hydraulic fracking - Science topic

For a simple graph $G$, a vertex labeling $\phi:V(G) \rightarrow \{1, 2,\ldots,k\}$ is called $k$-labeling. The weight of an edge $xy$ in $G$, written $w_{\phi}(xy)$, is the sum of the labels of end vertices $x$ and $y$, i.e., $w_{\phi}(xy)=\phi(x)+\phi(y)$. A vertex $k$-labeling is defined to be an edge irregular $k$-labeling of the graph $G$ if f...

Effective hydraulic conductivity is typically used to evaluate groundwater flow in faulted/fractured media. Estimating effective hydraulic conductivity relies on modelling the transmissivity and hydraulic connectivity of faults/fractures using a large dataset. As an alternative to evaluating hydraulic connectivity, flow dimension is an easily avail...

Oil production from tight reservoirs due to their very low permeability and high capillary pressure requires complex operations and materials, so that hydraulic fracturing in these reservoirs is recommended before any chemical injection. This operation turns the reservoir into a fractured one that can produce more oil by activating the imbibition m...

Today mobile users learn and share their traffic observations via crowdsourcing platforms (e.g., Google Maps and Waze). Yet such platforms simply cater to selfish users' myopic interests to recommend the shortest path, and do not encourage enough users to travel and learn other paths for future others. Prior studies focus on one-shot congestion gam...

We prove that, for $k \geq 10$, the Diophantine equation $(x^k-1)(y^k-1)^2=z^k-1$ in positive integers $x,y,z,k$ with $z > 1$, has no solutions satisfying $1 < x \leq y$ or $1 < y <x \leq((y^k-1)^{k-2}+1)^{\frac{1}{k}}$.

Shale oil reservoirs are characterized by extremely low porosity and permeability, necessitating the utilization of multi-fractured horizontal wells (MFHWs) for their development. Additionally, the complex phase behavior and desorption effect of two-phase fluids make the fluid flow characteristics of shale oil reservoirs exceptionally intricate. Ho...

We demonstrate that the Compton wavelength mathematically corresponds exactly to the photon wavelength of rest mass energy. On the other hand, the de Broglie wavelength is not defined for a rest-mass particle, but if the particle is nearly at rest, then the de Broglie wavelength approaches infinity, and the corresponding photon wavelength of the re...

This study deals with the existence of nodal solutions for the following gauged nonlinear Schrödinger equation with zero mass: -\Delta u+\left(\frac{{h}_{u}^{2}\left(| x| )}{{| x| }^{2}}+\underset{| x| }{\overset{+\infty }{\int }}\frac{{h}_{u}\left(s)}{s}{u}^{2}\left(s){\rm{d}}s\right)u={| u| }^{p-2}u,\hspace{1.0em}x\in {{\mathbb{R}}}^{2}, where p\...

Let H(V, E) be a k-regular connected hypergraph with rank R on n vertices and m edges. A set of vertices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S\subseteq V$$\...

Several researchers have reported the results of adding a variety of fibers to asphalt concrete described as fiber-reinforced asphalt concrete (FRAC). This research paper finds the most suitable prediction model for Marshall Stability and the optimistic bitumen content useful in glass fiber-reinforced asphalt mix by performing Marshall Stability te...

The integral circulant graph \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{ICG}_n (D)$$\end{document} has the vertex set \documentclass[12pt]{minimal} \usepac...

Collecting detailed hydrogeological data before, during, and after remediation campaigns is essential for effective management and monitoring of contaminated sites. As in-situ remediation injection treatment becomes more popular, recording the hydraulic response during these events offers an opportunity to collect detailed data on hydrogeological p...

The practice of cementing the bottomhole zone of wells in unstable formations shows that cement stone, designed to ensure rock stability, is the weakest link and can easily be destroyed under the influence of various loads. Such loads include perforation of the production string, hydraulic fracturing and other technological operations. The main fac...

For a finite graph \(G=(V,E)\) let \(G^*\) be obtained by considering a random perfect matching of V and adding the corresponding edges to G with weight \(\varepsilon \), while assigning weight 1 to the original edges of G. We consider whether for a sequence \((G_n)\) of graphs with bounded degrees and corresponding weights \((\varepsilon _n)\), th...

