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A small open economy operates with a unionized import-competing sector and an informal “self-employed” sector. Productivity varies across people in the informal sector. The full-employment structure accommodates “underemployment or involuntary self-employment” in the flexible-wage informal sector. Protection increases the cost of capital and may increase the set of people who are involuntarily employed in the informal sector. Even if one ignores the consumption distortion effect of a tariff, the tariff may fail to be second-best because it may raise underemployment. Our results on tariff-reform are consistent with some recent empirical evidence.

We revisit the Heckscher-Ohlin-Samuelson model in the presence of labour market frictions a la Mortensen-Pissarides. Relaxing the assumption of the one-worker- one-firm matching rule, we show that the Stolper-Samuelson theorem and the Rybczynski theorem may not hold in specific circumstances. We also demonstrate that the Factor Price Equalization theorem is valid only for capital and unemployed labour across countries, but not for employed labour. In equilibrium, trade patterns are determined by countries' factor endowments and relative factor intensities in sectors (independent of factor intensities in production). Finally, our results suggest an additional explanation for the 'missing trade' phenomenon. JEL classification: F 16, J64

This paper empirically examines the degree of regional consumption risk-sharing in China. It finds that less risk-sharing is taking place across Chinese provinces than across US states and Canadian provinces, although its extent across the latter is somewhat higher than across the national boundaries of industrial countries. Specifically, about half of the fitted annual variation in provincial consumption growth is common to all Chinese provinces, compared with more than two-thirds (less than one-third) in the case of US states and Canadian provinces (G-7 countries). My estimates reveal that Chinese households would be willing to pay dearly to insure their consumption against idiosyncratic shocks.

We present a model of biopolymer gels that includes two types of elastic nonlinearities, stiffening under extension and softening (due to buckling) under compression, to predict the elastic anisotropy induced by both external as well as internal (e.g., due to cell contractility) stresses in biopolymer gels. We show how the stretch-induced anisotropy and the strain-stiffening nonlinearity increase both the amplitude and power-law range of transmission of internal, contractile, cellular forces, and relate this to recent experiments.

The hydrodynamic reciprocal theorem for Stokes flows is generalized to incorporate the Navier slip boundary condition, which can be derived from Onsager's variational principle of least energy dissipation. The hydrodynamic reciprocal relations and the Jeffery orbit, both of which arise from the motion of a slippery anisotropic particle in a simple viscous shear flow, are investigated theoretically and numerically using the fluid particle dynamics method [Phys. Rev. Lett. 85, 1338 (2000)]. For a slippery elliptical particle in a linear shear flow, the hydrodynamic reciprocal relations between the rotational torque and the shear stress are studied and related to the Jeffery orbit, showing that the boundary slip can effectively enhance the anisotropy of the particle. Physically, by replacing the no-slip boundary condition with the Navier slip condition at the particle surface, the cross coupling between the rotational torque and the shear stress is enhanced, as manifested through a dimensionless parameter in both of the hydrodynamic reciprocal relations and the Jeffery orbit. In addition, simulations for a circular particle patterned with portions of no-slip and Navier slip are carried out, showing that the particle possesses an effective anisotropy and follows the Jeffery orbit as well. This effective anisotropy can be tuned by changing the ratio of no-slip portion to slip potion. The connection of the present work to nematic liquid crystals' constitutive relations is discussed.

In order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described in the presence of capillarity, wettability, and mixing effects. In the present work, we apply Onsager's variational principle to the formulation of thin film hydrodynamics for binary fluid mixtures. We first derive the dynamic equations in two spatial dimensions, one along the substrate and the other normal to the substrate. Then, using long-wave asymptotics, we derive the thin film equations in one spatial dimension along the substrate. This enables us to establish the connection between the present variational approach and the gradient dynamics formulation for thin films. It is shown that for the mobility matrix in the gradient dynamics description, Onsager's reciprocal symmetry is automatically preserved by the variational derivation. Furthermore, using local hydrodynamic variables, our variational approach is capable of introducing diffusive dissipation beyond the limit of dilute solute. Supplemented with a Flory-Huggins-type mixing free energy, our variational approach leads to a thin film model that treats solvent and solute in a symmetric manner. Our approach can be further generalized to include more complicated free energy and additional dissipative processes.

