Search results for: scalar implicature

Authors: Somnath Bhattacharyya

Abstract:

The mobile adsorbed surface charge on hydrophobic surfaces can modify the velocity slip condition as well as create a Marangoni stress at the interface. The functionalized hydrophobic walls of micro/nanopores, e.g., graphene nanochannels, may possess physio-sorbed ions. The lateral mobility of the physisorbed absorbed ions creates a friction force as well as an electric force, leading to a modification in the velocity slip condition at the hydrophobic surface. In addition, the non-uniform distribution of these surface ions creates a surface tension gradient, leading to a Marangoni stress. The impact of the mobile surface charge on streaming potential and electrochemical energy conversion efficiency in a pressure-driven flow of ionized liquid through the nanopore is addressed. Also, enhanced electro-osmotic flow through the hydrophobic nanochannel is also analyzed. The mean-filed electrokinetic model is modified to take into account the short-range non-electrostatic steric interactions and the long-range Coulomb correlations. The steric interaction is modeled by considering the ions as charged hard spheres of finite radius suspended in the electrolyte medium. The electrochemical potential is modified by including the volume exclusion effect, which is modeled based on the BMCSL equation of state. The electrostatic correlation is accounted for in the ionic self-energy. The extremal of the self-energy leads to a fourth-order Poisson equation for the electric field. The ion transport is governed by the modified Nernst-Planck equation, which includes the ion steric interactions; born force arises due to the spatial variation of the dielectric permittivity and the dielectrophoretic force on the hydrated ions. This ion transport equation is coupled with the Navier-Stokes equation describing the flow of the ionized fluid and the 3fourth-order Poisson equation for the electric field. We numerically solve the coupled set of nonlinear governing equations along with the prescribed boundary conditions by adopting a control volume approach over a staggered grid arrangement. In the staggered grid arrangements, velocity components are stored on the midpoint of the cell faces to which they are normal, whereas the remaining scalar variables are stored at the center of each cell. The convection and electromigration terms are discretized at each interface of the control volumes using the total variation diminishing (TVD) approach to capture the strong convection resulting from the highly enhanced fluid flow due to the modified model. In order to link pressure to the continuity equation, we adopt a pressure correction-based iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm, in which the discretized continuity equation is converted to a Poisson equation involving pressure correction terms. Our results show that the physisorbed ions on a hydrophobic surface create an enhanced slip velocity when streaming potential, which enhances the convection current. However, the electroosmotic flow attenuates due to the mobile surface ions.

Keywords: microfluidics, electroosmosis, streaming potential, electrostatic correlation, finite sized ions

Procedia PDF Downloads 42

Authors: Jeremie Coullon, Robert J. Webber

Abstract:

We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

Procedia PDF Downloads 128

Authors: Chiu-Yin Leung

Abstract:

This research investigates a complex assemblage among indigenous identities, socio-political organization and national apparatus in the border landscape of post-colonial Hong Kong. This former British colony had designated a transient mode of governance in its New Territories and particularly the northernmost borderland in 1951-2012. With a discriminated system of land provisions for the indigenous villagers, the place has been inherited with distinctive village-based culture, historic monuments and agrarian practices until its sovereignty return into the People’s Republic of China. In its latest development imperatives by the national strategic planning, the frontier area of Hong Kong has been identified as a strategy site for regional economic integration in South China, with cross-border projects of innovation and technology zones, mega-transport infrastructure and inter-jurisdictional arrangement. Contemporary literature theorizes borders as the material and discursive production of territoriality, which manifest in state apparatus and the daily lives of its citizens and condense in the contested articulations of power, security and citizenship. Drawing on the concept of assemblage, this paper attempts to tract how the border regime and infrastructure in Hong Kong as a city are deeply ingrained in the everyday lived spaces of the local communities but also the changing urban and regional strategies across different longitudinal moments. Through an intensive ethnographic fieldwork among the borderland villages since 2008 and the extensive analysis of colonial archives, new development plans and spatial planning frameworks, the author navigates the genealogy of the border landscape in Ta Kwu Ling frontier area and its implications as the milieu for new state space, covering heterogeneous fields particularly in indigenous rights, heritage preservation, rural sustainability and regional economy. Empirical evidence suggests an apparent bias towards indigenous power and colonial representation in classifying landscape values and conserving historical monuments. Squatter and farm tenants are often deprived of property rights, statutory participation and livelihood option in the planning process. The postcolonial bureaucracies have great difficulties in mobilizing resources to catch up with the swift, political-first approach of the mainland counterparts. Meanwhile, the cultural heritage, lineage network and memory landscape are not protected altogether with any holistic view or collaborative effort across the border. The enactment of land resumption and compensation scheme is furthermore disturbed by lineage-based customary law, technocratic bureaucracy, intra-community conflicts and multi-scalar political mobilization. As many traces of colonial misfortune and tyranny have been whitewashed without proper management, the author argues that postcolonial justice is yet reconciled in this fragmented border landscape. The assemblage of border in mainstream representation has tended to oversimplify local struggles as a collective mist and setup a wider production of schizophrenia experiences in the discussion of further economic integration among Hong Kong and other mainland cities in the Pearl River Delta Region. The research is expected to shed new light on the theorizing of border regions and postcolonialism beyond Eurocentric perspectives. In reassembling the borderland experiences with other arrays in state governance, village organization and indigenous identities, the author also suggests an alternative epistemology in reconciling socio-spatial differences and opening up imaginaries for positive interventions.

Keywords: heritage conservation, indigenous communities, post-colonial borderland, regional development, rural sustainability

Procedia PDF Downloads 179