Search

This paper is concerned with the time-asymptotic behavior of strong solutions to the initial-boundary value problem of the isothermal compressible fluid models of Korteweg type with density-depende...

We are concerned with the time-asymptotic behavior toward rarefaction waves for strong non-vacuum solutions to the Cauchy problem of the one-dimensional compressible Navier-Stokes equations with degenerate density-dependent viscosity. The case when the pressure p ( ρ ) = ρ γ and the viscosity coefficient μ ( ρ ) = ρ α for some parameters α , γ ∈ R is considered. For α ≥ 0 , γ ≥ max ⁡ { 1 , α } , if the initial data is assumed to be sufficiently regular, without vacuum and mass concentrations, we show that the Cauchy problem of the one-dimensional compressible Navier-Stokes equations admits a unique global strong non-vacuum solution, which tends to the rarefaction waves as time goes to infinity. Here both the initial perturbation and the strength of the rarefaction waves can be arbitrarily large. The proof is established via a delicate energy method and the key ingredient in our analysis is to derive the uniform-in-time positive lower and upper bounds on the specific volume.

This paper is concerned with the large-time behavior of solutions to the Cauchy problem of the one-dimensional compressible fluid models of Korteweg type with density- and temperature-dependent viscosity, capillarity, and heat conductivity coefficients, which models the motions of compressible viscous fluids with internal capillarity. We show that the combination of a viscous contact wave with two rarefaction waves is asymptotically stable with a large initial perturbation if the strength of the composite wave and the capillarity coefficient satisfy some smallness conditions. The proof is based on some refined L 2-energy estimates to control the possible growth of the solutions caused by the high nonlinearity of the system, the interactions of waves from different families and large data, and the key ingredient is to derive the uniform positive lower and upper bounds on the specific volume and the temperature.

This paper is concerned with the time-asymptotic behavior of strong solutions to an initial-boundary value problem of the compressible Navier-Stokes-Korteweg system on the half line $\mathbb{R}^+$. The asymptotic profile of the problem is shown to be a shifted viscous shock profile, which is suitably away from the boundary. Moreover, we prove that if the initial data around the shifted viscous shock profile and the strength of the shifted viscous shock profile are sufficiently small, then the problem has a unique global strong solution, which tends to the shifted viscous shock profile as time goes to infinity. The analysis is based on the elementary $L^2$-energy method and the key point is to deal with the boundary estimates.

Nitrogen-doped biochars derived from Phragmites australis (PA) were prepared using ammonium chloride (AC) and ammonium acetate (AA) as nitrogen sources by phosphoric acid activation via microwave assisted treatment. Their physicochemical properties, acid red 18 (AR18) adsorption performance and possible mechanisms were systematically evaluated. Nitrogen was successfully doped onto the biochar’s surface in the formation of pyrrole-N, pyridine-N and oxidized-N with pyridine-N being the major component (64%). The pH iep and basic foundational groups of the biochars increased consequently however their surface areas slightly decreased. The adsorption kinetic data were best fit to the pseudo-second order model and the equilibrium data were well simulated by Freundlich model for all biochars, indicating the important role of chemical interactions. The maximum AR18 adsorption capacities of PAB-AA and PAB-AC were 1.41 and 1.18 times higher compared with the non N-doped biochar, which were mainly attributed to the π-π EDA interaction between the pyridine-N and AR18 as revealed by the comparison of XPS analyses before and after AR18 adsorption. Meanwhile, other mechanisms such as pore filling effect, Lewis acid-base interaction, electrostatic attraction and hydrogen bonding also existed as demonstrated by BET, XPS and FTIR analyses.

Three organic acid ammoniums (ammonium succinate (AS), ammonium tartrate (AT) and ammonium citrate (AC)) were employed to modify Phragmites australis (PA)-based activated carbons during phosphoric acid activation via microwave irradiation to improve acid red 18 (AR 18) removals from aqueous solutions. The physicochemical properties of the modified (PAC-AS, PAC-AT and PAC-AC) and unmodified carbons (PAC) were systematically characterized. The nitrogen content, pHiep and basic foundational groups of the modified carbons increased however their surface areas decreased after modification. FTIR and XPS analyses revealed that N-containing groups such as NH, CONH and NH2 were effectively introduced on modified carbons' surfaces. Although PAC-AS and PAC-AT had lower surface area than PAC, their adsorption capacity were higher due to larger amount of N-containing groups. The adsorption kinetic data were simulated well by the Elovich equation and the equilibrium data were best fit to the Freundlich model for all PACs. The adsorption of AR 18 on PACs decreased with increasing pH values. The maximum AR 18 adsorption capacity followed an order of PAC-AS (115.93 mg/g) > PAC-AT (104.23 mg/g) > PAC (90.52 mg/g) > PAC-AC (57.99 mg/g), indicating that AS and AT are promising activating agents for activated carbons to improve their AR18 adsorption performances.

