits reduced and stabilized friction in comparison with a smooth control, which demonstrated pronounced stick-slip motion, and shows zero pull-off force in a sheared state, allowing the adhesion to be switched on and off. The presence of a fluid in the contact zone showed adhesion enhancement on both smooth and rough substrates. All these features lead us to conclude that MSAMS may have practical potential in a variety of applications.