Great achievements have been attained in agricultural production of China, while there are still many difficulties and challenges ahead that call for put more efforts to overcome to guarantee food security and protect environment simultaneously. Analyzing yield gap and nutrient use efficiency will help develop and inform agricultural policies and strategies to increase grain yield. On-farm datasets from 2001 to 2012 with 1,971 field experiments for maize (Zea mays L.) were collected in four maize agro-ecological regions of China, and the optimal management (OPT), farmers’ practice (FP), a series of nutrient omission treatments were used to analyze yield gap, nutrient use efficiency and indigenous nutrient supply by adopting meta-analysis and ANOVA analysis. Across all sites, the average yield gap between OPT and FP was 0.7 t ha-1, the yield response to nitrogen (N), phosphorus (P), and potassium (K) were 1.8, 1.0, and 1.2 t ha-1, respectively. The soil indigenous nutrient supply of N, P, and K averaged 139.9, 33.7, and 127.5 kg ha-1, respectively. As compared to FP, the average recovery efficiency (RE) of N, P, and K with OPT increased by percentage point of 12.2, 5.5, and 6.5, respectively. This study indicated that there would be considerable potential to further improve yield and nutrient use efficiency in China, and will help develop and inform agricultural policies and strategies, while some management measures such as soil, plant and nutrient are necessary and integrate with advanced knowledge and technologies.

This paper investigates the degree and the evolution of business cycle synchronization between Hong Kong SAR and Mainland China, as well as Hong Kong SAR and the United States with a two-step procedure. A structural VAR model is first set up to capture the dynamics of shocks to different regions. Then a state-space model is used to gauge the degree of symmetry of regional shocks, and to examine whether business cycles have been more synchronized over time. Our results cast doubt on the feasibility of a currency union between Hong Kong and Mainland China in the foreseeable future.

We illustrate that a statistical model can be used to gauge the degree of market integration. The model is applied to the case of China, which is undergoing transition from a central planning to a market economy and there is a growing interest as to the evolution of its market integration.

This paper analyzes the pattern of provincial economic integration in China for the period 1991–1998 by means of an error-components model that decomposes provincial sectoral real value-added growth into common national effects, industry-specific effects, and province-specific effects. We find significant comovements in the long run, although province-specific factors still account for one-third of the variance of real output growth in the short run. The results suggest that although economic integration of the Chinese provinces has progressed under reform, it is by no means complete.

Estimating balanced nutrient requirements for soybean (Glycine max [L.] Merr) in China is essential for identifying optimal fertilizer application regimes to increase soybean yield and nutrient use efficiency. We collected datasets from field experiments in major soybean planting regions of China between 2001 and 2015 to assess the relationship between soybean seed yield and nutrient uptake, and to estimate nitrogen (N), phosphorus (P), and potassium (K) requirements for a target yield of soybean using the quantitative evaluation of the fertility of tropical soils (QUEFTS) model. The QUEFTS model predicted a linear-parabolic-plateau curve for the balanced nutrient uptake with a target yield increased from 3.0 to 6.0 t ha-1 and the linear part was continuing until the yield reached about 60-70% of the potential yield. To produce 1000 kg seed of soybean in China, 55.4 kg N, 7.9 kg P, and 20.1 kg K (N:P:K = 7:1:2.5) were required in the above-ground parts, and the corresponding internal efficiencies (IE, kg seed yield per kg nutrient uptake) were 18.1, 126.6, and 49.8 kg seed per kg N, P, and K, respectively. The QUEFTS model also simulated that a balanced N, P, and K removal by seed which were 48.3, 5.9, and 12.2 kg per 1000 kg seed, respectively, accounting for 87.1%, 74.1%, and 60.8% of the total above-ground parts, respectively. These results were conducive to make fertilizer recommendations that improve the seed yield of soybean and avoid excessive or deficient nutrient supplies. Field validation indicated that the QUEFTS model could be used to estimate nutrient requirements which help develop fertilizer recommendations for soybean.

