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We prove Liouville type theorems, i.e., non-existence theorems for special classes of Riemannian almost product structures and submersions, that generalize well-known similar results of the theory of compact Riemannian manifolds.
Landauer’s formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of behavior: weak relaxation gives a contact-limited current; strong relaxation localizes electrons, distorting their natural dynamics and reducing the current; and in an intermediate regime the Landauer view of the system only is recovered. Lastly, we also demonstrate that a simple equation of motion emerges, which is suitable for efficiently simulating time-dependent transport.
We report non-equilibrium molecular dynamics simulations of heat transport in models of molecular fluids. We show that the “local” thermal conductivities obtained from non-equilibrium molecular dynamics simulations agree within numerical accuracy with equilibrium Green-Kubo computations. Our results support the local equilibrium hypothesis for transport properties. We show how to use the local dependence of the thermal gradients to quantify the thermal conductivity of molecular fluids for a wide range of thermodynamic states using a single simulation.
There has been sustained and growing interest in characterizing the net energy impact of information and communication technology (ICT), which results from indirect effects offsetting (or amplifying) the energy directly consumed by ICT equipment. These indirect effects may be either positive or negative, and there is considerable disagreement as to the direction of this sign as well as the effect magnitude. Literature in this area ranges from studies focused on a single service (such as e-commerce versus traditional retail) to macroeconomic studies attempting to characterize the overall impact of ICT. Methods. We review the literature on the indirect energy effect of ICT found via Google Scholar, our own research, and input from other researchers in the field. The various studies are linked to an effect taxonomy, which is synthesized from several different hierarchies present in the literature. References are further grouped according to ICT service (e.g., e-commerce, telework) and summarized by scope, method, and quantitative and qualitative findings. Review results. Uncertainty persists in understanding the net energy effects of ICT. Results of indirect energy effect studies are highly sensitive to scoping decisions and assumptions made by the analyst. Uncertainty increases as the impact scope broadens, due to complex and interconnected effects. However, there is general agreement that ICT has large energy savings potential, but that the realization of this potential is highly dependent on deployment details and user behavior. Discussion. While the overall net effect of ICT is likely to remain unknown, this review suggests several guidelines for improving research quality in this area, including increased data collection, enhancing traditional modeling studies with sensitivity analysis, greater care in scoping, less confidence in characterizing aggregate impacts, more effort on understanding user behavior, and more contextual integration across the different levels of the effect taxonomy.
Phonon lifetimes are a key component of quasiparticle theories of transport; yet first-principles lifetimes are rarely directly compared with inelastic neutron scattering (INS) results. Existing comparisons show discrepancies even at temperatures where perturbation theory is expected to be reliable. In this paper, we demonstrate that the reciprocal space voxel (q voxel), which is the finite region in reciprocal space required in INS data analysis, must be explicitly accounted for within theory in order to draw a meaningful comparison. Here, we demonstrate accurate predictions of peak widths of the scattering function when accounting for the q voxel in CaF 2 and ThO 2 . Passing this test implies high fidelity of the phonon interactions and the approximations used to compute the Green's function, serving as a critical benchmark of theory and indicating that other material properties should be accurately predicted, which we demonstrate for thermal conductivity.
In the transition toward sustainable agriculture, farms have emerged as eco-friendly pioneers, harnessing clean hybrid wind and solar systems to improve farm performance. A concern in this paradigm is the effective sizing of renewable energy systems to ensure optimal energy use within budget considerations. This research focuses on optimizing renewable energy sizing in small-scale ammonia production to meet specific farm demands and enhance local resilience, emphasizing the interplay between environmental and economic factors. These findings promise increased energy efficiency and sustainability in this innovative agricultural sector. Additionally, our approach considers small-scale ammonia plant needs and the dynamic relationships between ammonia, water, and farm demands. Simulations demonstrate substantial cost savings in farm electricity consumption. Specifically, scenarios with renewable energy integration in the farm can reduce at least 13% electricity cost compared to a grid-dependent system in the 15-year simulation.
With each CMOS technology generation, leakage energy consumption has been dramatically increasing and hence, managing leakage power consumption of large last-level caches (LLCs) has become a critical issue in modern processor design. In this paper, we present EnCache, a novel software-based technique which uses dynamic profiling-based cache reconfiguration for saving cache leakage energy. EnCache uses a simple hardware component called profiling cache, which dynamically predicts energy efficiency of an application for 32 possible cache configurations. Using these estimates, system software reconfigures the cache to the most energy efficient configuration. EnCache uses dynamic cache reconfiguration and hence, it does not require offline profiling or tuning the parameter for each application. Furthermore, EnCache optimizes directly for the overall memory subsystem (LLC and main memory) energy efficiency instead of the LLC energy efficiency alone. The experiments performed with an x86-64 simulator and workloads from SPEC2006 suite confirm that EnCache provides larger energy saving than a conventional energy saving scheme. For single core and dual-core system configurations, the average savings in memory subsystem energy over a shared baseline configuration are 30.0% and 27.3%, respectively.