Electrochemical reduction of CO2 into chemical fuels is crucial to clean energy production and environment remediation. First-principles calculations are performed to elucidate reaction mechanism of CO2 reduction to formic acid on Ni-based catalysts. The origin of CO poisoning is examined and a novel design strategy is proposed to eliminate CO poisoning. Three design criteria are derived based on which computational screening is performed to identify several Ni-based near-surface-alloys (NSAs) with both high selectivity and reactivity. The effect of elastic strain on CO2 reduction is studied on these NSAs. We predict that Ni/Ti, Cu/Ni, and strained Cu/Ni NSAs could lead to highly selective and efficient production of formic acid.

First-principles calculations are performed to gain fundamental understanding of recently developed Al/graphite battery that exhibits well-defined discharge voltage plateaus, high cycling stability, and ultrafast rate performance. Crucial issues pertaining to the unprecedented performance of the battery are understood, and key controversies in literature with respect to the geometry and gallery height of the intercalant are resolved. The stage and atomic structure of the graphite intercalation compounds (GICs) are elucidated, in line with the experimental finding. It is revealed that the intercalants tend to be inserted at relative high densities with a charging potential profile and theoretical specific capacity that agree well with the experiment. Four stable GIC configurations are identified with essentially the same chemical potential for the intercalant, giving rise to charging potential plateaus. Low diffusion energy barriers of the intercalants are found, which underlie the ultrafast (dis)charging ...

Tin (Sn) is known to be a good catalyst for electrochemical reduction of CO2 to formate in 0.5 M KHCO3. But when a thin layer of SnO2 is coated over Cu nanoparticles, the reduction becomes Sn-thickness dependent: the thicker (1.8 nm) shell shows Sn-like activity to generate formate whereas the thinner (0.8 nm) shell is selective to the formation of CO with the conversion Faradaic efficiency (FE) reaching 93% at −0.7 V (vs reversible hydrogen electrode (RHE)). Theoretical calculations suggest that the 0.8 nm SnO2 shell likely alloys with trace of Cu, causing the SnO2 lattice to be uniaxially compressed and favors the production of CO over formate. The report demonstrates a new strategy to tune NP catalyst selectivity for the electrochemical reduction of CO2 via the tunable core/shell structure.

A new calcium-modified and starch-stabilized ferromanganese binary oxide (Ca-SFMBO) sorbent was fabricated with different Ca concentrations for the adsorption of arsenic (As) and cadmium (Cd) in water. The maximum As(III) and Cd(II) adsorption capacities of 1% Ca-SFMBO were 156.25 mg/g and 107.53 mg/g respectively in single-adsorption systems. The adsorption of As and Cd by the Ca-SFMBO sorbent was pH-dependent at values from 1 to 7, with an optimal adsorption pH of 6. In the dual-adsorbate system, the presence of Cd(II) at low concentrations enhanced As(III) adsorption by 33.3%, while the adsorption of As(III) was inhibited with the increase of Cd(II) concentration. Moreover, the addition of As(III) increased the adsorption capacity for Cd(II) up to two-fold. Through analysis by X-ray photoelectron spectroscopy (XPS) and Fourier-transform infrared spectroscopy (FTIR), it was inferred that the mechanism for the co-adsorption of Cd(II) and As(III) included both competitive and synergistic effects, which resulted from the formation of ternary complexes. The results indicate that the Ca-SFMBO material developed here could be used for the simultaneous removal of As(III) and Cd(II) from contaminated water.

This paper is concerned with the global existence and large time behavior of strong solutions to the Cauchy problem of one-dimensional compressible isentropic micropolar fluid model with density-dependent viscosity and microviscosity coefficients, where the far-fields of the initial data are prescribed to be different. The pressure p ( ρ ) = ρ γ and the viscosity coefficient μ ( ρ ) = ρ α for some parameters α , γ ∈ R are considered. For the case when the corresponding Riemann problem of the resulting Euler equations admits two rarefaction waves solutions, it is shown that if the parameters α and γ satisfy some conditions and the initial data is sufficiently regular, without vacuum and mass concentrations, then the Cauchy problem of the one-dimensional compressible micropolar fluid model has a unique global strong nonvacuum solution, which tends to a superposition of these two rarefaction waves as time goes to infinity. This result holds for arbitrarily large initial perturbation and large-amplitudes rarefaction waves. Moreover, the exponential time decay rate of the microrotation velocity ω ( t , x ) under large initial perturbation is also derived. The proof is given by an elaborate energy method and the key ingredient is to deduce the uniform-in-time lower and upper bounds on the specific volume.