Inappropriate fertiliser applications have caused a series of environmental problems and threaten the sustainable production of rice in China. The aim of this study was to evaluate the effects of a new approach, Nutrient Expert (NE), a nutrient decision support tool for rice (Oryza sativa L.). Experimental validation was carried out under field conditions from 2013 to 2015 at 211 sites in the main rice-growing regions of China. The results showed that, compared with current farmers’ fertiliser practices (FP) and soil testing (ST), the NE approach balanced nutrient application – decreased the nitrogen (N) and potassium (K) rates, and increased the phosphorus (P) rate – and improved grain yield, nutrient uptake, and fertiliser use efficiency. The NE treatment produced a 3.5–6.3% higher grain yield, 2.3–14.2% higher N, P, and K uptake in aboveground plant dry matter, and higher agronomic efficiency, apparent recovery efficiency (RE), and partial factor productivity of applied N and K, but not for P. In particular, the RE of the NE approach was greater by 12.2 and 8.4 percentage points for N, 3.7 and 2.9 percentage points for P, and 16.3 and 6.4 percentage points for K, compared with FP and ST respectively. The results obtained from field validation suggested that the NE approach could predict target yields; nutrient uptake of N, P, and K within specific ranges; and could be used as a tool to make fertiliser recommendation for rice in China.

Engineering surfaces that promote rapid drop detachment is of importance to a wide range of applications including anti-icing, dropwise condensation6, and self-cleaning. Here we show how superhydrophobic surfaces patterned with lattices of submillimetre-scale posts decorated with nano-textures can generate a counter-intuitive bouncing regime: drops spread on impact and then leave the surface in a flattened, pancake shape without retracting. This allows for a four-fold reduction in contact time compared to conventional complete rebound. We demonstrate that the pancake bouncing results from the rectification of capillary energy stored in the penetrated liquid into upward motion adequate to lift the drop. Moreover, the timescales for lateral drop spreading over the surface and for vertical motion must be comparable. In particular, by designing surfaces with tapered micro/nanotextures which behave as harmonic springs, the timescales become independent of the impact velocity, allowing the occurrence of pancake bouncing and rapid drop detachment over a wide range of impact velocities., Comment: 11 pages, 4 figures, 31 references, + 5 pages of supplementary information

We numerically investigate the pool boiling of one-component fluids with a focus on the effects of surface wettability on the single-bubble dynamics. We employed the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], a diffuse-interface model for liquid-vapor flows involving liquid-vapor transition in nonuniform temperature fields. We first perform simulations for bubbles on homogeneous surfaces. We find that an increase in either the contact angle or the surface superheating can enhance the bubble spreading over the heating surface and increase the bubble departure diameter as well and therefore facilitate the transition into film boiling. We then examine the dynamics of bubbles on patterned surfaces, which incorporate the advantages of both hydrophobic and hydrophilic surfaces. The central hydrophobic region increases the thermodynamic probability of bubble nucleation while the surrounding hydrophilic region hinders the continuous bubble spreading by pinning the contact line at the hydrophobic-hydrophilic intersection. This leads to a small bubble departure diameter and therefore prevents the transition from nucleate boiling into film boiling. With the bubble nucleation probability increased and the bubble departure facilitated, the efficiency of heat transfer on such patterned surfaces is highly enhanced, as observed experimentally [Int. J. Heat Mass Transfer 57, 733 (2013)]. In addition, the stick-slip motion of contact line on patterned surfaces is demonstrated in one-component fluids, with the effect weakened by surface superheating.

