Hasil untuk "Descriptive and experimental mechanics"

Arunee Promsri, Punnakan Pitiwattanakulchai, Siwaporn Saodan et al.

<b>Background:</b> The 1 min sit-to-stand test (1-MSTST) is a widely used functional assessment involving repetitive sit-to-stand transitions. This study examined local dynamic stability during the 1-MSTST across three acceleration directions, compared young and middle-aged women, and explored associations between body composition and stability. <b>Methods:</b> Twenty-four young adult women (24.1 ± 5.2 years) and twenty-four middle-aged women (51.4 ± 5.9 years) performed the 1-MSTST. Trunk accelerations were recorded using a tri-axial accelerometer at L5. Local dynamic stability was quantified using the largest Lyapunov exponent (LyE), and movement magnitude using root mean square (RMS). Directional, group, and correlational analyses were performed with correction for multiple testing. <b>Results:</b> Significant directional differences were observed for both LyE and RMS, with all pairwise contrasts between mediolateral (ML), anteroposterior (AP), and vertical (VT) directions remaining significant after correction (<i>p</i> < 0.001). Apparent age effects in LyE were no longer significant after adjusting for cadence, BMI, and multiple testing, indicating no robust age-related difference in local dynamic stability. Body fat percentage showed moderate positive correlations with LyE in the VT (<i>p</i> = 0.003) and AP (<i>p</i> = 0.003) directions. Muscle mass percentage showed a moderate positive correlation with VT LyE (<i>p</i> = 0.002) and moderate negative correlations with ML (<i>p</i> = 0.002) and AP LyE (<i>p</i> = 0.002). <b>Conclusions:</b> Stability during the 1-MSTST differs by direction, with the greatest variability in the mediolateral axis. No independent age effect was found. Higher body fat relates to poorer stability, while greater muscle mass supports better movement control.

Andrew Sparrow, Jett Isley, Walter Smith et al.

Thorough investigation into Tesla valve (TV) design was conducted across a large design of experiments (DOE) consisting of four varying geometric parameters and six different Reynolds number regimes in order to develop an optimized pressure drop device utilizing machine learning (ML) methods. A non-standard TV design was geometrically parameterized, and an automation suite was created to cycle through numerous combinations of parameters. Data were collected from completed computational fluid dynamics (CFD) simulations. TV designs were tested in the restricted flow direction for overall differential pressure, and overall minimum pressure with consideration to the onset of cavitation. Qualitative observations were made on the effects of each geometric parameter on the overall valve performance, and particular parameters showed greater influence on the pressure drop compared to classically optimized parameters used in previous TV studies. The overall minimum pressure demonstrated required system pressure for a valve to be utilized such that onset to cavitation would not occur. Data were utilized to train an ML model, and an optimized geometry was selected for maximized pressure drop. Multiple optimization efforts were made to meet design pressure drop goals versus traditional diodicity metrics, and two geometries were selected to develop a final design tool for overall pressure drop component development. Future work includes experimental validation of the large dataset, as well as further validation of the design tool for use in industry.

Luara K. S. Sousa, Wagner Q. Barros, Adolfo P. Pires et al.

Miscible gas flooding improves oil displacement through mass exchange between oil and gas phases. It is one of the most efficient enhanced oil recovery methods for intermediate density oil reservoirs. In this work, analytical solutions for saturation, concentration and pressure are derived for oil displacement by a partially miscible gas injection at a constant rate. The mathematical model considers two-phase, three-component fluid flow in a one-dimensional homogeneous reservoir initially saturated by a single oil phase. Phase saturations and component concentrations are described by a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></semantics></math></inline-formula> hyperbolic system of partial differential equations, which is solved by the method of characteristics. Once this Goursat–Riemann problem is solved, the pressure drop between two points in the porous media is obtained by the integration of Darcy’s law. The solution of this problem may present three different fluid regions depending on the rock–fluid parameters: a single-phase gas region near the injection point, followed by a two-phase region where mass transfer takes place and a single-phase oil region. We considered the single-phase gas and the two-phase gas/oil regions as incompressible, while the single-phase oil region may be incompressible or slightly compressible. The solutions derived in this work are applied for a specific set of rock and fluid properties. For this data set, the two-phase region displays rarefaction waves, shock waves and constant states. The pressure behavior depends on the physical model (incompressible, compressible and finite or infinite porous media). In all cases, the injection pressure is the result of the sum of two terms: one represents the effect of the mobility contrast between phases and the other represents the single-phase oil solution. The solutions obtained in this work are compared to an equivalent immiscible solution, which shows that the miscible displacement is more efficient.