Rock bursts in roadway groups of deep mining workfaces are more likely to occur due to concentrated static loads, posing significant threats to mining safety and efficiency. In this study, the coal mine roadway groups in western China are taken as an engineering case to investigate the occurrence mechanism of rock bursts in deep mining workfaces ca...

We compare several machine learning (ML) models that predict the yield strength and plasticity of high-entropy alloys (HEAs) for achieving high-accuracy with notably low root mean square errors (RMSE). Our models, developed using a comprehensive database of single-phase body-centered cubic (BCC) HEAs and BCC + B2 HEAs (where B2 is ordered BCC), int...

We consider an initial-boundary value problem for the chemotaxis-Navier--Stokes system \begin{align*} \left\{ \begin{array}{c@{\quad}l@{\quad}l@{\,}c} n_{t}+u\cdot\nabla n=\nabla\cdot\big(D(n)\nabla n-nS(x,n,c)\cdot\nabla c\big),\ &x\in\Omega,& t>0,\\ c_{t}+u\cdot\nabla c=\Delta c-cn,\ &x\in\Omega,& t>0,\\ u_{t}+(u\cdot\nabla)u=\Delta u+\nabla P+n\...

The Fourier extension conjecture in $n\geq 2$ dimensions is, \begin{equation*} \left\Vert \widehat{fd\sigma _{n-1}}\right\Vert _{L^{p}\left( \mathbb{R}% ^{n}\right) }\leq C_{p}\left\Vert f\right\Vert _{L^{p}\left( \sigma _{n-1}\right) },\ \text{for }f\in L^{p}\left( \sigma _{n-1}\right) \text{ and }p>\frac{2n}{n-1}, \end{equation*} where $\sigma _{...

Prime numbers [See 1-7] are used especially in information technology, such as public-key cryptography , and recall that the distribution of prime numbers is closely related to the non-trivial zeros of the zeta function therefore related to the Riemann hypothesis. Here I introduce the function $\circledS$: $ (X,z) \longmapsto \prod_{p\in\mathcal{P...

Let f be a function defined on the real line, and {T}_{f} be the corresponding superposition operator which maps h to {T}_{f}\left(h) , i.e., {T}_{f}\left(h)=f\circ h . In this article, the sufficient and necessary conditions such that {T}_{f} maps periodic Hölder-Lipschitz spaces {H}_{p}^{\alpha } into itself with 0\lt \alpha \lt \frac{1}{p} and \...

This manuscript presents set-theoretical solutions to the Yang-Baxter equation within the framework of GE-algebras by constructing mappings that satisfy the braid condition and exploring the algebraic properties of GE-algebras. Detailed proofs and the use of left and right translation operators are provided to analyze these algebraic interactions,...

We present analytical results for the joint probability distribution $P(T_{FR}=t,S=s)$ of first return (FR) times t and of the number of distinct sites s visited by a random walk (RW) on a one dimensional lattice before returning to the origin. The RW on a one dimensional lattice is recurrent, namely the probability to return to the origin is $P_{R...

Shale gas reservoirs have a large amount of resources, a wide range of burial, and great development potential. In order to evaluate the elastic properties of the shale, elastic wave velocity and anisotropy measurements of Longmaxi shale samples were carried out in the laboratory. Combined with the results of back scattering scanning electron micro...

Earthquakes are known to be induced by a variety of anthropogenic causes, such as hydraulic fracturing. In the Neuquén Basin of Argentina, hydraulic fracturing has been used to produce hydrocarbons trapped in the shales of the Vaca Muerta Formation. Correspondingly, incidences of seismicity there have in- creased. We collect information on well sti...

We develop a method to evaluate the partition function and energy density of a massive scalar on a 2-sphere of radius $r$ and at finite temperature $\beta$ as power series in $\frac{\beta}{r}$. Each term in the power series can be written in terms of polylogarithms. We use this result to obtain the gap equation for the large $N$, critical $O(N)$ mo...

For an arbitrary dimension n$n$, we study: the polyharmonic Gaussian field hL$h_L$ on the discrete torus TLn=1LZn/Zn$\mathbb {T}^n_L = \frac{1}{L} \mathbb {Z}^{n} / \mathbb {Z}^{n}$, that is the random field whose law on RTLn$\mathbb {R}^{\mathbb {T}^{n}_{L}}$ given by cne−bn(−ΔL)n/4h2dh,$$\begin{equation*} \hspace*{-4.5pc}c_n\, \text{e}^{-b_n{\lef...

