Gutzwiller approximation for indistinguishable interacting Brownian particles on a lattice.

Nonequilibrium Brownian systems can be described using a creation and annihilation operator formalism for classical indistinguishable particles. This formalism has recently been used to derive a many-body master equation for Brownian particles on a lattice with interactions of arbitrary strength and range. One advantage of this formalism is the possibility of using solution methods for analogous many-body quantum systems. In this paper, we adapt the Gutzwiller approximation for the quantum Bose-Hubbard model to the many-body master equation for interacting Brownian particles in a lattice in the large-particle limit. Using the adapted Gutzwiller approximation, we numerically explore the complex behavior of nonequilibrium steady-state drift and number fluctuations throughout the full range of interaction strengths and densities for on-site and nearest-neighbor interactions.

Nonequilibrium master equation for interacting Brownian particles in a deep-well periodic potential.

Employing a creation and annihilation operator formulation, we derive an approximate many-body master equation describing discrete hopping from the more general continuous description of Brownian motion on a deep-well nonequilibrium periodic potential. The many-body master equation describes interactions of arbitrary strength and range arising from a "top-hat" two-body interaction potential. We show that this master equation reduces to the well-known asymmetric simple exclusion process and the zero range process in certain regimes. We also use the creation and annihilation operator formalism to derive results for the steady-state drift and the number fluctuations in special cases, including the unexplored limit of weak interparticle interactions.

Reconstructing free-energy landscapes for nonequilibrium periodic potentials.

We present a method for reconstructing the free-energy landscape of overdamped Brownian motion on a tilted periodic potential. Our approach exploits the periodicity of the system by using the k-space form of the Smoluchowski equation and we employ an iterative approach to determine the nonequilibrium tilt. We reconstruct landscapes for a number of example potentials to show the applicability of the method to both deep and shallow wells and near-to- and far-from-equilibrium regimes. The method converges logarithmically with the number of Fourier terms in the potential.

A mild thermomechanical process for the enzymatic conversion of radiata pine into fermentable sugars and lignin.

BACKGROUND: Conversion of softwoods into sustainable fuels and chemicals is important for parts of the world where softwoods are the dominant forest species. While they have high theoretical sugar yields, softwoods are amongst the most recalcitrant feedstocks for enzymatic processes, typically requiring both more severe pretreatment conditions and higher enzyme doses than needed for other lignocellulosic feedstocks. Although a number of processes have been proposed for converting softwoods into sugars suitable for fuel and chemical production, there is still a need for a high-yielding, industrially scalable and cost-effective conversion route. RESULTS: We summarise work leading to the development of an efficient process for the enzymatic conversion of radiata pine (Pinus radiata) into wood sugars. The process involves initial pressurised steaming of wood chips under relatively mild conditions (173 °C for 3-72 min) without added acid catalyst. The steamed chips then pass through a compression screw to squeeze out a pressate rich in solubilised hemicelluloses. The pressed chips are disc-refined and wet ball-milled to produce a substrate which is rapidly saccharified using commercially available enzyme cocktails. Adding 0.1% polyethylene glycol during saccharification was found to be particularly effective with these substrates, reducing enzyme usage to acceptable levels, e.g. 5 FPU/g OD substrate. The pressate is separately hydrolysed using acid, providing additional hemicellulose-derived sugars, for an overall sugar yield of 535 kg/ODT chips (76% of theoretical). The total pretreatment energy input is comparable to other processes, with the additional energy for attrition being balanced by a lower thermal energy requirement. This pretreatment strategy produces substrates with low levels of fermentation inhibitors, so the glucose-rich mainline and pressate syrups can be fermented to ethanol without detoxification. The lignin from the process remains comparatively unmodified, as evident from the level of retained ß-ether interunit linkages, providing an opportunity for conversion into saleable co-products. CONCLUSIONS: This process is an efficient route for the enzymatic conversion of radiata pine, and potentially other softwoods, into a sugar syrup suitable for conversion into fuels and chemicals. Furthermore, the process uses standard equipment that is largely proven at commercial scale, de-risking process scale-up.

Energy transfer in a molecular motor in the Kramers regime.

