Potential Energy Landscape Research Articles

Exploring Nanocluster Potential Energy Surfaces via Deep Reinforcement Learning: Strategies for Global Minimum Search.

The search for global minimum (GM) configurations in nanoclusters is complicated by intricate potential energy landscapes replete with numerous local minima. The complexity of these landscapes escalates with increasing cluster size and compositional diversity. Evolutionary algorithms, such as genetic algorithms, are hampered by slow convergence rates and a propensity for prematurely settling on suboptimal solutions. Likewise, the basin hopping technique faces difficulties in navigating these complex landscapes effectively, particularly at larger scales. These challenges highlight the need for more sophisticated methodologies to efficiently scan the potential energy surfaces of nanoclusters. In response, our research has developed a novel deep reinforcement learning (DRL) framework specifically designed to explore the potential energy surfaces (PES) of nanoclusters, aiming to identify the GM configurations along with other low-energy states. This study demonstrates the framework's effectiveness in managing various nanocluster types, including both mono- and multimetallic compositions, and its proficiency in navigating complex energy landscapes. The model is characterized by remarkable adaptability and sustained efficiency, even as cluster sizes and feature vector dimensions increase. The demonstrated adaptability of DRL in this context underscores its considerable potential in materials science, particularly for the efficient discovery and optimization of novel nanomaterials. To the best of our knowledge, this is the first DRL framework designed for the GM search in nanoclusters, representing a significant innovation in the field.

Multistable Composite Laminate Grids as a Design Tool for Soft Reconfigurable Multirotors

Adaptive‐morphology multirotors exhibit superior versatility and task‐specific performance compared to traditional multirotors owing to their functional morphological adaptability. However, a notable challenge lies in the contrasting requirements of locking each morphology for flight controllability and efficiency while permitting low‐energy reconfiguration. A novel design approach is proposed for reconfigurable multirotors utilizing soft multistable composite laminate airframes. These airframes show kinematically determinate morphologies corresponding to multiple minima in their elastic potential energy landscape. By varying design parameters, the methodology allows for tuning the energy landscape characteristics governing each morphology's structural stability and reconfiguration energetics. The airframe, composed of multistable composite laminate grids, is optimized to maximize rigidity under flight loads and minimize reconfiguration work. The 130‐g reconfigurable multirotor design demonstrates self‐locking properties in an open and a folded configuration, enabling a 48% reduction in width‐span without compromising stability during flight. Soft pneumatic actuators, actuated using a tethered compressed air supply, enable reversible reconfiguration on the ground between open and folded configurations. The design resolves the conflicting requirements of high‐stiffness to lock each flight configuration and low‐actuation work for reconfigurability. By exploiting soft yet multistable structures, the approach combines the stability observed in rigid‐linked reconfigurable multirotors with the low‐effort reconfigurability of soft multirotors, offering new methods for designing adaptive‐morphology multirotors.

Infrared Spectroscopy and Photochemistry of Ethyl Maltol in Low-Temperature Argon Matrix

Ethyl maltol was investigated using matrix isolation infrared spectroscopy and DFT calculations. In an argon matrix (14.5 K), the compound was found to exist in a single conformer (form I), characterized by an intramolecular hydrogen bond with an estimated energy of ~17 kJ mol−1. The IR spectrum of this conformer was assigned, and the molecule’s potential energy landscape was explored to understand the relative stability and isomerization dynamics of the conformers. Upon annealing the matrix to 41.5 K, ethyl maltol was found to predominantly aggregate into a centrosymmetric dimer (2× conformer I) bearing two intermolecular hydrogen bonds with an estimated energy of ca. 28 kJ mol−1 (per bond). The UV-induced (λ > 235 nm) photochemistry of the matrix-isolated ethyl maltol was also investigated. After 1 min of irradiation, band markers of two rearrangement photoproducts formed through the photoinduced detachment-attachment (PIDA) mechanism, in which the ethyl maltol radical acts as an intermediate, were observed: 1-ethyl-3-hydroxy-6-oxibicyclo [3.1.0] hex-3-en-2-one and 2-ethyl-2H-pyran-3,4-dione. The first undergoes subsequent reactions, rearranging to 4-hydroxy-4-propanoylcyclobut-2-en-1-one and photofragmenting to cyclopropenone and 2-hydroxybut-1-en-1-one. Other final products were also observed, specifically acetylene and CO (the expected fragmentation products of cyclopropenone), and CO2. Overall, the study demonstrated ethyl maltol’s high reactivity under UV irradiation, with significant photochemical conversion occurring within minutes. The rapid photochemical conversion, with complete consumption of the compound in 20 min, should be taken into account in designing practical applications of ethyl maltol.

