A Detailed Characterization of the Expert Problem-Solving Process in Science and Engineering: Guidance for Teaching and Assessment.

A primary goal of science and engineering (S&E) education is to produce good problem solvers, but how to best teach and measure the quality of problem solving remains unclear. The process is complex, multifaceted, and not fully characterized. Here, we present a detailed characterization of the S&E problem-solving process as a set of specific interlinked decisions. This framework of decisions is empirically grounded and describes the entire process. To develop this, we interviewed 52 successful scientists and engineers ("experts") spanning different disciplines, including biology and medicine. They described how they solved a typical but important problem in their work, and we analyzed the interviews in terms of decisions made. Surprisingly, we found that across all experts and fields, the solution process was framed around making a set of just 29 specific decisions. We also found that the process of making those discipline-general decisions (selecting between alternative actions) relied heavily on domain-specific predictive models that embodied the relevant disciplinary knowledge. This set of decisions provides a guide for the detailed measurement and teaching of S&E problem solving. This decision framework also provides a more specific, complete, and empirically based description of the "practices" of science.

Nonlinear microrheology of active Brownian suspensions.

The rheological properties of active suspensions are studied via microrheology: tracking the motion of a colloidal probe particle in order to measure the viscoelastic response of the embedding material. The passive probe particle with size R is pulled through the suspension by an external force Fext, which causes it to translate at some speed Uprobe. The bath is comprised of a Newtonian solvent with viscosity ηs and a dilute dispersion of active Brownian particles (ABPs) with size a, characteristic swim speed U0, and a reorientation time τR. The motion of the probe distorts the suspension microstructure, so the bath exerts a reactive force on the probe. In a passive suspension, the degree of distortion is governed by the Péclet number, Pe = Fext/(kBT/a), the ratio of the external force to the thermodynamic restoring force of the suspension. In active suspensions, however, the relevant parameter is Ladv/l = UprobeτR/U0τR∼Fext/Fswim, where Fswim = ζU0 is the swim force that propels the ABPs (ζ is the Stokes drag on a swimmer). When the external forces are weak, Ladv≪l, the autonomous motion of the bath particles leads to "swim-thinning," though the effective suspension viscosity is always greater than ηs. When advection dominates, Ladv≫l, we recover the familiar behavior of the microrheology of passive suspensions. The non-Newtonian behavior for intermediate values of Ladv/l is determined by l/Rc = U0τR/Rc-the ratio of the swimmer's run length l to the geometric length scale associated with interparticle interactions Rc = R + a. The results in this manuscript are approximate as they are based on numerical solutions to mean-field equations that describe the motion of the active bath particles.

Fluctuation-dissipation in active matter.

In a colloidal suspension at equilibrium, the diffusive motion of a tracer particle due to random thermal fluctuations from the solvent is related to the particle's response to an applied external force, provided this force is weak compared to the thermal restoring forces in the solvent. This is known as the fluctuation-dissipation theorem (FDT) and is expressed via the Stokes-Einstein-Sutherland (SES) relation D = kBT/ζ, where D is the particle's self-diffusivity (fluctuation), ζ is the drag on the particle (dissipation), and kBT is the thermal Boltzmann energy. Active suspensions are widely studied precisely because they are far from equilibrium-they can generate significant nonthermal internal stresses, which can break the detailed balance and time-reversal symmetry-and thus cannot be assumed to obey the FDT a priori. We derive a general relationship between diffusivity and mobility in generic colloidal suspensions (not restricted to near equilibrium) using generalized Taylor dispersion theory and derive specific conditions on particle motion required for the FDT to hold. Even in the simplest system of active Brownian particles (ABPs), these conditions may not be satisfied. Nevertheless, it is still possible to quantify deviations from the FDT and express them in terms of an effective SES relation that accounts for the ABPs conversion of chemical into kinetic energy.

Do hydrodynamic interactions affect the swim pressure?