Francisco José de Souza, Jonathan Utzig, Guilherme do Nascimento et al.

This work presents a one-dimensional (1D) model for simulating the behavior of an FCC riser reactor processing bio-oil. The FCC riser is modeled as a plug-flow reactor, where the bio-oil feed undergoes vaporization followed by catalytic cracking reactions. The bio-oil droplets are represented using a Lagrangian framework, which accounts for their movement and evaporation within the gas-solid flow field, enabling the assessment of droplet size impact on reactor performance. The cracking reactions are modeled using a four-lumped kinetic scheme, representing the conversion of bio-oil into gasoline, kerosene, gas, and coke. The resulting set of ordinary differential equations is solved using a stiff, second- to third-order solver. The simulation results are validated against experimental data from a full-scale FCC unit, demonstrating good agreement in terms of product yields. The findings indicate that heat exchange by radiation is negligible and that the Buchanan correlation best represents the heat transfer between the droplets and the catalyst particles/gas phase. Another significant observation is that droplet size, across a wide range, does not significantly affect conversion rates due to the bio-oil’s high vaporization heat. The proposed reduced-order model provides valuable insights into optimizing FCC riser reactors for bio-oil processing while avoiding the high computational costs of 3D CFD simulations. The model can be applied across multiple applications, provided the chemical reaction mechanism is known. Compared to full models such as CFD, this approach can reduce computational costs by thousands of computing hours.

Rafael Bizarelo, Luiz Paulo Pimenta Rambal, Taís de Souza Lopes et al.

Flexed and tensed arm (FTA) circumference is a fundamental anthropometric measurement for determining the mesomorphic component in somatotype. This study examined the impact of contralateral limb opposition (+OP) on arm circumference measurement and biceps brachii muscle activation. Fifty physically active men and women, mean (22.7 ± 2.9 years), participated in this study. FTA circumference measurements were taken with FTA + OP and without opposition FTA, following ISAK protocols. Additionally, biceps brachii muscle activation was assessed using surface electromyography (sEMG). Significant differences were identified in the flexed and tensed arm circumference (>1%) and in the mesomorphic component between the FTA and FTA + OP conditions (<i>p</i> < 0.001). In addition, contralateral limb opposition resulted in a significant average increase of 39.02% in biceps brachii muscle activation, with variations between 24.57% to 47.46% across the time intervals analyzed (<i>p</i> < 0.05). A moderate correlation was observed between the percentage difference in sEMG and arm circumference during the middle second of contraction (<i>r</i> = 0.418). However, during the first (<i>r</i> = 0.393), third (<i>r</i> = 0.376), and mean (<i>r</i> = 0.385) contraction periods, the correlation was considered weak. Contralateral limb opposition caused greater biceps brachii muscle activation, resulting in an increase in flexed and tensed arm circumference in physically active young adults.

Alexandre Epalle, Isabelle Ramière, Guillaume Latu et al.

Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper introduces a scalable, robust, and efficient algorithm to deal with 2D and 3D elastostatics contact problems between deformable bodies in a finite element framework. The proposed solution combines a treatment of the contact problem by a node-to-node pairing algorithm with a penalization technique and a non-conforming h-adaptive refinement of quadrilateral/hexahedral meshes based on an estimate-mark-refine approach in a parallel framework. One of the special features of our parallel strategy is that contact paired nodes are hosted by the same MPI tasks, which reduces the number of exchanges between processes for building the contact operator. The mesh partitioning introduced in this paper respects this rule and is based on an equidistribution of elements over processes, without any other constraints. In order to preserve the domain curvature while hierarchical mesh refinement, super-parametric elements are used. This functionality enables the contact zone to be well detected during the AMR process, even for an initial coarse mesh and low-order discretization schemes. The efficiency of our contact-AMR-HPC strategy is assessed on 2D and 3D Hertzian contact problems. Different AMR detection criteria are considered. Various convergence analyses are conducted. Parallel performances up to 1024 cores are illustrated. Furthermore, memory footprint and preconditionners performance are analyzed.

J. Mercado Colmenero, M. LaRubia, E. Mata Garcia et al.

The purpose of this study is to investigate the numerical-experimental mechanical behavior modeling of the recycled polymer, that is, recyclable polyethylene terephthalate (rPET), manufactured by a deposition FFF process under compressive stresses for new sustainable designs. In all, 42 test specimens were manufactured and analyzed according to the ASTM D695-15 standards. Eight numerical analyzes were performed on a real design manufactured with rPET using Young's compression modulus from the experimental tests. Finally, eight additional experimental tests under uniaxial compression loads were performed on the real sustainable design for validating its mechanical behavior versus computational numerical tests. As a result of the experimental tests, rPET behaves linearly until it reaches the elastic limit, along each manufacturing axis. The results of this study confirmed the design's structural safety by the load scenario and operating boundary conditions. Experimental and numerical results show a difference of 0.001-0.024 mm, allowing for the rPET to be configured as isotropic in numerical simulation software without having to modify its material modeling equations. The results obtained are of great help to industry, designers and researchers because they validate the use of recycled rPET for the ecological production of real-sustainable products using MEX technology under compressive stress and its configuration for numerical simulations. Major design companies are now using recycled plastic materials in their high-end designs. Validation results have been presented on test specimens and real items, comparing experimental material configuration values with numerical results.

Louis Y. Kim, Michelle Karker, Victoria Valledor et al.

Recent advances in open-vocabulary object detection models will enable Automatic Target Recognition systems to be sustainable and repurposed by non-technical end-users for a variety of applications or missions. New, and potentially nuanced, classes can be defined with natural language text descriptions in the field, immediately before runtime, without needing to retrain the model. We present an approach for improving non-technical users' natural language text descriptions of their desired targets of interest, using a combination of analysis techniques on the text embeddings, and proper combinations of embeddings for contrastive examples. We quantify the improvement that our feedback mechanism provides by demonstrating performance with multiple publicly-available open-vocabulary object detection models.

Jana Juroš, Laura Majer, Jan Šnajder

News headlines often evoke sentiment by intentionally portraying entities in particular ways, making targeted sentiment analysis (TSA) of headlines a worthwhile but difficult task. Due to its subjectivity, creating TSA datasets can involve various annotation paradigms, from descriptive to prescriptive, either encouraging or limiting subjectivity. LLMs are a good fit for TSA due to their broad linguistic and world knowledge and in-context learning abilities, yet their performance depends on prompt design. In this paper, we compare the accuracy of state-of-the-art LLMs and fine-tuned encoder models for TSA of news headlines using descriptive and prescriptive datasets across several languages. Exploring the descriptive--prescriptive continuum, we analyze how performance is affected by prompt prescriptiveness, ranging from plain zero-shot to elaborate few-shot prompts. Finally, we evaluate the ability of LLMs to quantify uncertainty via calibration error and comparison to human label variation. We find that LLMs outperform fine-tuned encoders on descriptive datasets, while calibration and F1-score generally improve with increased prescriptiveness, yet the optimal level varies.