This paper investigates nonlinear Landau damping in the 3D Vlasov-Poisson (VP) system. We study the asymptotic stability of the Poisson equilibrium $\mu(v)=\frac{1}{\pi^2(1+|v|^2)^2}$ under small perturbations. Building on the foundational work of Ionescu, Pausader, Wang, and Widmayer \cite{AIonescu2022}, we provide a streamlined proof of nonlinear...

For a sequence of vectors $\{v_n\}_{n\in\mathbb{N}}$ in the uniformly convex Banach space $X$ which for all $n, m\in \mathbb{N}$ satisfy $\|v_{n+m}\|\le \|v_n + v_m\|$ we show the existence of the limit $\lim_{n\to \infty} \frac{v_n}{n}$. This extends the classical Fekete's subadditivite lemma to Banach space-valued sequences.

We investigate normalized solutions for a class of nonlinear Schr\"{o}dinger (NLS) equations with potential $V$ and inhomogeneous nonlinearity $g(|u|)u=|u|^{q-2}u+\beta |u|^{p-2}u$ on a bounded domain $\Omega$. Firstly, when $2+\frac{4}{N}<q<p\leq2^*:=\frac{2N}{N-2}$ and $\beta=-1$, under an explicit smallness assumption on $V$, we prove the existe...

Consider the energy per particle on the lattice given by $\min_{ \Lambda }\sum_{ \mathbb{P}\in \Lambda} \left|\mathbb{P}\right|^4 e^{-\pi \alpha \left|\mathbb{P}\right|^2 }$, where $\alpha >0$ and $\Lambda$ is a two dimensional lattice. We prove that for $\alpha\geq\frac{3}{2}$, among two dimensional lattices with unit density, such energy minimum...

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S\subseteq V(G)$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepack...

Oil and natural gas (ONG) extraction emits volatile organic compounds (VOCs). Certain VOCs are identified as hazardous air pollutants (HAPS) while others contribute to ozone formation. This study examines the impact of ONG operations on VOC levels during the development of multi-well ONG pads in suburban Broomfield, Colorado. From October 2018 to D...

This paper is devoted to investigating Freidlin–Wentzell’s large deviation principle for one (spatial) dimensional nonlinear stochastic wave equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemar...

Multistage horizontal fracturing technology of reservoirs has been widely used to enhance tight hydrocarbon resource recovery. Determining the proper perforation cluster spacing is crucial to developing a complex fracture network that connects natural rock fractures and facilitates gas flow in reservoirs. The stress shadow effect that occurs betwee...

The immiscible multiphase fluid flow in intact and fractured porous media is relevant to numerous engineering sectors, including industrial processes, geo‐engineering, and civil engineering. These encompass crucial applications that pose significant challenges in modeling, such as carbon dioxide () storage in underground reservoirs, contaminant tra...

The North Kuwait region has been facing with a range of challenges related to inconsistent drilling downtime and varying sealing conditions caused by abnormal pore pressure. In order to address these issues effectively, a comprehensive analysis was conducted using image logs, well cores, and seismic data collected from 23 wells in the Sabriyah fiel...

For given k-uniform hypergraphs \({\mathcal {G}}\) and \({\mathcal {H}}\), the Ramsey number \(R({\mathcal {G}},{\mathcal {H}})\) is the smallest positive integer N such that in every red-blue coloring of the edges of the complete k-uniform hypergraph on n vertices there is either a red copy of \({\mathcal {G}}\) or a blue copy of \({\mathcal {H}}\...

We obtain Riesz transform bounds and characterise operator-adapted Hardy spaces to solve boundary value problems for singular Schr\"odinger equations $-\mathrm{div}(A\nabla u)+aVu=0$ in the upper half-space $\mathbb{R}^{1+n}_{+}$ with boundary dimension $n\geq 3$. The coefficients $(A,a,V)$ are assumed to be independent of the transversal direction...

Suppose that $A \subset \{1,\dots, N\}$ has no two elements differing by a square. Then $|A| \ll N e^{-(\log N)^c}$ for any $c < \frac{1}{4}$.

The object of this work is to study the trichotomy dynamics of fractional heat equation with critical exponent in \({\mathbb {R}}^{n}\) where \(4s<n<6s,\) \(0<s<1.\) For \(t_{0}\) sufficiently large, we construct the positive solution, which is smooth and globally defined in time, provided that the initial value satisfies \(u_{0}(x)\sim |x|^{-\gamm...

