Simulation of proppant transport at intersection of hydraulic fracture and natural fracture of wellbores using CFD-DEM

Proppants transport is an advanced technique to improve the hydraulic fracture phenomenon,in order to promote the versatility of gas/oil reservoirs.A numerical ...     

On the contribution of circumferential resonance modes in acoustic radiation force experienced by cylindrical shells

A body insonified by a constant (time-varying) intensity sound field is known to experience a steady (oscillatory) force that is called the steady-state (dynamic) acoustic radiation force. Using the classical resonance scattering theorem (RST) which suggests the scattered field as a superposition of a resonance field and a background (non-resonance) component, we show that the radiation force acting on a cylindrical shell may be synthesized as a composition of three components: background part, resonance part and their interaction. The background component reveals the pure geometrical reflection effects and illustrates a regular behavior with respect to frequency, while the others demonstrate a singular behavior near the resonance frequencies. The results illustrate that the resonance effects associated to partial waves can be isolated by the subtraction of the background component from the total (steady-state or dynamic) radiation force function (i.e., residue component). In the case of steady-state radiation force, the components are exerted on the body as static forces. For the case of oscillatory amplitude excitation, the components are exerted at the modulation frequency with frequency-dependant phase shifts. The results demonstrate the dominant contribution of the non-resonance component of dynamic radiation force at high frequencies with respect to the residue component, which offers the potential application of ultrasound stimulated vibro-acoustic spectroscopy technique in low frequency resonance spectroscopy purposes. Furthermore, the proposed formulation may be useful essentially due to its intrinsic value in physical acoustics. In addition, it may unveil the contribution of resonance modes in the dynamic radiation force experienced by the cylindrical objects and its underlying physics.     

Solutions of the two-body Salpeter equation under the Coulomb and exponential potential for any l state with Laplace approach

In this paper we have solved the two-body spinless-Salpeter (SS) equation under the Coulomb and exponential type potentials. We have applied an approximation for the centrifugal term in our calculations. The energy eigenvalues and the corresponding eigenfunctions are reported by using the Laplace transform approach for any n, l states.     

New N-nicotinyl and N-isonicotinyl, N′,N″-diaryl phosphorictriamides with new Er(III) complex: synthesis, spectroscopic study and crystal structures

Ten new N-nicotinyl and N-isonicotinyl phosphoramidates with formula XP(O)R₂, X?=?Nicotinamide(nia), R?=?NHCH₂Ph (1), N(CH₃)CH₂Ph (2), NHCH(CH₃)Ph (3), NH-CH₂C₄H₃O (4), NHCH₂(C₅H₄N) (5), 3-NH-C₅H₄N (6), and YP(O)R₂, Y?=?isonicotinamide(iso), R?=?NHCH₂Ph (7), N(CH₃)CH₂Ph (8), NHCH(CH₃)Ph (9), NH-CH₂C₄H₃O (10) plus one new Er(III) complex with formula Er(L)₂(NO₃)₃ (11), L?=?(iso)PO(NHCH₂C₄H₃O)₂ (10), were synthesized and characterized by elemental analysis and ¹H, ¹³C, ³¹P NMR, IR, UV?Cvis spectroscopy. Crystal structures of compounds 10 and 11 were also determined by X-ray crystallography. Interestingly, the ¹H NMR spectra of compounds 1, 2, 6, 7, 9 indicated long-range ⁿ J _P,H (n?=?5,6,7) coupling constants, in the range of 1.4?C1.9?Hz, for the splitting of pyridine ring protons with phosphorus atom. IR results showed that the ??(C=O) values of compounds 7?C10 are greater than those of compounds 1?C5 which means that isonicotinyl moiety is more electron withdrawing than nicotinyl group. X-ray outcomes revealed that in complex 11 three phosphoric triamide ligands have been connected to each Er(III); one from N_pyridine and two from P=O donor sites. One of the P=O donor ligands is mono dentate while the other one acts as a bidentate ligand and coordinates to another Er atom via its N_pyridine site. By forming complex 11 the P=O and C?CN_amide bond lengths of ligand is increased in both, mono and bi dentate, ligands while the C=O bond length is decreased to lower values. These variations are in good agreement with IR results. All H-bonds and electrostatic interactions lead to form a three-dimensional polymeric cluster in the crystal lattice of 10 and 11.     

Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module

Let ${(R, \mathfrak{m})}$ be a commutative Noetherian local ring of Krull dimension d, and let C be a semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing module if and only if the top local cohomology module of ${R, H _{\mathfrak{m}} ^{d} (R)}$ , has finite G _C -injective dimension. This generalizes a recent result due to Yoshizawa, where the ring is assumed to be complete Cohen-Macaulay.     

k-torsionless modules with finite Gorenstein dimension

Let R be a commutative Noetherian ring. It is shown that the finitely generated R-module M with finite Gorenstein dimension is reflexive if and only if M _p is reflexive for p ∈ Spec(R) with depth(R _p) ? 1, and $G - {\dim _{{R_p}}}$ (M _p) ? depth(R _p) ? 2 for p ∈ Spec(R) with depth(R _p) ? 2. This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for n ? 2 we give a characterization of n-Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown that every R-module has a k-torsionless cover provided R is a k-Gorenstein ring.     

Shellable quasi-forests and their h-triangles

In this paper we show that a quasi-forest is shellable if and only if its h-triangle satisfies ${h_{i,j}(\Delta)=0 \quad \forall i, \forall j >1 }$ . In addition, it will be shown that a quasi-forest is sequentially Cohen-Macaulay if and only if it is shellable.     

A Facile One‐Pot Synthesis of Substituted Quinolines via New Multicomponent Reaction

An efficient synthesis of quinoline derivatives is described via the reaction between ethyl chloropyruvate or alkyl 4‐chloroacetoacetate and activated acetylenic compounds in the presence of nucleophilic form of isatin in water as the solvent. Nucleophilic form of isatin is produced from the reaction of isatin and triethylamin.     

Exact S‐wave solution of the trigonometric pöschl‐teller potential

The trigonometric Pöschl‐Teller (PT) potential describes the diatomic molecular vibration. By using the Nikiforov‐Uvarov method, we have obtained the exact analytical s‐wave solutions of the radial Schrödinger equation (SE) for the trigonometric PT potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented too. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A Method to Solve the Schrödinger Equation for Any Power Hypercentral Potentials

An exact closed form of solution to the hyperradial Schrödinger equation is constructed for any general case comprising any hypercentral power and inverse-power potential. The hypercentral potential depends only on the hyperradius, which itself is a function of Jacobi relative coordinates that are functions of particle positions (r₁,r₂,…, r_N). This article is mainly devoted to the dernonstrat of the fact that any ψ of the form ψ=power series× exp(polynomial)=[f(x)exp(g(x))] is potentially a solution of the Schrödinger equation, where the polynomial g(x) is an ansatz depending on the interaction potential.