We study the motion of a spherical active Brownian particle (ABP) of size a, moving with a fixed speed U0, and reorienting on a time scale τR in the presence of a confining boundary. Because momentum is conserved in the embedding fluid, we show that the average force per unit area on the boundary equals the bulk mechanical pressure P∞ = p∞f + Π∞, where p∞f is the fluid pressure and Π∞ is the particle pressure; this is true for active and passive particles alike regardless of how the particles interact with the boundary. As an example, we investigate how hydrodynamic interactions (HI) change the particle-phase pressure at the wall, and find that Πwall = n∞(kBT + ζ(Δ)U0l(Δ)/6), where ζ is the (Stokes) drag on the swimmer, l = U0τR is the run length, and Δ is the minimum gap size between the particle and the wall; as Δ â†’ ∞ this is the familiar swim pressure [Takatori et al., Phys. Rev. Lett., 2014, 113, 1-5].

Tracer diffusion in active suspensions.

We study the diffusion of a Brownian probe particle of size R in a dilute dispersion of active Brownian particles of size a, characteristic swim speed U_{0}, reorientation time τ_{R}, and mechanical energy k_{s}T_{s}=ζ_{a}U_{0}^{2}τ_{R}/6, where ζ_{a} is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity D_{P}=k_{B}T/ζ_{P}, where k_{B}T is the thermal energy of the solvent and ζ_{P} is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by Pe_{s}=U_{0}a/D_{P}. The active contribution to the diffusivity scales as Pe_{s}^{2} for weak swimming and Pe_{s} for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale τ_{R}, the active diffusivity scales as k_{s}T_{s}/ζ_{P}: the probe moves as if it were immersed in a solvent with energy k_{s}T_{s} rather than k_{B}T.

Modeling enzymatic hydrolysis of lignocellulosic substrates using fluorescent confocal microscopy II: pretreated biomass.

In this study, we extend imaging and modeling work that was done in Part I of this report for a pure cellulose substrate (filter paper) to more industrially relevant substrates (untreated and pretreated hardwood and switchgrass). Using confocal fluorescence microscopy, we are able to track both the structure of the biomass particle via its autofluorescence, and bound enzyme from a commercial cellulase cocktail supplemented with a small fraction of fluorescently labeled Trichoderma reseii Cel7A. Imaging was performed throughout hydrolysis at temperatures relevant to industrial processing (50°C). Enzyme bound predominantly to areas with low autofluorescence, where structure loss and lignin removal had occurred during pretreatment; this confirms the importance of these processes for successful hydrolysis. The overall shape of both untreated and pretreated hardwood and switchgrass particles showed little change during enzymatic hydrolysis beyond a drop in autofluorescence intensity. The permanence of shape along with a relatively constant bound enzyme signal throughout hydrolysis was similar to observations previously made for filter paper, and was consistent with a modeling geometry of a hollowing out cylinder with widening pores represented as infinite slits. Modeling estimates of available surface areas for pretreated biomass were consistent with previously reported experimental results.

Modeling enzymatic hydrolysis of lignocellulosic substrates using confocal fluorescence microscopy I: filter paper cellulose.

Enzymatic hydrolysis is one of the critical steps in depolymerizing lignocellulosic biomass into fermentable sugars for further upgrading into fuels and/or chemicals. However, many studies still rely on empirical trends to optimize enzymatic reactions. An improved understanding of enzymatic hydrolysis could allow research efforts to follow a rational design guided by an appropriate theoretical framework. In this study, we present a method to image cellulosic substrates with complex three-dimensional structure, such as filter paper, undergoing hydrolysis under conditions relevant to industrial saccharification processes (i.e., temperature of 50°C, using commercial cellulolytic cocktails). Fluorescence intensities resulting from confocal images were used to estimate parameters for a diffusion and reaction model. Furthermore, the observation of a relatively constant bound enzyme fluorescence signal throughout hydrolysis supported our modeling assumption regarding the structure of biomass during hydrolysis. The observed behavior suggests that pore evolution can be modeled as widening of infinitely long slits. The resulting model accurately predicts the concentrations of soluble carbohydrates obtained from independent saccharification experiments conducted in bulk, demonstrating its relevance to biomass conversion work.