In this paper, we give the first rigorous justification of the Benjamin-Ono equation: as an internal water wave model on the physical time scale. Here, \({\varepsilon }\) is a small parameter measuring the weak nonlinearity of the waves, \(\mu \) is the shallowness parameter, and \(\gamma \in (0,1)\) is the ratio between the densities of the two fl...

In 1971 Cusick proved that every real number $x\in[0,1]$ can be expressed as a sum of two continued fractions with no partial quotients equal to $1$. In other words, if we define a set $$ S(k):= \{ x\in[0,1] : a_n(x) \geq k \text{ for all } n\in\mathbb{N} \}, $$ then $$ S(2)+S(2) = [0,1]. $$ He also conjectured that this result is unique in the sen...

We revisit Euler's partition function recurrence, which asserts, for integers $n\geq 1,$ that $$ p(n)=p(n-1)+p(n-2)-p(n-5)-p(n-7)+\dots = \sum_{k\in \mathbb{Z}\setminus \{0\}} (-1)^{k+1} p(n-\omega(k)), $$ where $\omega(m):=(3m^2+m)/2$ is the $m$th pentagonal number. We prove that this classical result is the $\nu=0$ case of an infinite family of `...

Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second law of thermodynamics, the strain equivalence principle, the non-associated...

The magnetic moment of a hadron is an important spectroscopic parameter as its mass and encodes valuable information about its internal structure. In this present study, we systematically study magnetic moments of the $P_{c}(4457)$ and its related hidden-charm pentaquark states with and without strangeness employing a comprehensive analysis that en...

In the development of unconventional shale play, simulation of the performance for wells needs to incorporate sufficient complexity in geology to take fully into account the variabilities in petrophysical and geomechanical properties. These parameters controlling the effective stimulated rock volume (eSRV) represent the heterogeneity and strong-lay...

In this paper, we propose an adaptive time filter algorithm for the 2D/3D unsteady triple‐porosity Stokes model arising in super‐hydrophobic proppant modification in hydraulic fracturing systems. The time filter algorithm with variable time steps is given, which can improve the time accuracy from the first order to the second order without increasi...

In this paper, we obtain some exact $L_2$ Bernstein-Markov inequalities for generalized Hermite and Gegenbauer weight. More precisely, we determine the exact values of the extremal problem $$M_n^2(L_2(W_\lambda),{\rm D}):=\sup_{0\neq p\in\mathcal{P}_n}\frac{\int_I\left|{\rm D} p(x)\right|^2W_\lambda(x){\rm d}x}{\int_I| p(x)|^2W_\lambda(x){\rm d}x},...

We investigate the stability of persistence diagrams \( D \) under non-uniform scaling transformations \( S \) in \( \mathbb{R}^n \). Given a finite metric space \( X \subset \mathbb{R}^n \) with Euclidean distance \( d_X \), and scaling factors \( s_1, s_2, \ldots, s_n > 0 \) applied to each coordinate, we derive explicit bounds on the bottleneck...

Given a graph $G$, its Hall ratio $\rho(G)=\max_{H\subseteq G}\frac{|V(H)|}{\alpha(H)}$ forms a natural lower bound on its fractional chromatic number $\chi_f(G)$. A recent line of research studied the fundamental question of whether $\chi_f(G)$ can be bounded in terms of a (linear) function of $\rho(G)$. In a breakthrough-result, Dvo\v{r}\'{a}k, O...

We study shortest curves in proximally smooth subset of a finite or infinite dimensional Hilbert space. We consider an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R$...

The disc cutter is the core component of a tunnel boring machine (TBM), whose performance is related to the safety and efficiency of tunnel construction. The accurate performance prediction of the disc cutter is crucial. In this paper, a new rolling force and normal force prediction model is proposed. The model considers the effect of the curvature...

The current mindset in the upstream oil and gas industry is that unconventional reservoirs such as shales and tight gas sands need to be hydraulically fractured because they have very low permeability and are unable to produce naturally. If that premise were true, then why were shale reservoirs such as the Monterey in California and the Marcellus s...

In this paper, we study a class of eigenvalue problems involving both local as well as nonlocal operators, precisely the classical Laplace operator and the fractional Laplace operator in the presence of mixed boundary conditions, that is \begin{equation} \label{1} \left\{\begin{split} \mathcal{L}u\: &= \lambda u,~~u>0~ \text{in} ~\Omega, u&=0~~\tex...