Photo-induced loss of H2 from H2S, CH4, H2O and SiH4, when and why is it possible

We have explored the possibility of forming H⋅ and H2 from H2S, CH4, H2O and SiH4 in a series of ab initio calculations. The key finding is that H2S can give rise to direct photolytic ultrafast formation of H2 This finding is in agreement with the available experimental data and is a result of a directed pathway that leads toward H2 formation at easily accessible wavelengths. It arises at the (conical) intersection between the two lowest-lying electronic states. This intersection is a result of the valence orbital interaction of the two hydrogen atoms. This interaction is becoming more favorable as the S-H bonds simultaneously becomes longer. The H-S σ-σ∗ bonding interaction cannot compete with the bond formation that takes place between the hydrogens as two bonds stretch simultaneously. For oxygen this interaction it predominant. The reason is that sulfur has a higher principal quantum number and the interaction with the 1s of hydrogen therefore is less favorable. The excited states that are involved in the H2 formation from H2S could be populated by, for example, a two-photon 400 nm excitation. The other hydrides have a more entangled potential energy landscape close to the Franck-Condon region in the direction of the reaction coordinate that leads to H2 loss and as a result the direct loss of a hydrogen atom is favored. A two-photon excitation could be induced by femtosecond laser pulses that at the same time is proposed as a future platform for sensing the H2S molecules with the backward transient absorption scheme. The implication would be that both sensing and photoinduced H2 formation could be in place at the same time which justifies the use of expensive femtosecond light sources getting “two for the price of one”.

A Mode Evolution Metric to Extract Reaction Coordinates for Biomolecular Conformational Transitions.

The complex, multidimensional energy landscape of biomolecules makes the extraction of suitable, nonintuitive collective variables (CVs) that describe their conformational transitions challenging. At present, dimensionality reduction approaches and machine learning (ML) schemes are employed to obtain CVs from molecular dynamics (MD)/Monte Carlo (MC) trajectories or structural databanks for biomolecules. However, minimum sampling conditions to generate reliable CVs that accurately describe the underlying energy landscape remain unclear. Here, we address this issue by developing a Mode evolution Metric (MeM) to extract CVs that can pinpoint new states and describe local transitions in the vicinity of a reference minimum from nonequilibrated MD/MC trajectories. We present a general mathematical formulation of MeM for both statistical dimensionality reduction and machine learning approaches. Application of MeM to MC trajectories of model potential energy landscapes and MD trajectories of solvated alanine dipeptide reveals that the principal components which locate new states in the vicinity of a reference minimum emerge well before the trajectories locally equilibrate between the associated states. Finally, we demonstrate a possible application of MeM in designing efficient biased sampling schemes to construct accurate energy landscape slices that link transitions between states. MeM can help speed up the search for new minima around a biomolecular conformational state and enable the accurate estimation of thermodynamics for states lying on the energy landscape and the description of associated transitions.