Recent trends of CMOS scaling and use of large last level caches (LLCs) have led to significant increase in the leakage energy consumption of LLCs and hence, managing their energy consumption has become extremely important in modern processor design. The conventional cache energy saving techniques require offline profiling or provide only coarse granularity of cache allocation. We present FlexiWay, a cache energy saving technique which uses dynamic cache reconfiguration. FlexiWay logically divides the cache sets into multiple (e.g. 16) modules and dynamically turns off suitable and possibly different number of cache ways in each module. FlexiWay has very small implementation overhead and it provides fine-grain cache allocation even with caches of typical associativity, e.g. an 8-way cache. Microarchitectural simulations have been performed using an x86-64 simulator and workloads from SPEC2006 suite. Also, FlexiWay has been compared with two conventional energy saving techniques. The results show that FlexiWay provides largest energy saving and incurs only small loss in performance. For single, dual and quad core systems, the average energy saving using FlexiWay are 26.2%, 25.7% and 22.4%, respectively.
Computation of micromechanical fields in heterogeneous materials is usually performed using either the finite element method or the Green’s function method based on FFTs. The finite element method allows for accurate discretization and for non-periodic boundary conditions but is computationally expensive. On the other hand, the FFT-based method is computationally efficient but requires discretization on a regular grid of hexahedral voxels. In this paper, a Green’s function method allowing for accurate discretization using tetrahedral elements and for non-periodic boundary conditions is proposed. The convolution is computed using the fast multipole method, which provides good accuracy even for low-order expansion due to the fast decay of interactions between elements. The proposed Green’s function fast multipole method is verified by comparison with analytical and FFT-based solutions. Furthermore, the computational time is analyzed and compared to the FFT-based method for non-periodic convolution. Finally, effective properties of an elastic polycrystalline microstructure containing thin intergranular cracks are computed and analyzed.
In this work, we propose an expression for the periodic first derivative of Green's function in real space. The proposed expression allows an alternative way of computing the periodic Green's operator based on periodically summing the free-space Green's operator in terms of an appropriate quadrature rule. We provide computational examples, which show the accuracy of the proposed approach, together with reduced spurious oscillations in the solution fields.
Biological-mediated conversion of pretreated lignocellulosic biomass to biofuels and biochemicals is a promising avenue towards energy sustainability. However, a critical impediment to the commercialization of cellulosic biofuel production is the high cost of cellulase enzymes needed to deconstruct biomass into fermentable sugars. One major factor driving cost is cellulase adsorption and inactivation in the presence of lignin, yet we currently have a poor understanding of the protein structure-function relationships driving this adsorption. In this work, we have systematically investigated the role of protein surface potential on lignin adsorption using a model monomeric fluorescent protein. We have designed and experimentally characterized 16 model protein variants spanning the physiological range of net charge (-24 to +16 total charges) and total charge density (0.28 to 0.40 charges per sequence length) typical for natural proteins. Protein designs were expressed, purified, and subjected to in silico and in vitro biophysical measurements to evaluate the relationship between protein surface potential and lignin adsorption properties. The designs were comparable to model fluorescent protein in terms of thermostability and heterologous expression yield, although the majority of the designs unexpectedly formed homodimers. Protein adsorption to lignin was studied at two different temperatures using Quartz Crystal Microbalance with Dissipation Monitoring and a subtractive mass balance assay. We found a weak correlation between protein net charge and protein-binding capacity to lignin. No other single characteristic, including apparent melting temperature and 2nd virial coefficient, showed correlation with lignin binding. Analysis of an unrelated cellulase dataset with mutations localized to a family I carbohydrate-binding module showed a similar correlation between net charge and lignin binding capacity. Altogether, our study provides strategies to identify highly active, low lignin-binding cellulases by either rational design or by computational screening genomic databases.