Aikaterini C. Stamou, Jovana Radulovic, James M. Buick

Blood is a shear-thinning non-Newtonian fluid in which the viscosity reduces with the shear rate. When simulating arterial flow, it is well established that the non-Newtonian nature is important in the smallest vessels; however, there is no consistent view as to whether it is required in larger arteries, such as the carotid. Here, we investigate the importance of incorporating a non-Newtonian model when applying a plaque deposition model which is based on near-wall local haemodynamic markers: the time-averaged near wall velocity and the ratio of the oscillatory shear index to the wall shear stress. In both cases the plaque deposition was similar between the Newtonian and non-Newtonian simulations, with the observed differences being no more significant than the differences between the selected markers. More significant differences were observed in the haemodynamic properties in the stenosed region, the most significant being that lower levels of near-wall reverse flow were observed for a non-Newtonian fluid.

Risheng Pei, Joé Petrazoller, Achraf Atila et al.

Solute segregation at low-angle grain boundaries (LAGBs) critically affects the microstructure and mechanical properties of magnesium (Mg) alloys. In modern alloys containing multiple substitutional elements, understanding solute-solute interactions at microstructural defects becomes essential for alloy design. This study investigates the co-segregation mechanisms of calcium (Ca), zinc (Zn), and aluminum (Al) at a LAGB in a dilute AZX010 Mg alloy by combining atomic-scale experimental and modeling techniques. Three-dimensional atom probe tomography (3D-APT) revealed significant segregation of Ca, Zn, and Al at the LAGB, with Ca forming linear segregation patterns along dislocation arrays characteristic of the LAGB. Clustering analysis showed increased Ca-Ca pairs at the boundary, indicating synergistic solute interactions. Atomistic simulations and elastic dipole calculations demonstrated that larger Ca atoms prefer tensile regions around dislocations, while smaller Zn and Al atoms favor compressive areas. These simulations also found that Ca-Ca co-segregation near dislocation cores is energetically more favorable than other solute pairings, explaining the enhanced Ca clustering observed experimentally. Thermodynamic modeling incorporating calculated segregation energies and solute-solute interactions accurately predicted solute concentrations at the LAGB, aligning with experimental data. The findings emphasize the importance of solute interactions at dislocation cores in Mg alloys, offering insights for improving mechanical performance through targeted alloying and grain boundary engineering.

Adrián García-Gutiérrez, Jesús Gonzalo, Deibi López et al.

The feasibility, safety, and efficiency of a drone mission in an urban environment are heavily influenced by atmospheric conditions. However, numerical meteorological models cannot cope with fine-grained grids capturing urban geometries; they are typically tuned for best resolutions ranging from 1 to 10 km. To enable urban air mobility, new now-casting techniques are being developed based on different techniques, such as data assimilation, variational analysis, machine-learning algorithms, and time series analysis. Most of these methods require generating an urban wind field database using CFD codes coupled with the mesoscale models. The quality and accuracy of that database determines the accuracy of the now-casting techniques. This review describes the latest advances in CFD simulations applied to urban wind and the alternatives that exist for the coupling with the mesoscale model. First, the distinct turbulence models are introduced, analyzing their advantages and limitations. Secondly, a study of the meshing is introduced, exploring how it has to be adapted to the characteristics of the urban environment. Then, the several alternatives for the definition of the boundary conditions and the interpolation methods for the initial conditions are described. As a key step, the available order reduction methods applicable to the models are presented, so the size and operability of the wind database can be reduced as much as possible. Finally, the data assimilation techniques and the model validation are presented.