We propose a multiscale computational framework to design core/shell nanoparticles (NPs) for oxygen reduction reaction (ORR). Essential to the framework are linear scaling relations between oxygen adsorption energy and surface strain, which can be determined for NP facets and edges from first-principles and multiscale QM/MM calculations, respectively. Based on the linear scaling relations and a microkinetic model, we can estimate ORR rates as a function of surface strain on core/shell NPs. Employing the multiscale framework, we have systematically examined the ORR activity on Pd-based core/shell NPs as a function of their shape, size, shell thickness, and alloy composition of the core. Three NP shapes—icosahedron, octahedron, and truncated octahedron—are explored, and the truncated octahedron is found to be the most active and the icosahedron is the least active. NixPd1–x@Pd NPs with high Ni concentrations and thin shells could exhibit higher ORR rates than the pure Pt(111) surface and/or Pt NPs. AgxPd1–x...

Surface engineering has proved effective in enhancing activities of CO2 reduction reaction (CO2RR) on Cu. However, predictive guidance is necessary for the surface engineering to reach its full potential. We propose that the generalized coordination number (GCN) can be used as a descriptor to characterize CO2RR on Cu surfaces. A set of linear scaling relations between the binding energy of CO2RR intermediates and GCN are established to construct a volcano-type coordination–activity plot and from which we can derive the theoretical overpotential limit on Cu surfaces. We predict that the dimerized (111) surface yields the lowest possible overpotential on Cu for CO2RR to methane, and surface engineering by creating adatoms could lower CO2RR overpotentials and simultaneously suppress the competing hydrogen evolution reaction.

We consider the large time behavior of a non-autonomous third grade fluid system, which could be viewed as a perturbation of the classical Navier-Stokes system. Under proper assumptions, we firstly prove that the family of processes generated by the problem admits a uniform attractor in the natural phase space. Then we prove the upper-semicontinuity of the uniform attractor when the perturbation tends to zero.

This paper is concerned with the large-time behavior of smooth non-vacuum solutions with large initial data to the Cauchy problem of the one-dimensional isothermal compressible fluid models of Korteweg type with the viscosity coefficient μ ( ρ ) = ρ α and the capillarity coefficient κ ( ρ ) = ρ β . Here α ∈ R and β ∈ R are some parameters. Depending on whether the far-fields of the initial data are the same or not, we prove that the corresponding Cauchy problem admits a unique global smooth solution which tends to constant states or rarefaction waves respectively, as time goes to infinity, provided that α and β satisfy some conditions. Note that the initial perturbation can be arbitrarily large. The proofs are given by the elementary energy method and Kanel’s technique (Kanel, 1968). Compared with former results in this direction obtained by Germain and LeFloch (2016), and Chen et al. (2015), the main novelties of this paper lie in the following: First, we obtain the global existence of smooth solutions with large data for some new varieties of parameters α and β . Second, the large-time behavior of smooth large solutions around constant states is established.

A field study was conducted to investigate the effect of Fe-based biochar application on the extractability and availability of Cd and As, as well as its impact on crop growth and yield under a two-years wheat-rice rotation system. The Fe-based biochar was applied to the soil at 1.5 and 3.0 t ha–1, manure compost was also applied as a comparison, as well as a non-treated control. The application of the Fe-based biochar significantly (p

We are concerned with the large time behavior of solutions to the Cauchy problem of the one-dimensional compressible micropolar fluid model without viscosity, where the far-field states of the initial data are prescribed to be different. If the corresponding Riemann problem of the compressible Euler system admits a contact discontinuity and two rarefaction waves solutions, we show that for such a non-viscous model, the combination of the viscous contact wave with two rarefaction waves is time-asymptotically stable provided that the strength of the composite wave and the initial perturbation are sufficiently small. The proof is given by an elementary $L^2$ energy method., 26pages. arXiv admin note: text overlap with arXiv:1712.09485

This paper is concerned with a singular limit for the one-dimensional compressible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie (2011) [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact discontinuity wave in the L∞-norm away from the discontinuity line at a rate of e 1 4 , as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie's convergence rate is improved to e 7 8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

The global solutions with large initial data for the isothermal compressible fluid models of Korteweg type has been studied by many authors in recent years. However, little is known of global large solutions to the nonisothermal compressible fluid models of Korteweg type up to now. This paper is devoted to this problem, and we are concerned with the global existence of smooth and non-vacuum solutions with large initial data to the Cauchy problem of the one-dimensional nonisothermal compressible fluid models of Korteweg type. The case when the viscosity coefficient $\mu(\rho)=\rho^\alpha$, the capillarity coefficient $\kappa(\rho)=\rho^\beta$, and the heat-conductivity coefficient $\tilde{\alpha}(\theta)=\theta^\lambda$ for some parameters $\alpha,\beta,\lambda\in \mathbb{R}$ is considered. Under some assumptions on $\alpha,\beta$ and $\lambda$, we prove the global existence and time-asymptotic behavior of large solutions around constant states. The proofs are given by the elementary energy method combined with the technique developed by Y. Kanel' \cite{Y. Kanel} and the maximum principle., Comment: 30pages