This paper examines empiricallywhether more stringent domestic environmental policiesreduce the international competitiveness ofenvironmentally sensitive goods (ESGs). Our timeseries evidence indicates that there are no systematicchanges in trade patterns of ESGs in the last threedecades, despite the introduction of more stringentenvironmental regulations in most of the developedcountries in the 1970s and 1980s. This observedphenomenon is then subjected to a multi-countryeconometric test using an extended gravity-equationframework. The test suggests that, overall, morestringent environmental regulations do not reducetotal exports, exports of ESGs and exports ofnon-resource-based ESGs. Neither was there anyevidence to support the hypothesis that new tradebarriers emerge to offset the effects of morestringent environmental regulations.

This paper examines the effects of environmental regulations on the international competitiveness of domestic industries. A generalised GDP function, which incorporates both technology changes and increasing returns to scale is set up and a flexible translog function form is used to approximate this GDP function. A seemingly unrelated regression estimation technique is employed to estimate a system of sectoral share equations derived from the generalised GDP function. The basic hypothesis is that while the environmental factor is not a significant determinant of the international competitiveness of environmentally sensitive industries, technology is. The result supports this hypothesis and suggests that so-called eco-dumping is not an effective strategy in this context.

In this paper I examine whether stringent environmental standards reduce the international competitiveness of environmentally sensitive industries using a comprehensive dataset of trade flows of environmentally sensitive goods (ESGs) disaggregated at the four-digit level of the Standard International Trade Classification. The data relate 1965–95 and cover 34 countries, accounting for nearly 80% of world exports of ESGs in 1995. I find that export performance of ESGs for most countries remained unchanged between the 1960s and 1990s, despite the introduction of stringent environmental standards in most developed countries in the 1970s and 1980s.

In order to make clear the recent status and trend of wheat (Triticum aestivum L.) production in China, datasets from multiple field experiments and published literature were collected to study the agronomic characteristics related to grain yield, fertilizer application and nutrient use efficiency from the year 2000 to 2011. The results showed that the mean grain yield of wheat in 2000–2011 was 5950 kg/ha, while the N, P2O5 and K2O application rates were 172, 102 and 91 kg/ha on average, respectively. The decrease in N and P2O5 and increase in K2O balanced the nutrient supply and was the main reason for yield increase. The partial factor productivity (PFP, kg grain yield produced per unit of N, P2O5 or K2O applied) values of N (PFP-N), P (PFP-P) and K (PFP-K) were in the ranges of 29.5~39.6, 43.4~74.9 and 44.1~76.5 kg/kg, respectively. While PFP-N showed no significant changes from 2000 to 2010, both PFP-P and PFP-K showed an increased trend over this period. The mean agronomic efficiency (AE, kg grain yield increased per unit of N, P2O5 or K2O applied) values of N (AEN), P (AEP) and K (AEK) were 9.4, 10.2 and 6.5 kg/kg, respectively. The AE values demonstrated marked inter-annual fluctuations, with the amplitude of fluctuation for AEN greater than those for AEP and AEK. The mean fertilizer recovery efficiency (RE, the fraction of nutrient uptake in aboveground plant dry matter to the nutrient of fertilizer application) values of N, P and K in the aboveground biomass were 33.1%, 24.3% and 28.4%, respectively. It was also revealed that different wheat ecological regions differ greatly in wheat productivity, fertilizer application and nutrient use efficiency. In summary, it was suggested that best nutrient management practices, i.e. fertilizer recommendation applied based on soil testing or yield response, with strategies to match the nutrient input with realistic yield and demand, or provided with the 4R’s nutrient management (right time, right rate, right site and right fertilizer) should be adopted widely to improve the yield production and nutrient use efficiency.