Shervin R. Arashloo

The support vector data description (SVDD) approach serves as a de facto standard for one-class classification where the learning task entails inferring the smallest hyper-sphere to enclose target objects while linearly penalising any errors/slacks via an $\ell_1$-norm penalty term. In this study, we generalise this modelling formalism to a general $\ell_p$-norm ($p\geq1$) slack penalty function. By virtue of an $\ell_p$ slack norm, the proposed approach enables formulating a non-linear cost function with respect to slacks. From a dual problem perspective, the proposed method introduces a sparsity-inducing dual norm into the objective function, and thus, possesses a higher capacity to tune into the inherent sparsity of the problem for enhanced descriptive capability. A theoretical analysis based on Rademacher complexities characterises the generalisation performance of the proposed approach in terms of parameter $p$ while the experimental results on several datasets confirm the merits of the proposed method compared to other alternatives.

Matteo Zancanaro, Markus Mrosek, Giovanni Stabile et al.

Geometrically parametrized partial differential equations are currently widely used in many different fields, such as shape optimization processes or patient-specific surgery studies. The focus of this work is some advances on this topic, capable of increasing the accuracy with respect to previous approaches while relying on a high cost–benefit ratio performance. The main scope of this paper is the introduction of a new technique combining a classical Galerkin-projection approach together with a data-driven method to obtain a versatile and accurate algorithm for the resolution of geometrically parametrized incompressible turbulent Navier–Stokes problems. The effectiveness of this procedure is demonstrated on two different test cases: a classical academic back step problem and a shape deformation Ahmed body application. The results provide insight into details about the properties of the architecture we developed while exposing possible future perspectives for this work.

Jingtao Ma, Fang-Bao Tian, John Young et al.

The dynamic behaviours of a filament in a viscoelastic uniform flow were investigated by an immersed boundary-lattice Boltzmann method. The effects of the Reynolds numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula>, ranging from 10 to 200) and the Weissenberg number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>, ranging from 0 to 1.2) on the filament flapping motion and the drag and lift coefficients on the filament were studied. It was found that a higher inertial effect (larger <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula>) promotes the flapping motion of the filament. In addition, the major effect of the viscoelasticity of the Giesekus fluid is to decrease the critical Reynolds number for the flapping motion of the filament and to promote the flapping motion. The drag coefficient on the filament in a Giesekus uniform flow decreases with the increase of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula> at low <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo><</mo><mn>100</mn></mrow></semantics></math></inline-formula>), and experiences oscillations with similar amplitudes at all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula> at a sufficiently high <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo>></mo><mn>100</mn></mrow></semantics></math></inline-formula>). In contrast, the viscoelasticity of the FENE-CR fluid increases the critical Reynolds number at lower <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi><mo><</mo><mn>0.8</mn></mrow></semantics></math></inline-formula>), and shows little influence on the critical Reynolds number at higher <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi><mo>≥</mo><mn>0.8</mn></mrow></semantics></math></inline-formula>). In addition, the viscoelasticity of the FENE-CR fluid hinders the flapping motion of the filament, and increases the drag coefficient on the filament at low <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo><</mo><mn>100</mn></mrow></semantics></math></inline-formula>).

Aishvarya Kumar, Jamshid Nouri, Ali Ghobadian

The occurrence of vortices in the sac volume of automotive multi-hole fuel injectors plays an important role in the development of vortex cavitation, which directly influences the flow structure and emerging sprays that, in turn, influence the engine performance and emissions. In this study, the RANS-based turbulence modelling approach was used to predict the internal flow in a vertical axis-symmetrical multi-hole (6) diesel fuel injector under non-cavitating conditions. The project aimed to predict the aforementioned vortical structures accurately at two different needle lifts in order to form a correct opinion about their occurrence. The accuracy of the simulations was assessed by comparing the predicted mean axial velocity and RMS velocity of LDV measurements, which showed good agreement. The flow field analysis predicted a complex, 3D, vortical flow structure with the presence of different types of vortices in the sac volume and the nozzle hole. Two main types of vortex were detected: the “hole-to-hole” connecting vortex, and double “counter-rotating” vortices emerging from the needle wall and entering the injector hole facing it. Different flow patterns in the rotational direction of the “hole-to-hole” vortices have been observed at the low needle lift (anticlockwise) and full needle lift (clockwise), due to their different flow passages in the sac, causing a much higher momentum inflow at the lower lift with its much narrower flow passage.