Computational crystal construction algorithms were used to create twelve metal–organic frameworks containing a newly synthesized [2,2'-bithiazole]-5,5'-dicarboxylic acid (H 2 TzTz) spacer and assorted transition metal nodes. Among the twelve structures, the zirconium-based MOF of general formula [Zr 6 O 4 (OH) 4 (TzTz) 6 ] (1) was found to be the best candidate for carbon dioxide uptake, as judged from the results of the grand canonical Monte Carlo (GCMC) simulations of CO 2 adsorption isotherms. Guided by the simulation results, 1 was synthesized in the laboratory and thoroughly characterized. 1 is isoreticular to its bithiophene and bis(benzene) (UiO-67) analogues; it crystallizes in the cubic Pn$\bar{3}$ with combining macron] space group with fcu topology, and it features octahedral [Zr 6 ] nodes connected by twelve carboxylate groups from six bridging TzTz 2- spacers. It is a predominantly microporous material (micropore volume = 84% of the total pore volume), with a BET area of 840 m 2 g -1 and a maximum CO 2 uptake at ambient pressure of 2.3 mmol g -1 (10.0 wt%) or 1.7 mmol g -1 (7.5 wt%) at 273 or 298 K, respectively. The CO 2 affinity (isosteric heat of adsorption Qst = 18.7 kJ mol -1 ; CO 2 /N 2 Henry selectivity = 10; CO 2 /N 2 IAST selectivity = 8.4) is similar to that of its bithiophene analogue. After partial removal of solvent (activation), 1 was tested as a heterogeneous catalyst in the reaction of CO 2 with epoxides bearing a –CH 2 X pendant arm (X = Cl: epichlorohydrin; X = Br: epibromohydrin) to give the corresponding cyclic carbonates at T = 393 K and p CO 2 = 1 bar under green (solvent- and co-catalyst-free) conditions. A good conversion of 74% and a turnover frequency of 12.3 mmol (cyclic carbonate) per mmol Zr per h have been recorded with epibromohydrin as a substrate.
We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.
We have studied the scaling properties of the electromagnetic response functions of 4 He and 12 C nuclei computed by the Green's function Monte Carlo approach, retaining only the one-body current contribution. Longitudinal and transverse scaling functions have been obtained in the relativistic and nonrelativistic cases and compared to experiment for various kinematics. The characteristic asymmetric shape of the scaling function exhibited by data emerges in the calculations in spite of the nonrelativistic nature of the model. The results are mostly consistent with scaling of zeroth, first, and second kinds. Our analysis reveals a direct correspondence between the scaling and the nucleon-density response functions. In conclusion, the scaling function obtained from the proton-density response displays scaling of the first kind, even more evidently than the longitudinal and transverse scaling functions
Molecular dynamics simulations are used to calculate transport coefficients in a two-component plasma interacting through a repulsive Coulomb potential. The thermal conductivity, electrical conductivity, electrothermal coefficient, thermoelectric coefficient, and shear viscosity are computed using the Green–Kubo formalism over a broad range of Coulomb coupling strength, 0.01 ≤ Γ ≤ 140. Emphasis is placed on testing standard results of the Chapman–Enskog solution in the weakly coupled regime (Γ ≪ 1) using these first-principles simulations. As expected, the results show good agreement for Γ ≲ 0.1. However, this agreement is only possible if careful attention is paid to the definitions of linear constitutive relations in each of the theoretical models, a point that is often overlooked. For example, the standard Green–Kubo expression for thermal conductivity is a linear combination of thermal conductivity, electrothermal, and thermoelectric coefficients computed in the Chapman–Enskog formalism. Meaningful results for electrical conductivity are obtained over the full range of coupling strengths explored, but it is shown that potential and virial components of the other transport coefficients diverge in the strongly coupled regime (Γ ≫ 1). In this regime, only the kinetic components of the transport coefficients are meaningful for a classical plasma.
The valorization and dissolution of lignin using ionic liquids (ILs) is critical for developing sustainable biorefineries and a circular bioeconomy. This review aims to critically assess the current state of computational and machine learning methods for understanding and optimizing IL-based lignin dissolution and valorization processes reported since 2022. The paper examines various computational approaches, from quantum chemistry to machine learning, highlighting their strengths, limitations, and recent advances in predicting and optimizing lignin-IL interactions. Key themes include the challenges in accurately modeling lignin’s complex structure, the development of efficient screening methodologies for ionic liquids to enhance lignin dissolution and valorization processes, and the integration of machine learning with quantum calculations. These computational advances will drive progress in IL-based lignin valorization by providing deeper molecular-level insights and facilitating the rapid screening of novel IL-lignin systems.
We introduce an embedding scheme for the locally self-consistent method to study disordered electron systems. We test this approach in a tight-binding basis and apply it to the single band Anderson model. The local interaction zone is used to efficiently compute the local Green's function of a supercell embedded into a local typical medium. We find a quick convergence as the size of the local interaction zone which reduces the computational costs as expected. This method captures the Anderson localization transition and accurately predicts the critical disorder strength. The current work opens the path towards the development of a typical medium embedding scheme for the O(N) multiple scattering methods.
We present a novel definition of variable-order fractional Laplacian on R n based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n/2). We then discuss some properties of the fractional Poisson’s equation involving this operator and we compute the corresponding Green’s function, for which we provide some instructive examples for specific problems.