An improved particle shifting technique for incompressible smoothed particle hydrodynamics methods

The smoothed particle hydrodynamics (SPH) method is one of the powerful Lagrangian tools for modeling free surface flows. However, it suffers from particle disorder, which leads to interpolation and numerical errors. To overcome this problem, several techniques have been introduced until now, among which the particle shifting technique (PST) based on Fick's law is an efficient one. The current form of this method needs tuning parameters to fulfill numerical stability criteria. In this study, to eliminate calibration factors, a new shifting coefficient is derived theoretically based on particle positions before and after shifting, regardless of other parameters such as velocity, pressure, time step intervals, etc. The only required input is particle positions, and the main concern is conserving particle densities in their updated positions. In addition to the proposed PST, a new distribution index (DI) is introduced for measuring the spatial uniformity of particles. Furthering the research, some novel treatments are also studied to improve particle movements near free surface boundary. The proposed idea is only assessed for ISPH method in this study, and its performance in other SPH schemes needs more investigations. Following this innovative method, it is validated by modeling different cases including dam break flow, paddle movement, and elliptical water drop. In all cases, particle arrangements have been improved by means of the modified shifting method. In that sense, good agreements between simulation results with experimental data, analytical solutions, and other numerical methods approve the ability of the developed method in simulating free surface flows.     

On unimodular graphs

We study graphs whose adjacency matrices have determinant equal to 1 or −1, and characterize certain subclasses of these graphs. Graphs whose adjacency matrices are totally unimodular are also characterized. For bipartite graphs having a unique perfect matching, we provide a formula for the inverse of the corresponding adjacency matrix, and address the problem of when that inverse is diagonally similar to a nonnegative matrix. Special attention is paid to the case that such a graph is unicyclic.     

Synthesis of new N-alkyl(aryl)-2,4-diaryl-1H-pyrrol-3-ols <Emphasis Type="Italic">via</Emphasis> aldol Paal–Knorr reactions

New N-alkyl(aryl)-2,4-diaryl-1H-pyrrol-3-ol derivatives have been synthesized in moderate to good yields in a novel and efficient process by aldol reaction of 1-(4-methoxyphenyl)propan-2-ones with phenylglyoxal in the presence of DABCO in water, followed by Paal–Knorr reaction with amines in the presence of a catalytic amount of p-TSA in toluene at reflux.     

Nano-TiO<Subscript>2</Subscript>: An eco-friendly and re-usable catalyst for the synthesis of 14-Aryl or alkyl-14<Emphasis Type="Italic">H</Emphasis>-dibenzo[<Emphasis Type="Italic">a,j</Emphasis>]xanthenes

Synthesis of 14-aryl or alkyl-14H-dibenzo[a,j]xanthenes using nano-TiO₂ as eco-friendly and efficient catalyst is reported. Short reaction times, high yields, a clean process, simple methodology, easy work-up and green conditions are advantages of this protocol.     

Equimatchable claw-free graphs

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm.     

On the Finiteness of Noetherian Rings with Finitely Many Regular Elements

Let R be a left Noetherian ring and ZD(R) be the set of all zero-divisors of R. In this paper, it is shown that if R \ ZD(R) is finite, then R is finite.     

On the role of anisotropic turbomachinery flow structures in inter-scale turbulence energy flux as deduced from SPIV measurements

The present study uses stereoscopic particle image velocimetry in the rotor exit of a centrifugal turbomachine to analyse anisotropy and geometrical characteristics of tensorial flow quantities. The purpose is to identify dominant topologies of turbulence stress tensor and principal directions of flow structures. The misalignment between principal directions of strain and turbulence stress tensors is more evident in the jet–wake interaction regions and questions the eddy-viscosity models which assume an exact alignment between stress/strain eigenvectors. Anisotropy analysis based on the barycentric approach shows that the disk-like structure and/or the rod-like structure limiting states of turbulence are the most frequent topologies of turbulence stress. Additionally, planar straining is the dominant deformation characteristic in the measurement area. These anisotropic behaviours considerably attribute to the turbulence energy cascade. Conditional isolation of flow structures based on inter-scale energy flux shows that a larger extent of turbulence stress anisotropy results in a larger energy flux and therefore significantly affects the dynamics of turbulent flow structures.     

Orientations of graphs avoiding given lists on out-degrees

Let $G$ be a graph and $F:V\left(G\right)\to 2^{\mathbb{N}}$ be a mapping. The graph $G$ is said to be $F$- avoiding if there exists an orientation $O$ of $G$ such that $d_O^{+}\left(v\right)\notin F\left(v\right)$ for every $v\in V\left(G\right)$, where $d_O^{+}\left(v\right)$ denotes the out-degree of $v$ in the directed graph $G$ with respect to $O$. In this paper it is shown that if $G$ is bipartite and $\mid F\left(v\right)\mid \le d_G\left(v\right)/2$ for every $v\in V\left(G\right)$, then $G$ is $F$-avoiding. The bound $\mid F\left(v\right)\mid \le d_G\left(v\right)/2$ is best possible. For every graph $G$, we conjecture that if $\mid F\left(v\right)\mid \le \frac{1}{2}\left(d_G\left(v\right)-1\right)$ for every $v\in V\left(G\right)$, then $G$ is $F$-avoiding. We also argue about this conjecture for the best possibility of the conditions and also show some partial solutions.     

The effect of rib shape on the behavior of laminar flow of oil/MWCNT nanofluid in a rectangular microchannel

Journal of Thermal Analysis and Calorimetry - In this research, the laminar and forced flow and heat transfer of oil/multi-walled carbon nanotubes nanofluid in a microchannel have been numerically...     

A sulfonic acid functionalized ionic liquid as a homogeneous and recyclable catalyst for the one-pot synthesis of α-aminophosphonates

A sulfonic acid functionalized ionic liquid is used as a Brønsted acid catalyst for the one-pot, three-component synthesis of α-aminophosphonates from aldehydes and ketones at room temperature in water. This homogeneous catalytic procedure is simple and efficient and the catalyst can be reused at least six times without any noticeable decrease in catalytic activity.