Supriyo Naskar, Prabal K. Maiti

The flexibility and stiffness of small DNA play a fundamental role ranging from several biophysical processes to nano-technological applications. Here, we estimate the mechanical properties of short double-stranded DNA (dsDNA) having length ranging from 12 base-pairs (bps) to 56 bps, paranemic crossover (PX) DNA, and hexagonal DNA nanotubes (DNTs) using two widely used coarse-grain models $-$ Martini and oxDNA. To calculate the persistence length ($L_p$) and the stretch modulus ($γ$) of the dsDNA, we incorporate the worm-like chain and elastic rod model, while for DNT, we implement our previously developed theoretical framework. We compare and contrast all the results with previously reported all-atom molecular dynamics (MD) simulation and experimental results. The mechanical properties of dsDNA ($L_p$ $\sim$ 50nm, $γ\sim$ 800-1500 pN), PX DNA ($γ\sim$ 1600-2000 pN) and DNTs ($L_p \sim 1-10\ μ$m, $γ\sim$ 6000-8000 pN) estimated using Martini soft elastic network and oxDNA are in very good agreement with the all-atom MD and experimental values, while the stiff elastic network Martini reproduces order of magnitude higher values of $L_p$ and $γ$. The high flexibility of small dsDNA is also depicted in our calculations. However, Martini models proved inadequate to capture the salt concentration effects on the mechanical properties with increasing salt molarity. OxDNA captures the salt concentration effect on small dsDNA mechanics. But it is found to be ineffective to reproduce the salt-dependent mechanical properties of DNTs. Also, unlike Martini, the time evolved PX DNA and DNT structures from the oxDNA models are comparable to the all-atom MD simulated structures. Our findings provide a route to study the mechanical properties of DNA nanostructures with increased time and length scales and has a remarkable implication in the context of DNA nanotechnology.

Qing Gao

Chaotic inflation is inconsistent with the observational constraint at 68\% CL. Here, we show that the enhancement mechanism with a peak function in the noncanonical kinetic term not only helps the chaotic model $V(φ)=V_0φ^{1/3}$ satisfy the observational constraint at large scales but also enhances the primordial scalar power spectrum by seven orders of magnitude at small scales. The enhanced curvature perturbations can produce primordial black holes of different masses and secondary gravitational waves with different peak frequencies. We also show that the non-Gaussianities of curvature perturbations have little effect on the abundance of primordial black holes and energy density of the scalar-induced secondary gravitational waves.

André Nachbin

A new class of problems in free surface hydrodynamics appeared after the groundbreaking discovery by Yves Couder and Emmanuel Fort. A bouncing droplet in association with Faraday surface waves gives rise to new nonlinear dynamics, in analogy with the pilot-wave proposed by de Broglie. The droplet and the underlying vibrating bath are of silicon oil. A weakly viscous potential theory model should be used. Numerical simulations are presented with one and two bouncing droplets oscillating while confined to their cavities. These oscillators are implicitly coupled by the underlying surface wave field. In certain regimes, the oscillators can spontaneously synchronize, even when placed at a distance. Cavity parameters are varied in order to highlight the sensitive wave-mediated coupling. The present nonlinear wave-mediated oscillator synchronization is more general than that displayed by the celebrated Kuramoto model and therefore of general interest.

Andrei Medved, Riley Davis, Paula A. Vasquez

The Langevin equations (LE) and the Fokker&#8722;Planck (FP) equations are widely used to describe fluid behavior based on coarse-grained approximations of microstructure evolution. In this manuscript, we describe the relation between LE and FP as related to particle motion within a fluid. The manuscript introduces undergraduate students to two LEs, their corresponding FP equations, and their solutions and physical interpretation.