Using a continuum model capable of describing the one-component liquid-gas hydrodynamics down to the contact line scale, we carry out numerical simulation and physical analysis for the droplet motion driven by thermal singularity. For liquid droplets in one-component fluids on heated or cooled substrates, the liquid-gas interface is nearly isothermal. Consequently, a thermal singularity occurs at the contact line and the Marangoni effect due to temperature gradient is suppressed. Through evaporation or condensation in the vicinity of the contact line, the thermal singularity makes the contact angle increase with the increasing substrate temperature. This effect on the contact angle can be used to move the droplets on substrates with thermal gradients. Our numerical results for this kind of droplet motion are explained by a simple fluid dynamical model at the droplet length scale. Since the mechanism for droplet motion is based on the change of contact angle, a separation of length scales is exhibited through a comparison between the droplet motion induced by a wettability gradient and that by a thermal gradient. It is shown that the flow field at the droplet length scale is independent of the statics or dynamics at the contact line scale.

Droplet motion on solid substrates has been widely studied not only because of its importance in fundamental research but also because of its promising potentials in droplet-based devices developed for various applications in chemistry, biology, and industry. In this paper, we investigate the motion of an evaporating droplet in one-component fluids on a solid substrate with a wettability gradient. As is well known, there are two major difficulties in the continuum description of fluid flows and heat fluxes near the contact line of droplets on solid substrates, namely, the hydrodynamic (stress) singularity and thermal singularity. To model the droplet motion, we use the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)] for the hydrodynamic equations in the bulk region, supplemented with the boundary conditions at the fluid-solid interface. In this continuum hydrodynamic model, various physical processes involved in the droplet motion can be taken into account simultaneously, e.g., phase transitions (evaporation or condensation), capillary flows, fluid velocity slip, and substrate cooling or heating. Due to the use of the phase field method (diffuse interface method), the hydrodynamic and thermal singularities are resolved automatically. Furthermore, in the dynamic van der Waals theory, the evaporation or condensation rate at the liquid-gas interface is an outcome of the calculation rather than a prerequisite as in most of the other models proposed for evaporating droplets. Numerical results show that the droplet migrates in the direction of increasing wettability on the solid substrates. The migration velocity of the droplet is found to be proportional to the wettability gradients as predicted by Brochard [Langmuir 5, 432 (1989)]. The proportionality coefficient is found to be linearly dependent on the ratio of slip length to initial droplet radius. These results indicate that the steady migration of the droplets results from the balance between the (conservative) driving force due to the wettability gradient and the (dissipative) viscous drag force. In addition, we study the motion of droplets on cooled or heated solid substrates with wettability gradients. The fast temperature variations from the solid to the fluid can be accurately described in the present approach. It is observed that accompanying the droplet migration, the contact lines move through phase transition and boundary velocity slip with their relative contributions mostly determined by the slip length. The results presented in this paper may lead to a more complete understanding of the droplet motion driven by wettability gradients with a detailed picture of the fluid flows and phase transitions in the vicinity of the moving contact line.

In two-phase flows, the interface intervening between the two fluid phases intersects the solid wall at the contact line. A classical problem in continuum fluid mechanics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a nonintegrable stress singularity. Recently, various diffuse-interface models have been proposed to explain the contact line motion using mechanisms missing from the sharp-interface treatments in fluid mechanics. In one-component two-phase (liquid-gas) systems, the contact line can move through the mass transport across the interface while in two-component (binary) fluids, the contact line can move through diffusive transport across the interface. While these mechanisms alone suffice to remove the stress singularity, the role of fluid slip at solid surface needs to be taken into account as well. In this paper, we apply the diffuse-interface modeling to the study of contact line motion in one-component liquid-gas systems, with the fluid slip fully taken into account. The dynamic van der Waals theory has been presented for one-component fluids, capable of describing the two-phase hydrodynamics involving the liquid-gas transition [A. Onuki, Phys. Rev. E 75, 036304 (2007)]. This theory assumes the local equilibrium condition at the solid surface for density and also the no-slip boundary condition for velocity. We use its hydrodynamic equations to describe the continuum hydrodynamics in the bulk region and derive the more general boundary conditions by introducing additional dissipative processes at the fluid-solid interface. The positive definiteness of entropy production rate is the guiding principle of our derivation. Numerical simulations based on a finite-difference algorithm have been carried out to investigate the dynamic effects of the newly derived boundary conditions, showing that the contact line can move through both phase transition and slip, with their relative contributions determined by a competition between the two coexisting mechanisms in terms of entropy production. At temperatures very close to the critical temperature, the phase transition is the dominant mechanism, for the liquid-gas interface is wide and the density ratio is close to 1. At low temperatures, the slip effect shows up as the slip length is gradually increased. The observed competition can be interpreted by the Onsager principle of minimum entropy production.