Moiré-pattern-tuned interlayer friction of two-dimensional α- and β-tellurene via first-principles calculations and experimental validation

Tellurene, as an emerging class of two-dimensional (2D) materials, exhibit distinctive physicochemical properties derived from their varied structural morphologies, particularly in van der Waals (vdW) heterostructures formed between their allotropes, demonstrating substantial potential for superlubricity applications. This study employs a synergistic approach that combines theoretical calculations with experimental investigations to investigate the tribological performance of two tellurene allotropes (α- and β-Te) and their allotropic homojunctions (α-Te/β-Te). The frictional forces of the tellurene systems under varying twist angles were predicted by applying potential energy surfaces (PESs) to the Prandtl–Tomlinson (PT) model. These findings indicate that a reduction in energy barriers leads to decreased frictional forces, thereby enhancing the system's superlubricity. Notably, the frictional response is influenced not only by the interlayer sliding barriers but also by the shape and periodicity of the potential energy landscapes. Furthermore, leveraging the concept of the lubricating figure of merit, this study provides an in-depth analysis of the intrinsic frictional characteristics within a tellurene system. Experimentally, few-layer α- and β-Te tellurene were successfully synthesized, and their interlayer frictional properties were measured, showing high congruence with theoretical predictions. The outcomes reveal the exceptional interlayer frictional performance of tellurene under controlled twist angles, with the β-Te phase exhibiting superior lubricity over α-Te and the formation of an allotropic homojunction (α-Te/β-Te) further enhancing the interlayer superlubricity. These results not only deepen our understanding of the tribological performance of tellurene but also offer a new perspective on the frictional behavior of 2D materials.

Unraveling the mechanism of carbonic anhydrase IX inhibition by alkaloids from Ruta chalepensis: A synergistic analysis of in vitro and in silico data

Due to the pivotal role of carbonic anhydrase IX (CA IX) in pathological conditions, there's a pressing need for novel inhibitors to improve patient outcomes and clinical management. Herein, we investigated the inhibitory efficacy of six alkaloids from Ruta chalepensis against CA IX through in vitro inhibition assay and computational modeling. Skimmianine and maculosidine displayed significant inhibitory activity in vitro, with low IC50 values of 105.2 ± 3.2 and 295.7 ± 14.1 nM, respectively. Enzyme kinetics analyses revealed that skimmianine exhibited a mixed inhibition mode, contrasting with the noncompetitive inhibition mechanism observed for the reference drug (acetazolamide), as indicated by intersecting lines in the Lineweaver-Burk plots. The findings of docking calculations revealed that skimmianine and maculosidine exhibited extensive polar interactions with the enzyme. These alkaloids demonstrate substantial binding interactions and occupy identical binding site as acetazolamide, thereby enhancing their efficacy as inhibitors of CA IX. Utilizing a 100 ns molecular dynamics (MD) simulation, the dynamic interactions between isolated alkaloids and CA IX were intensively assessed. Analysis of diverse MD parameters revealed that skimmianine and maculosidine displayed consistent trajectories and notable energy stabilization during their interaction with CA IX. The findings of MM/PBSA analysis depicted the minimum binding free energy for skimmianine and maculosidine. In addition, the Potential Energy Landscape (PEL) analysis revealed distinct and stable conformational states for the CA IX-ligand complexes, with Skimmianine showing the most stable and lowest energy configuration. These computational findings align with experimental results, emphasizing the potential efficacy of skimmianine and maculosidine as inhibitors of CA IX.

Ab initio computations from 78Ni towards 70Ca along neutron number N = 50

We present coupled-cluster computations of nuclei with neutron number N=50 “south” of 78Ni using nucleon-nucleon and three-nucleon forces from chiral effective field theory. We find an erosion of the magic number N=50 toward 70Ca manifesting itself by an onset of deformation and increased complexity in the ground states. For 78Ni, we predict a low-lying rotational band consistent with recent data, which up until now has been a challenge for ab initio nuclear models. Ground states are deformed in 76Fe, 74Cr, and 72Ti, although the spherical states are too close in energy to unambiguously identify the shape of the ground state within the uncertainty estimates. In 70Ca, the potential energy landscape from quadrupole-constrained Hartree-Fock computations flattens, and the deformation becomes less rigid. We also compute the low-lying spectra and B(E2) values for these neutron-rich N=50 nuclei.

