Large Language Models (LLMs) are commonly used to generate solutions for mathematical reasoning problems in the following formats: natural language, code, or a combination of both. In this paper, we explore fundamental questions related to solving mathematical reasoning problems using natural language and code with state-of-the-art LLMs, including GPT-4o-mini and LLama-3.1-8b-Turbo. Our findings show that LLMs are better at reasoning in natural language compared to code. Additionally, although natural language and code serve as complementary forms of reasoning, they can affect each other in a negative way in certain scenarios. These insights motivate our development of a new prompting method, MetaMath, which leverages an LLM to dynamically select the most appropriate reasoning form, resulting in improved performance over comparable baselines with GPT-4o-mini.
Here, using homogeneous nonequilibrium molecular dynamics simulations, we report the thermal transport characteristics of thin Si nanowires (NWs) with varying size and isotope doping ratio. It is identified that crossover in the thermal conductivity (κ) of both isotope doping-free and isotope doped Si-NWs appears at critical sizes, below whichκis enlarged with decreasing size because the hydrodynamic phonon flow predominates, above which, due to the dominant phonon boundary scattering, opposite behavior is observed. With increasing isotope doping, however, the critical size in minimizing theκis moved to small values because the phonon impurity scattering caused by isotope doping is critically involved. Moreover, there is a critical isotope doping (<50%) in the critical size motion, originating from that, above which, the critical size no longer moves due to the persistence of hydrodynamic phonon flow. This study provides new insights into the thermal transport behaviors of quasi-1D structures.
Using molecular dynamics simulations, we investigated the effect of external electric field on ice formation with the present of a substrate surface. It turns out that the electric field can affect the ice formation on substrate surface by altering the dipole orientation of interfacial water molecules (IWs): a crossover from inhibiting to promoting ice formation with the increase of electric field strength. According to the influence of the electric field on ice formation, the electric field strength range of 0.0 V nm-1-7.0 V nm-1can be divided into three regions. In the region I and region III, there are both ice formation on the substrate surface. While, the behavior of IWs in the region I and region III are distinguished, including the arrangements of oxygen atoms and the dipole orientation distribution. In region II, ice formation does not occur in the system within 5 × 200 ns simulations. The IWs show a disorder structure, preventing the ice formation process on substrate. The interfacial water molecular orientation distribution and two-dimensional free energy landscape reveals that the electric field can alter the dipole orientation of the interfacial water and lead a free energy barrier, making the ice formation process harder. Our result demonstrates the external electric field can regulate the behavior of IWs, and further affect the ice formation process. The external electric field act as a crystallization switch of ice formation on substrate, shedding light into the studies on the control of ice crystallization.
Natural gas hydrates (NGHs) hold immense potential as a future energy resource and for sustainable applications such as gas capture and storage. Due to the challenging formation conditions, however, their mechanical properties remain poorly understood. Herein, the mechanical characteristics of tetrahydrofuran (THF) hydrates, a proxy for methane hydrates, were investigated at different ice contents, strain rates, and temperatures using uniaxial compressive experiments. The results unveil a distinct behavior in the peak strength of THF hydrates with a varying ice content, strain rate and temperature, exhibiting an increase as the strain rate and temperature decrease, in contrast to the peak strength-strain rate relationship observed in polycrystalline ice. Based on the experimental data, four machine learning (ML) models including extreme gradient boosting (XGboost), multilayer perceptron (MLP), gradient boosting decision tree (GBDT) and decision tree (DT) were developed to predict the peak strength. The XGboost model demonstrates superior predictive performance, emphasizing the significant influence of ice content and temperature on the peak strength of hydrates. Furthermore, molecular dynamics (MD) simulations were employed to gain insights into the dissociation and formation processes of clathrate cages, as well as phase transitions and amorphization occurring at grain boundaries (GBs) involving diverse unconventional clathrate cages, including 5
Abstract The mechanical properties of graphene oxides (GOs) are of great importance for their practical applications. Herein, extensive first-principles-based ReaxFF molecular dynamics (MD) simulations predict the wrinkling morphology and mechanical properties of nanocrystalline GOs (NCGOs), with intricate effects of grain size, oxidation, hydroxylation, epoxidation, grain boundary (GB) hydroxylation, GB epoxidation, GB oxidation being considered. NCGOs show brittle failures initiating at GBs, obeying the weakest link principle. By training the MD data, four machine learning models are developed with capability in estimating the tensile strength of NCGOs, with sorting as eXtreme Gradient Boosting (XGboost) > multilayer perceptron > gradient boosting decision tree > random forest. In the XGboot model, it is revealed that the strength of NCGOs is greatly dictated by oxidation and grain size, and the hydroxyl group plays more critical role in the strength of NCGOs than the epoxy group. These results uncover the pivotal roles of structural signatures in the mechanical strength of NCGOs, and provide critical guidance for mechanical designs of chemically-functionalized nanostructures.
The thermal transport properties of five-fold twinned (5FT) germanium–silicon (Ge–Si) heteronanowires (h-NWs) with varying cross-sectional areas, germanium (Ge) domain ratios and heterostructural patterns are investigated using homogeneous nonequilibrium molecular dynamics (HNEMD) simulations.
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