We extend the classic Balassa-Samuelson model to an environment with search unemployment. We show that the classic Balassa-Samuelson model with the assumption of full employment emerges as a special case of our more generalized model. In our generalized model, the degree of labor market rigidities affects the strength of the structural relationship between real exchange rate and sectoral productivity and in some circumstances, the standard Balassa-Samuelson effect may not hold. Empirical evidence supports our theory: controlling for the difference in labor market rigidities across countries provides a better fit in estimating the Balassa-Samuelson effect.

Following the huge Enron scandal that rocked the financial system of the United States, many firms were asked to restate their accounts by the regulatory authorities. We provide a theoretical model of overstatement in which managers inflate actual profits to attract share capital and shareholders find it too costly to monitor such action. We completely characterize such equilibrium and argue that more competitive industries are likely to discourage such earning manipulations. We also show that in case only some firms in an industry engage in such malpractice, the margin of manipulation will be greater. However, greater entry will reduce the extent of overstatement.

We extend the classic Balassa-Samuelson model to an environment with search unemployment. We show that the classic Balassa-Samuelson model with the assumption of full employment emerges as a special case of our more generalized model. In our generalized model, the degree of labor market rigidities affects the strength of the structural relationship between real exchange rate and sectoral productivity and in some circumstances, the standard Balassa-Samuelson effect may not hold. Empirical evidence supports our theory: controlling for the difference in labor market rigidities across countries provides a better fit in estimating the Balassa-Samuelson effect.

This paper analyzes the pattern of provincial economic integration in China for the period 1991−98 by means of an errorcomponents model that decomposes provincial sectoral real valueadded growth into common national effects, industry-specific effects and province-specific effects. We find significant comovements in the long run although province-specific factors still account for one-third of the variance of real output growth in the short run. After filtering out province-specific effects, we construct a hypothetical economy where provincial factors are removed. Most strikingly, we are able to trace out the nation’s business cycle during the 1990s using the disaggregate pooled dataset. JEL Classifications: E32, F15, O18, O53.

The effects of environmental regulations on the international competitiveness of domestic industries have become an increasing concern in the trade liberalisation process in the 1990s. This paper examines the significance of environmental policy for trade. A generalised GNP function, which incorporates both technology changes and increasing returns to scale is set up and a flexible translog function form is used to approximate this generalised GNP function. Seemingly unrelated regression is employed to estimate a system of sectoral share equations derived from the generalised GNP function. The basic hypothesis is that while the environmental factor is not a significant determinant of the international competitiveness of environmentally sensitive industries, technology is. The result supports this hypothesis and suggests that socalled eco-dumping is not an effective strategy in this context.

The effects of environmental regulations on the international competitiveness of domestic industries have become an increasing concern in the trade liberalisation process in the 1990s. This paper examines the significance of environmental policy for trade. A generalised GNP function, which incorporates both technology changes and increasing returns to scale is set up and a flexible translog function form is used to approximate this generalised GNP function. Seemingly unrelated regression is employed to estimate a system of sectoral share equations derived from the generalised GNP function. The basic hypothesis is that while the environmental factor is not a significant determinant of the international competitiveness of environmentally sensitive industries, technology is. The result supports this hypothesis and suggests that socalled eco-dumping is not an effective strategy in this context.

