Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Mathematics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A mathematical design framework for membrane pre-concentration in energy-efficient recovery of fermentation products

Due to the dilute nature of products manufactured via fermentation and cell-free bioprocessing, dewatering is a common unit operation in downstream processing (DSP) for bioproduct recovery, but it is typically energy intensive. To improve DSP energy efficiency for bio-based small molecules, integrating high-pressure membrane pre-concentration is a promising process option. However, this approach is typically constrained by a tradeoff between concentration factor (CF) and product recovery (PR), namely increasing the CF typically results in greater product loss, and vice versa. Here we developed a model that enables process design guidelines to: (i) identify scenarios in which the additional energy consumption and product loss from membrane pre-concentration are justified for use in DSP, and (ii) determine the optimal CF that minimizes process specific energy consumption. We compared the energy consumption of high-pressure membrane-integrated processes to evaporation-only processes and applied the model to an experimental case study for the separation and purification of butyric acid from Clostridium tyrobutyricum fermentation using an in situ product recovery (ISPR) process. The model estimated that integrating a tangential-flow reverse osmosis (RO) pre-concentration unit could reduce process energy consumption up to 45%. The use of advanced membrane pre-concentration technologies, such as negative rejection membranes and organic solvent reverse osmosis (OSRO), have the potential to further reduce the overall process specific energy consumption up to 96%, projected based on modeling. Overall, membrane pre-concentration, especially when strategically integrated prior to an evaporation step with optimized process conditions, holds significant potential for improving DSP energy efficiency, particularly in applications requiring substantial solvent removal for product recovery from dilute mixtures.

09 BIOMASS FUELS↗
DOE OSTI2019

Mathematical Reconstruction of Land Carbon Models From Their Numerical Output: Computing Soil Radiocarbon From C Dynamics

Radiocarbon ( 14 C) is a powerful tracer of the global carbon cycle that is commonly used to assess carbon cycling rates in various Earth system reservoirs and as a benchmark to assess model performance. Therefore, it has been recommended that Earth System Models (ESMs) participating in the Coupled Model Intercomparison Project Phase 6 report predicted radiocarbon values for relevant carbon pools. However, a detailed representation of radiocarbon dynamics may be an impractical burden on model developers. Here, we present an alternative approach to compute radiocarbon values from the numerical output of an ESM that does not explicitly represent these dynamics. The approach requires computed 12 C stocks and fluxes among all carbon pools for a particular simulation of the model. From this output, a time-dependent linear compartmental system is computed with its respective state-transition matrix. Using transient atmospheric 14 C values as inputs, the state-transition matrix is then applied to compute radiocarbon values for each pool, the average value for the entire system, and component fluxes. We demonstrate the approach with ELMv1-ECA, the land component of an ESM model that explicitly represents 12 C, and 14 C in 7 soil pools and 10 vertical layers. Results from our proposed method are highly accurate (relative error <0.01%) compared with the ELMv1-ECA 12 C and 14 C predictions, demonstrating the potential to use this approach in CMIP6 and other model simulations that do not explicitly represent 14 C.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A mathematical model of solid-state dewetting of barium thin films on W (112)

Solid state dewetting occurs when a thin solid film is heated. The temperature of dewetting depends on the thickness of the film; dewetting can be observed in the range of 1/3 to 1/2 of the bulk melting temperature. While remaining solid, the film behaves in a manner similar to liquids dewetting and agglomerating to forming islands or droplets. One of the possible mechanisms is the conversion of a metastable thin film geometry into a more stable form. Heating the metastable film gives the film atoms higher mobility, and the films retract, dewetting the surface. This atomic motion can be restricted due to surface anisotropy. Herein we present in situ emission microscopy observations of barium thin films deposited onto W (112) by thermal evaporation. From the modeling viewpoint, the evolution of the film in this system could be divided in four stages: (i) the nucleation and growth of the thin film as a simply connected region; (ii) formation of droplets/islands/hillocks; (iii) nucleation of holes; (iv) evolution of the components of the disconnected film to their equilibrium state. We present a continuum model that is qualitatively consistent with the evolution of the film observed at the initial stage of the experiment and discuss the later stages of the evolution of surface structures.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A mathematical model of asynchronous data flow in parallel computers *

Abstract We present a simplified model of data flow on processors in a high-performance computing framework involving computations necessitating inter-processor communications. From this ordinary differential model, we take its asymptotic limit, resulting in a model which treats the computer as a continuum of processors and data flow as an Eulerian fluid governed by a conservation law. We derive a Hamilton–Jacobi equation associated with this conservation law for which the existence and uniqueness of solutions can be proven. We then present the results of numerical experiments for both discrete and continuum models; these show a qualitative agreement between the two and the effect of variations in the computing environment’s processing capabilities on the progress of the modelled computation.