The aim of this work is to study (Multi-window) Gabor systems in the space \(\ell^2(\mathbb{Z} \times \mathbb{Z}, \mathbb{H})\), denoted by $\mathcal{G}(g,L,M,N)$, and defined by: \[ \left\{ (k_1,k_2)\in \mathbb{Z}^2\mapsto e^{2\pi i \frac{m_1}{M}k_1} g_l(k - nN) e^{2\pi j \frac{m_2}{M}k_2} \right\}_{l \in \mathbb{N}_L, (m_1, m_2) \in \mathbb{N}_M^...

A single planar hydraulic fracture is typically the primary component used to simulate hydraulic fracturing stimulation in conventional reservoirs. However, in ultra-low-permeability shale reservoirs, a large system of fracture networks must be generated to produce hydrocarbons economically. Therefore, traditional modeling approaches centered on si...

In this paper, we consider a Keller-Segel-Navier–Stokes system involving subquadratic logistic degradation: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{align...

The process $e^+e^-\to K^0_S K^0_S \psi(3686)$ is studied by analyzing $e^+e^-$ collision data samples collected at eight center-of-mass energies ranging from 4.682 to 4.951 GeV with the BESIII detector operating at the BEPCII collider, corresponding to an integrated luminosity of $4.1~{\rm fb}^{-1}$. Observation of the $e^+e^-\to K^0_S K^0_S \psi(...

In 1914, Ramanujan presented a collection of 17 elegant and rapidly converging formulae for $\pi$. Among these, one of the most celebrated is the following series: \[\frac{1}{\pi}=\frac{2\sqrt{2}}{9801}\sum_{n=0}^{\infty}\frac{26390n+1103}{\left(n!\right)^4}\cdot \frac{\left(4n\right)!}{396^{4n}}\] In this paper, we give a proof of this classic for...

Wave surging, fracking operations, and tides can cause seepage flow with hydraulic gradient reversals, resulting in complex hydraulic conditions. These complex hydraulic conditions can lead to more intricate suffusion processes, affecting the movement and loss of fine particles, and thereby weakening the internal stability of hydraulic structures....

Coal, a vital strategic resource, facilitates industrial development and socio-economic progress. Ensuring the high-quality development of the coal industry is crucial for national energy security and safety. Coal and gas outbursts are frequent hazards in coal mining processes. This research delves into the impact of heterogeneous coal seam strengt...

This paper deals with the long-term behavior of positive solutions for the following parabolic-elliptic chemotaxis competition system with weak singular sensitivity and logistic source \begin{equation} \label{abstract-eq} \begin{cases} u_t=\Delta u-\chi \nabla\cdot (\frac{u}{v^{\lambda}} \nabla v) +ru- \mu u^2, \quad &x\in \Omega,\cr 0=\Delta v- \a...

In this study, we obtain the weighted Hardy-Adams inequality of any even dimension n\ge 4 . Namely, for u\in {C}_{0}^{\infty }\left({{\mathbb{B}}}^{n}) with \mathop{\int }\limits_{{{\mathbb{B}}}^{n}}{| {\nabla }^{\frac{n}{2}}u| }^{2}{\rm{d}}x-\mathop{\prod }\limits_{k=1}^{n/2}{\left(2k-1)}^{2}\mathop{\int }\limits_{{{\mathbb{B}}}^{n}}\frac{{u}^{2}}...

In this paper, we give an explicit formula for the rank of the $Q$-walk matrix of the Dynkin graph $A_n$. Moreover, we prove that its Smith normal form is $$ \mathrm{diag}\left( \underset{r=\lceil \frac{n}{2} \rceil}{\underbrace{1,2,2,...,2}},0,...,0 \right), $$ where $r$ is the rank of the $Q$-walk matrix $W_Q\left( A_n \right) $ of the Dynkin gra...

For the following quasilinear Choquard-type equation: -\Delta u-\Delta \left({u}^{2})u+V\left(x)u=\left({I}_{\mu }* {| u| }^{p}){| u| }^{p-2}u,\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N\ge 3,0\lt \mu \lt N , V\left(x)=a-\frac{b}{1+{| x| }^{2}} , 1\lt a\lt +\infty , 0\lt b\lt \frac{1}{2} , \frac{2\left(N+\mu )}{N}\lt p\lt \frac{2\left(N+\mu )}{N-2...

