Scaling laws of compressible turbulence

Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using a dimensional analysis. We apply the Barenblatt＇s incomplete similarity theory to both kinetic and density-weighted energy spectra. It shows that, within the initial subrange, both energy spectra approach the -5/3 and -2 power laws of the wavenumber when the Mach number tends to unity and infinity, respectively.

Incompatible deformation field and Riemann curvature tensor

Compatibility conditions of a deformation field in continuum mechanics have been revisited via two different routes. One is to use the deformation gradient, and the other is a pure geometric one. Variations of the displacement vector and the displacement density tensor are obtained explicitly in terms of the Riemannian curvature tensor. The explicit relations reconfirm that the compatibility condition is equivalent to the vanishing of the Riemann curvature tensor and reveals the non-Euclidean nature of the space in which the dislocated continuum is imbedded. Comparisons with the theory of Kr¨oner and Le-Stumpf are provided.

Thirty years of turbulence study in China

This paper provides a comprehensive introduction to the major progress in transition and turbulence studies in China over the past thirty years. Despite the author's best efforts, there are some unavoidable omissions. We expect that with the continued deepening of turbulence research, Chinese scholars will make increasing contributions in this field, which will certainly have strong influence on the establishment of a China School of Turbulence.

Corrigendum:incompatible deformation field and Riemann curvature tensor

The“Corollary 1”formulation in SUN,B.H.Incompatible deformation field and Riemann curvature tensor.Applied Mathematics and Mechanics(English Edition),38(3),311–332(2017)is corrected.It can be stated as follows:The symmetric part of the deformation gradient has no contribution to the trace of the displacement density

On Chien's question to the Hu-Washizu three-field functional and variational principle

There is an open question,namely Chien’s question,in construction of a generalized functional in elasticity,i.e.,why the stress-strain relation can still be derived from the Hu-Washizu generalized variational principle while the Lagrangian multiplier method is applied in vain?This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics.This investigation finds that as long as the functional has one of the combinations(A(ε_(ij))-σ_(ij)ε_(ij))or(B(σ_(ij))-σ_(ij)ε_(ij)),its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method.This research proves that the Hu-Washizu functionalΠ(u_(ij),ε_(ij),σ_(ij))is real three-field functional,and resolves the historic academic controversy on the issue of constructing a three-field functional.

Catalytic degradation of chlorinated volatile organic compounds(CVOCs)over Ce-Mn-Ti composite oxide catalysts

Developing industrially moldable catalysts with harmonized redox performance and acidity is of great significance for the efficient disposal of chlorinated volatile organic compounds(CVOCs)in actual exhaust gasses.Here,commercial TiO_(2),typically used for molding catalysts,was chosen as the carrier to fabricate a series of Ce_(0.02)Mn_(0-0.24)TiO_(x) materials with different Mn doping ratios and employed for chlorobenzene(CB)destruction.The introduction of Mn remarkedly facilitated the synergistic effect of each element via the electron transfer processes:Ce^(3+)+Mn^(4+/3+)■Ce^(4+)+Mn^(3+/2+)and Mn^(4+/3+)+Ti^(4+)■Mn^(3+/2+)+Ti^(3+).These synergistic interactions in Ce_(0.02)Mn_(0.04-0.24)TiO_(x),especially Ce_(0.02)Mn_(0.16)TiO_(x),significantly elevated the active oxygen species,oxygen vacancies and redox properties,endowing the superior catalytic oxidation of CB.When the Mn doping amount increased to 0.24,a separate Mn_(3)O_(4) phase appeared,which in turn might weaken the synergistic effect.Furthermore,the acidity of Ce_(0.02)Mn_(0.04-0.24)TiO_(x) was decreased with the Mn doping,regulating the balance of redox property and acidity.Notably,Ce_(0.02)Mn_(0.16)TiO_(x) featured relatively abundant B-acid sites.Its coordinating redox ability and moderate acidity promoted the deep oxidation of CB and RCOOH-intermediates,as well as the rapid desorption of Cl species,thus obtaining sustainable reactivity.In comparison,CeTiO_(x) owned the strongest acidity,however,its poor redox property was not sufficient for the timely oxidative decomposition of the easier adsorbed CB,resulting in its rapid deactivation.This finding provides a promising strategy for the construction of efficient commercial molding catalysts to decompose the industrial-scale CVOCs.

Unlocking single-atom catalysts via amorphous substrates

Single-atom catalysts(SACs)reveal great potential for application in catalysis due to their fully exposed active sites.In general,single atoms(SAs)and the coordination substrates need to have strong interactions or charge transfer to ensure the atomic dispersion,which requires the selection of a suitable substrate to stabilize the target atoms.Recent studies have demonstrated that amorphous materials with abundant defects and coordinatively unsaturated sites can be used as substrates for more efficient capturing SAs,further enhancing the catalytic performance.In this review,we discuss recent research progress of SAs loaded on amorphous substrates for enhanced catalytic activity.Firstly,we summarize the commonly used amorphous substrates for stabilizing SAs.Subsequently,we present several advanced applications of amorphous SACs in the field of catalysis,including electrocatalysis and photocatalysis.And then,we also clarify the synergistic mechanism between SAs and amorphous substrate on catalytic process.Finally,we summarize the challenges with our personal views and provide a critical outlook on how amorphous SACs continue to evolve.