In this paper I examine whether stringent environmental standards reduce the international competitiveness of environmentally sensitive industries using a comprehensive dataset of trade flows of environmentally sensitive goods (ESGs) disaggregated at the four-digit level of the Standard International Trade Classification. The data relate to the period from 1965 to 1995 and cover 34 countries which accounted for nearly 80 per cent of world exports of ESGs in 1995. The important empirical finding is that export performance of ESGs for most of the countries remained unchanged between the 1960s and 1990s despite the introduction of stringent environmental standards in most developed countries in the 1970s and 1980s. Thus the claim that higher environmental standards reduce the international competitiveness of ESGs can not be justified in the light of available data.

For a one-component fluid on a solid substrate, a thermal singularity may occur at the contact line where the liquid-vapor interface intersects the solid surface. Physically, the liquid-vapor interface is almost isothermal at the liquid-vapor coexistence temperature in one-component fluids while the solid surface is almost isothermal for solids of high thermal conductivity. Therefore, a temperature discontinuity is formed if the two isothermal interfaces are of different temperatures and intersect at the contact line. This leads to the so-called thermal singularity. The localized hydrodynamics involving evaporation/condensation near the contact line leads to a contact angle depending on the underlying substrate temperature. This dependence has been shown to lead to the motion of liquid droplets on solid substrates with thermal gradients (Xu and Qian 2012 Phys. Rev. E 85 061603). In the present work, we carry out molecular dynamics (MD) simulations as numerical experiments to further confirm the predictions made from our previous continuum hydrodynamic modeling and simulations, which are actually semi-quantitatively accurate down to the small length scales in the problem. Using MD simulations, we investigate the motion of evaporative droplets in one-component Lennard-Jones fluids confined in nanochannels with thermal gradients. The droplet is found to migrate in the direction of decreasing temperature of solid walls, with a migration velocity linearly proportional to the temperature gradient. This agrees with the prediction of our continuum model. We then measure the effect of droplet size on the droplet motion. It is found that the droplet mobility is inversely proportional to a dimensionless coefficient associated with the total rate of dissipation due to droplet movement. Our results show that this coefficient is of order unity and increases with the droplet size for the small droplets (~10 nm) simulated in the present work. These findings are in semi-quantitative agreement with the predictions of our continuum model. Finally, we measure the effect of liquid-vapor coexistence temperature on the droplet motion. Through a theoretical analysis on the size of the thermal singularity, it can be shown that the droplet mobility decreases with decreasing coexistence temperature. This is observed in our MD simulations.

A continuum hydrodynamic model is presented for one-component liquid–gas flows on nonisothermal solid substrates. Numerical simulations are carried out for evaporative droplets moving on substrates with thermal gradients. For droplets in one-component fluids on heated/cooled substrates, the free liquid–gas interfaces are nearly isothermal. Consequently, a thermal singularity occurs at the contact line while the Marangoni effect due to interfacial temperature variation is suppressed. Through evaporation/condensation near the contact line, the thermal singularity makes the contact angle increase with the increasing substrate temperature. Due to this effect, droplets will move toward the cold end on substrates with thermal gradients. The droplet migration velocity is found to be proportional to the change of substrate temperature across the droplet. It follows that for two droplets of different sizes on a substrate with temperature gradient, the larger droplet moves faster and will catch up with the smaller droplet ahead. As soon as they touch, they coalesce rapidly into an even larger droplet that will move even faster.

Cet article analyse le modele d'integration economique provincial de la Chine pour la periode 1991 a 1998 a l'aide d'un modele qui decompose la croissance de la valeur ajoutee reelle sectorielle provinciale entre des effets nationaux communs, des effets specifiques a chaque industrie et des effets specifiques a chaque province. Nous obtenons des co-variations significatives a long terme, bien que des facteurs specifiques aux provinces comptent toujours pour environ un tiers de la variance de la croissance du produit reel a court terme. Les resultats suggerent que meme si l'integration des provinces chinoises a progresse durant les reformes, elle est indeniablement loin d'etre terminee.