True Random Number Generator Based on Chaotic Oscillation of a Tunable Double-Well MEMS Resonator.

Chaotic systems have aroused interest across various scientific disciplines such as physics, biology, chemistry, and meteorology. The deterministic but unpredictable nature of a chaotic system is an ideal feature for random number generation. Microelectromechanical systems (MEMS) are a promising technology that effectively harnesses chaos, offering advantages such as a compact footprint, scalability, and low power consumption. This paper presents a true random number generator (TRNG) based on a double-well MEMS resonator integrated with an actuator and position sensor. The potential energy landscape of the proposed MEMS resonator is actively tunable with a direct current voltage. Experimental demonstrations of tunable bistability and chaotic resonance are reported in this paper. A chaotic time sequence is generated through piezoresistive sensing of the position of the MEMS resonator once it is driven into the chaotic regime. Subsequently, the randomness of the bit sequence, achieved by applying the exclusive or function to a digital chaotic sequence and its delayed differential is confirmed to meet the National Institute of Standards and Technology specifications. Moreover, the throughput and energy efficiency of the proposed MEMS-based TRNG can be adjusted from 50 kb s-1 and 0.44 pJ per bit at a low energy barrier to 167 kb s-1 and 6.74 pJ per bit at a high energy barrier by changing the MEMS device's potential well. The tunability of the proposed double-well MEMS resonator not only offers continuous adjustments in the energy efficiency of TNRG but also unveils vast and diverse research opportunities in analog computing, encryption, and secure communications.

A physics-informed neural SDE network for learning cellular dynamics from time-series scRNA-seq data.

Learning cellular dynamics through reconstruction of the underlying cellular potential energy landscape (aka Waddington landscape) from time-series single-cell RNA sequencing (scRNA-seq) data is a current challenge. Prevailing data-driven computational methods can be hampered by the lack of physical principles to guide learning from complex data, resulting in reduced prediction accuracy and interpretability when applied to infer cell population dynamics. Here, we propose PI-SDE, a physics-informed neural stochastic differential equation (SDE) framework that combines the Hamilton-Jacobi (HJ) equation and neural SDE to learn cellular dynamics. Grounded in potential energy theory of biological systems, PI-SDE integrates the principle of least action by enforcing the HJ equation when reconstructing cellular potential energy function. This approach not only facilitates accurate predictions, but also improves interpretability, especially in the reconstructed potential energy landscape. Through benchmarking on two real scRNA-seq datasets, we demonstrate the importance of incorporating the HJ regularization term in dynamic inference, especially in predicting gene expression at held-out time points. Meanwhile, the learned potential energy landscape provides biologically interpretable insights into the process of cell differentiation. Our framework enhances model performance, while maintaining robustness and stability. PI-SDE software is available at https://github.com/QiJiang-QJ/PI-SDE.

Computational Characterization of the On-Surface Synthesis of Low-Dimensional Nanostructures