With the goal of better understanding stimulation in crystalline rock for improving enhanced geothermal systems (EGS), the EGS Collab Project performed a series of stimulations and flow tests at 1.25 and 1.5 km depths. The tests were performed in two well-instrumented testbeds in the Sanford Underground Research Facility in Lead, South Dakota, Unit...

We utilize a modulation restricted normal form approach to establish local well-posedness of the periodic Korteweg-de Vries equation in $H^s(\mathbb{T})$ for $s> -\frac23$. This work creates an analogue of the mKdV result by Nakanishi, Takaoka, and Tsutsumi for KdV, extending the currently best-known result of $s \geq -\frac12$ without utilizing th...

In the third part of this series of papers, we address the same Cauchy problem that was considered in part 1, namely the nonlocal Fisher-KPP equation in one spatial dimension, $u_t = D u_{xx} + u(1-\phi_T*u)$, where $\phi_T*u$ is a spatial convolution with the top hat kernel, $\phi_T(y) \equiv H\left(\frac{1}{4}-y^2\right)$, except that now we incl...

Due to the high flow resistance of shale oil and gas, creating artificial flow channels with high conductivity in shale formation was the main challenge for the development of shale oil and gas resources. To further understand the fracture propagation mechanism in shale formation, this paper proposed a global cohesive element method to simulate the...

Soliton solutions play a crucial role in modeling stable phenomena across optical communications, fluid dynamics, and plasma physics, owing to their stability and persistence in solving nonlinear equations. This study centers on the extended Sakovich equation, emphasizing the importance of soliton solutions in predicting and controlling localized w...

Using variational methods we prove the existence of nonnegative solutions for the following class of quasilinear problems given by: −div(|x|−ϒp|∇u|p−2∇u)+|x|−bp∗|u|p−2u=λ|x|−bp∗a(x)g(u)+γ|x|−bp∗|u|p∗−2uinRN, for the subcritical case (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \...

We extend the relativistic quantum solutions for heavy positronium of paper \cite{jxzj-pimuE} to a heavy protonium, i.e. a relativistic proton $p^*$ and antiproton $\bar{p}^*$ orbiting at about the speed of light $c$ under a formal Coulomb potential $\bar{V}_{c}$, in this paper. The $p^*,\bar{p}^*$ reduced masses in orbital $k =n$ (level), $n,l$ (s...

Recently, Jiang--Jiang (J. Differential Equations 282, 2021) showed the existence of unique strong solutions in spatial periodic domain (denoted by $\mathbb{T}^3$), whenever the elasticity coefficient is larger than the initial velocity perturbation of the rest state. Motivated by Jiang--Jiang's result, we revisit the Cauchy problem of the compress...

Based on a geology-engineering sweet spot evaluation, the high-quality reservoir zones and horizontal well landing points were determined. Subsequently, fracture propagation and production were simulated with a multilayer fracturing scenario. The optimal hydraulic fracturing strategy for the multilayer fracturing network was determined by introduci...

In this paper, for general curves $(t,\gamma(t))$ satisfying some suitable curvature conditions, we obtain some $L^p(\mathbb{R})\times L^q(\mathbb{R}) \rightarrow L^r(\mathbb{R})$ estimates for the bilinear fractional integrals $H_{\alpha,\gamma}$ along the curves $(t,\gamma(t))$, where $$H_{\alpha,\gamma}(f,g)(x):=\int_{0}^{\infty}f(x-t)g(x-\gamma...

In this paper, we study the almost sure well-posedness theory and orbital stability for the nonlinear Schr\"odinger equation with potential \begin{equation*} \left\{\begin{array}{l} i \partial_t u+\Delta u-V(x)u+|u|^{2}u=0,\ (x, t) \in \mathbb{R}^4 \times \mathbb{R}, \\ \left.u\right|_{t=0}=f \in H ^s(\mathbb{R}^4), \end{array}\right. \end{equation...

During thermal steam stimulation in the unconsolidated oilsands reservoir, fractures are often created to enhance injectivity. This process involves pressurizing and heating the reservoir, leading to changes in stress. The current understanding of the in-situ stress fields in mature oilsands reservoirs post thermal stimulation is limited, and the i...