Environmental impact and health risk assessment of volatile organic compound emissions during different seasons in Beijing

Volatile organic compounds(VOCs)are major contributors to air pollution.Based on the emission characteristics of 99 VOCs that daily measured at 10 am in winter from 15 December 2015 to 17 January 2016 and in summer from 21 July to 25 August 2016 in Beijing,the environmental impact and health risk of VOC were assessed.In the winter polluted days,the secondary organic aerosol formation potential(SOAP)of VOC(199.70±15.05 mg/m^3)was significantly higher than that on other days.And aromatics were the primary contributor(98.03%)to the SOAP during the observation period.Additionally,the result of the ozone formation potential(OFP)showed that ethylene contributed the most to OFP in winter(26.00%and 27.64%on the normal and polluted days).In summer,however,acetaldehyde was the primary contributor to OFP(22.00%and 21.61%on the normal and polluted days).Simultaneously,study showed that hazard ratios and lifetime cancer risk values of acrolein,chloroform,benzene,1,2-dichloroethane,acetaldehyde and 1,3-butadiene exceeded the thresholds established by USEPA,thereby presenting a health risk to the residents.Besides,the ratio of toluene-to-benzene indicated that vehicle exhausts were the main source of VOC pollution in Beijing.The ratio of m-/p-xylene-toethylbenzene demonstrated that there were more prominent atmospheric photochemical reactions in summer than that in winter.Finally,according to the potential source contribution function(PSCF)results,compared with local pollution sources,the spread of pollution from long-distance VOCs had a greater impact on Beijing.

Kepler＇s third law of n-body periodic orbits in a Newtonian gravitation field

One of the central and most vivid problems of celestial mechanics in the 18th and 19th centuries was the motion description of the Sun-Earth-Moon system under the Newtonian gravitation field（Figure 1（a））.Notable work was done by Euler（1760）,Lagrange（1776）,Laplace（1799）,Hamilton（1834）,Liouville（1836）,Jacobi（1843）,and Poincar′e（1889）[1]and Xia（1992）[2].

Singularity-free approximate analytical solution of capillary rise dynamics

Capillary rise is one of the most well-known and vivid illustrations of capillarity （shown in Figure 1）. Knowledge of capillarity laws is important in oil recovery, civil engineering, dyeing of textile fabrics, ink printing, and a variety of other fields. It is capillarity that brings water to the upper layer of soils, drives sap in plants, or lays the basis for the operation of pens [1-10].

Capillary wrinkling scaling laws of floating elastic thin film with a liquid drop

The deformation patterns of elastic membranes under tension is called wrinkling. Wrinkling, which is caused by capillary surface tension, is called capillary wrinkling （Figure 1）. In recent years wrinkling patterns have drawn particular at- tention [1-11], since it can be an useful tool to infer material parameters that might otherwise be inaccessible. For exam- ple, the commonly observed tearing instability of an elastic sheet, adhered to a rigid substrate, can be used to character- ize the adhesion energy.

Scaling laws of aquatic locomotion

In recent years studies of aquatic locomotion have provided some remarkable insights into the many features of fish swimming performances. This paper derives a scaling relation of aquatic locomotion CD(Re)~2 =(Sw)~2 and its corresponding log law and power law. For power scaling law,(Sw)~2 = β_nRe^((2-1)/n), which is valid within the full spectrum of the Reynolds number Re=UL/v from low up to high, can simply be expressed as the power law of the Reynolds number Re and the swimming number Sw=ωAL/v as Re ∝ (Sw)~σ,with σ=2 for creeping flows,σ=4/3 for laminar flows, σ=10/9 and σ=14/13 for turbulent flows. For log law this paper has derived the scaling law as Sw ∝ Re=(lnRe+1.287), which is even valid for a much wider range of the Reynolds number Re. Both power and log scaling relationships link the locomotory input variables that describe the swimmer's gait A;ω via the swimming number Sw to the locomotory output velocity U via the longitudinal Reynolds number Re, and reveal the secret input-output relationship of aquatic locomotion at different scales of the Reynolds number.

Simulation of crooked plate energy absorption structure under impact

Due to their simple structure,crooked plates are widely processed into energy absorption structures.There are obvious differences in the final deformation of crooked plates with different materials and dynamic conditions under the impact of constant-input kinetic energy.To better understand this phenomenon,we solved the Zhang-Yu equation with Maple software,obtained the law of generalized coordinates(rotation angle)of the energy absorber changing with time,and compared the energy absorption capacity of a crooked plate energy absorber under different parameters.To better understand how the motion of the energy absorber is affected by the change of parameters,we calculated the phase diagram of the energy absorber dynamics.After many numerical simulations,we found that the four-crooked plate energy absorber should have a mass-sensitive structure.We established the finite element model of dynamic buckling of mild steel and 6061-T6 aluminum alloy,and compared it with the Calladine-English dynamic experiment and Zhang-Yu rigid viscoplastic model.The results show that:(1)the Zhang-Yu rigid viscoplastic model has more guiding significance for mild steel(strain rate-sensitive material),and has greater error for 6061-T6 aluminum alloy(strain rate-insensitive material),and the prediction error further increases with the initial angle;and(2)by modifying the equivalent plastic length A of a plastic hinge according to the finite element model,the prediction accuracy of the Zhang-Yu rigid viscoplastic model can be improved.Our research results certain guiding significance for the design and manufacture of energy-absorbing structures of crooked plates.

New development in near-wall PIV measurements

Very recently,obvious advances have been made in fluid mechanics theoretically[1-6].The progress of experiment and related method is also worthy of attention.The detailed physics of a near-wall flow is essential for understanding theflow behavior. Very near-wall measurement is widely con- sidered as one of the major technical challenges for fluid me- chanics studies, which have a great significance for practical engineering designs and fundamental scientific researches.