Barnard, Richard C.↗
DOE OSTI2020

Mathematics of Gas Ingress of Hermetic Packages

Herein, we have derived a gas ingress and egress equation from the first principles of ideal gases. This work is intended to benefit the hermetic microelectronics packaging community, but it may be applied to other fields that require a deep understanding of gas ingress and egress dynamics. The equation outlined herein encompasses package material properties, package characteristics, hermetic testing conditions, and service conditions. It serves as a practical utility for calculating package pressure changes due to gas ingress and egress and, therefore, a power tool for component and system service life predictions.

42 ENGINEERING↗
DOE OSTI2020

Mathematical modeling of hepatitis C RNA replication, exosome secretion and virus release

Hepatitis C virus (HCV) causes acute hepatitis C and can lead to life-threatening complications if it becomes chronic. The HCV genome is a single plus strand of RNA. Its intracellular replication is a spatiotemporally coordinated process of RNA translation upon cell infection, RNA synthesis within a replication compartment, and virus particle production. While HCV is mainly transmitted via mature infectious virus particles, it has also been suggested that HCV-infected cells can secrete HCV RNA carrying exosomes that can infect cells in a receptor independent manner. In order to gain insight into these two routes of transmission, we developed a series of intracellular HCV replication models that include HCV RNA secretion and/or virus assembly and release. Fitting our models to in vitro data, in which cells were infected with HCV, suggests that initially most secreted HCV RNA derives from intracellular cytosolic plus-strand RNA, but subsequently secreted HCV RNA derives equally from the cytoplasm and the replication compartments. Furthermore, our model fits to the data suggest that the rate of virus assembly and release is limited by host cell resources. Including the effects of direct acting antivirals in our models, we found that in spite of decreasing intracellular HCV RNA and extracellular virus concentration, low level HCV RNA secretion may continue as long as intracellular RNA is available. This may possibly explain the presence of detectable levels of plasma HCV RNA at the end of treatment even in patients that ultimately attain a sustained virologic response.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

The effect of enrofloxacin on enteric Escherichia coli : Fitting a mathematical model to in vivo data

Antimicrobial drugs administered systemically may cause the emergence and dissemination of antimicrobial resistance among enteric bacteria. To develop logical, research-based recommendations for food animal veterinarians, we must understand how to maximize antimicrobial drug efficacy while minimizing risk of antimicrobial resistance. Our objective is to evaluate the effect of two approved dosing regimens of enrofloxacin (a single high dose or three low doses) on Escherichia coli in cattle. We look specifically at bacteria above and below the epidemiological cutoff (ECOFF), above which the bacteria are likely to have an acquired or mutational resistance to enrofloxacin. We developed a differential equation model for the antimicrobial drug concentrations in plasma and colon, and bacteria populations in the feces. The model was fit to animal data of drug concentrations in the plasma and colon obtained using ultrafiltration probes. Fecal E. coli counts and minimum inhibitory concentrations were measured for the week after receiving the antimicrobial drug. We predict that the antimicrobial susceptibility of the bacteria above the ECOFF pre-treatment strongly affects the composition of the bacteria following treatment. Faster removal of the antimicrobial drugs from the colon throughout the study leads to improved clearance of bacteria above the ECOFF in the low dose regimen. If we assume a fitness cost is associated with bacteria above the ECOFF, the increased fitness costs leads to reduction of bacteria above the ECOFF in the low dose study. These results suggest the initial E. coli susceptibility is a strong indicator of how steers respond to antimicrobial drug treatment.

59 BASIC BIOLOGICAL SCIENCES↗