On-surface chemistry represents a fast-growing field allowing to synthesize molecular structures not available by traditional wet chemistry. In this context, high-resolution scanning probe microscopy techniques are able to provide unprecedented spatial resolution, allowing to precisely identify individual products of the reactions. Nevertheless, a deep understanding of the reaction mechanism under the conditions imposed by the substrate remains unknown.Nowadays, various computational strategies are employed to characterize the optimal reaction pathways of the chemical processes that take place on the surfaces of solids. For example, one of the most popular approaches is the nudged elastic band (NEB) as well as different transition state theory methods beyond it. These approaches had demonstrated their capability to characterize the potential energy landscape of the reaction pathways [1-2]. Another approach that had attracted the interest of the on-surface synthesis community is the application of molecular dynamics (MD) methods, within the canonical ensemble, and based on the QM/MM (quantum mechanics/molecular mechanics) of the interatomic forces [3-4]. This approach, which combines Density functional theory (DFT) and empirical force fields to describe the interaction forces, allows to simulate very large systems, at a very low computational cost while still accounting for the crucial quantum mechanics interactions. Also, such temperature-dependent simulations include the effect of entropy, vibrations modes, concerted motion, etc.I will present the experimental and computational results of different projects in which we have made use of the aforementioned computational approaches to achieve a better understanding of the on-surface synthesis experiments performed by the group. For example, the rationalization of the selective cyclodehydrogenation of non-benzenoid nanographenes deposited on a Au(111) substrate by means of temperature-dependent MD calculations and the analysis of the obtained vibrational modes (See Figure 1a). The group had also studied the stepwise transformation of coronene-based organometallic networks into two-dimensional covalent patches through intermolecular homocoupling (See Figure 1b). We had as well investigated the transformation of indenyl precursors, through a triple C-H cleavage followed by a peripheral directed homocoupling, to form a polyacetylene backboned polymer that features a parity dependent and highly delocalized soliton in-gap state (See Figure 1c).

Examination of static fission properties of 236\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{236}$$\\end{document}U and 233\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{233}$$\\end{document}Th using Cassinian oval parametrization within the macroscopic–microscopic approach

We have conducted a thorough analysis of the potential energy surfaces (PES) in 236\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{236}$$\\end{document}U and 233\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{233}$$\\end{document}Th using the Cassini-ovals parameterization within the macro–micro approach. We employed the state-of-the-art immersion water flow (IWF) method to study the saddles on four-dimensional energy grids encompassing reflection-asymmetric shapes. For 233\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{233}$$\\end{document}Th, we computed the adiabatic potential energy surfaces by minimizing configurations with one blocked neutron within ten levels below and above the Fermi level. Our results show satisfactory agreement with empirical and experimental estimates for both nuclei, specifically regarding the first and second fission barriers. This suggests that our method holds promise in efficiently describing non-compact shapes while reducing the dimensionality of the space without sacrificing accuracy. Interestingly, employing Cassinian oval parameterization fails to reveal a pronounced, hyper-deformed third minimum in the potential energy landscape. Instead, only a shallow third minimum is observed for 233\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{233}$$\\end{document}Th, while in 236\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{236}$$\\end{document}U, this minimum ultimately vanishes. This finding holds significant importance when considering the modeling of fission cross-sections.

Protonation Effects on the Benzoxazine Formation Pathways and Products Distribution.

The effect of acidic media on the formation of the 3,4-dihydro-2H-3-phenyl-1,3-benzoxazine Bz is evaluated, focusing on the differentiation of intermediates and products formed by the distinct pathways observed in the presence and absence of acid. The use of real-time mass spectrometry (PSI-ESI-MS) coupled to tandem mass spectrometry and infrared multiple photon dissociation (IRMPD) allowed the differentiation of the species observed during the synthesis of benzoxazines in these different conditions. The results suggest that formic acid promotes the formation of aniline and phenol condensation products (IC and IIC) by protecting the aniline amino group and enhancing the formaldehyde electrophilicity. The results also suggest that although the presence of acid allow a more efficient potential energy landscape to be accessed, the last cyclization step for the formation of benzoxazines cannot be mediated by the protonation route intermediate (ROP Bz). Overall, the conclusions presented here provide important information about the synthesis of benzoxazines under acidic conditions, allowing the development of optimal reaction conditions.

Recent Progress in the Physical Principles of Dynamic Ground Self-Righting.