We present a theoretical treatment of energy transfer in a molecular motor described in terms of overdamped Brownian motion on a multidimensional tilted periodic potential. The tilt represents a thermodynamic force driving the system out of equilibrium and, for nonseparable potentials, energy transfer occurs between degrees of freedom. For deep potential wells, the continuous theory transforms to a discrete master equation that is tractable analytically. We use this master equation to derive formal expressions for the hopping rates, drift and diffusion, and the efficiency and rate of energy transfer in terms of the thermodynamic force. These results span both strong and weak coupling between degrees of freedom, describe the near and far from equilibrium regimes, and are consistent with generalized detailed balance and the Onsager relations. We thereby derive a number of diverse results for molecular motors within a single theoretical framework.

Tight-binding approach to overdamped Brownian motion on a multidimensional tilted periodic potential.

We present a theoretical treatment of overdamped Brownian motion on a multidimensional tilted periodic potential that is analogous to the tight-binding model of quantum mechanics. In our approach, we expand the continuous Smoluchowski equation in the localized Wannier states of the periodic potential to derive a discrete master equation. This master equation can be interpreted in terms of hopping within and between Bloch bands, and for weak tilting and long times we show that a single-band description is valid. In the limit of deep potential wells, we derive a simple functional dependence of the hopping rates and the lowest band eigenvalues on the tilt. We also derive formal expressions for the drift and diffusion in terms of the lowest band eigenvalues.

Optimizing the enzyme loading and incubation time in enzymatic hydrolysis of lignocellulosic substrates.

A mathematical model for costing enzymatic hydrolysis of lignocellulosics is presented. This model is based on three variable parameters describing substrate characteristics and three unit costs for substrate, enzymes and incubation. The model is used to minimize the cost of fermentable sugars, as intermediate products on the route to ethanol or other biorefinery products, by calculating optimized values of enzyme loading and incubation time. This approach allows comparisons between substrates, with processing conditions optimized independently for each substrate. Steam-exploded pine wood was hydrolyzed in order to test the theoretical relationship between sugar yield and processing conditions.

Thermodynamic analysis of a high-yield biochemical process for biofuel production.

This paper presents a thermodynamic analysis of a high-yield biochemical process for biofuel production from lignocelluosic biomass based on a previously proposed process. Unlike the standard biochemical process, which ferments sugar intermediates to ethanol, the process under consideration converts sugars to acetic acid which is esterified and hydrogenated to produce ethanol. This process has a significantly higher yield and produces no carbon dioxide. However, we find that the thermodynamic efficiency of the process is not increased in proportion to the yield gain. An additional survey of various biofuel production processes showed no direct correlation between yield and thermodynamic efficiency. This survey and the detailed thermodynamic analyses lead us to conclude that yield alone is an unreliable performance metric for biofuel technologies.

Thermodynamic analysis of lignocellulosic biofuel production via a biochemical process: guiding technology selection and research focus.

The aim of this paper is to present an exergy analysis of bioethanol production process from lignocellulosic feedstock via a biochemical process to asses the overall thermodynamic efficiency and identify the main loss processes. The thermodynamic efficiency of the biochemical process was found to be 35% and the major inefficiencies of this process were identified as: the combustion of lignin for process heat and power production and the simultaneous scarification and co-fermentation process accounting for 67% and 27% of the lost exergy, respectively. These results were also compared with a previous analysis of a thermochemical process for producing biofuel. Despite fundamental differences, the biochemical and thermochemical processes considered here had similar levels of thermodynamic efficiency. Process heat and power production was the major contributor to exergy loss in both of the processes. Unlike the thermochemical process, the overall efficiency of the biochemical process largely depends on how the lignin is utilized.

Scaling laws and technology development strategies for biorefineries and bioenergy plants.

The economies of scale of larger biorefineries or bioenergy plants compete with the diseconomies of scale of transporting geographically distributed biomass to a central location. This results in an optimum plant size that depends on the scaling parameters of the two contributions. This is a fundamental aspect of biorefineries and bioenergy plants and has important consequences for technology development as "bigger is better" is not necessarily true. In this paper we explore the consequences of these scaling effects via a simplified model of biomass transportation and plant costs. Analysis of this model suggests that there is a need for much more sophisticated technology development strategies to exploit the consequences of these scaling effects. We suggest three potential strategies in terms of the scaling parameters of the system.

Decoherence due to three-body loss and its effect on the state of a Bose-Einstein condensate.

A Born-Markov master equation is used to investigate the decoherence of the state of a macroscopically occupied mode of a cold atom trap due to three-body loss. In the large-number limit only coherent states remain pure for times longer than the decoherence time: the time it takes for just three atoms to be lost from the trap. For large numbers of atoms (N>10(4)) the decoherence time is found to be much faster than the phase-collapse time caused by intratrap atomic collisions.