Animals and robots must self-right on the ground after overturning. Biology research has described various strategies and motor patterns in many species. Robotics research has devised many strategies. However, we do not well understand the physical principles of how the need to generate mechanical energy to overcome the potential energy barrier governs behavioral strategies and 3D body rotations given the morphology. Here, I review progress on this which I led studying cockroaches self-righting on level, flat, solid, low-friction ground, by integrating biology experiments, robotic modeling, and physics modeling. Animal experiments using three species (Madagascar hissing, American, and discoid cockroaches) found that ground self-righting is strenuous and often requires multiple attempts to succeed. Two species (American and discoid cockroaches) often self-right dynamically, using kinetic energy to overcome the barrier. All three species use and often stochastically transition across diverse strategies. In these strategies, propelling motions are often accompanied by perturbing motions. All three species often display complex yet stereotyped body rotation. They all roll more in successful attempts than in failed ones, which lowers the barrier, as revealed by a simplistic 3D potential energy landscape of a rigid body self-righting. Experiments of an initial robot self-righting via rotation about a fixed axis revealed that the longer and faster appendages push, the more mechanical energy can be gained to overcome the barrier. However, the cockroaches rarely achieve this. To further understand the physical principles of strenuous ground self-righting, we focused on the discoid cockroach's leg-assisted winged self-righting. In this strategy, wings propel against the ground to pitch the body up but are unable to overcome the highest pitch barrier. Meanwhile, legs flail in the air to perturb the body sideways to self-right via rolling. Experiments using a refined robot and an evolving 3D potential energy landscape revealed that, although wing propelling cannot generate sufficient kinetic energy to overcome the highest pitch barrier, it reduces the barrier to allow small kinetic energy from the perturbing legs to probabilistically overcome the barrier to self-right via rolling. Thus, only by combining propelling and perturbing can self-righting be achieved when it is so strenuous; this physical constraint leads to the stereotyped body rotation. Finally, multi-body dynamics simulation and template modeling revealed that the animal's substantial randomness in wing and leg motions helps it, by chance, to find good coordination, which accumulates more mechanical energy to overcome the barrier, thus increasing the likelihood of self-righting.

Enabling high throughput deep reinforcement learning with first principles to investigate catalytic reaction mechanisms

Exploring catalytic reaction mechanisms is crucial for understanding chemical processes, optimizing reaction conditions, and developing more effective catalysts. We present a reaction-agnostic framework based on high-throughput deep reinforcement learning with first principles (HDRL-FP) that offers excellent generalizability for investigating catalytic reactions. HDRL-FP introduces a generalizable reinforcement learning representation of catalytic reactions constructed solely from atomic positions, which are subsequently mapped to first-principles-derived potential energy landscapes. By leveraging thousands of simultaneous simulations on a single GPU, HDRL-FP enables rapid convergence to the optimal reaction path at a low cost. Its effectiveness is demonstrated through the studies of hydrogen and nitrogen migration in Haber-Bosch ammonia synthesis on the Fe(111) surface. Our findings reveal that the Langmuir-Hinshelwood mechanism shares the same transition state as the Eley-Rideal mechanism for H migration to NH2, forming ammonia. Furthermore, the reaction path identified herein exhibits a lower energy barrier compared to that through nudged elastic band calculation.

Stability of floating objects at a two-fluid interface

We explore the stability of floating objects at a two-fluid interface through mathematical modeling and experimentation. Our models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes’ Principle extended to the two-fluid scenario. We investigate floating shapes with uniform, two-dimensional cross sections and identify analytically and/or computationally a potential energy landscape that helps identify stable and unstable floating orientations. We compare our analyses and computations to experiments on floating objects designed and created through 3D printing. Additionally, the paper includes open problems for further study.

Is the glassy dynamics same in 2D as in 3D? The Adam Gibbs relation test.

It has been recognized of late that even amorphous, glass-forming materials in two dimensions (2D) are affected by Mermin-Wagner-type long wavelength thermal fluctuation, which is inconsequential in three dimensions (3D). We consider the question of whether the effect of spatial dimension on dynamics is only limited to such fluctuations or if the nature of glassy dynamics is intrinsically different in 2D. To address it, we study the relationship between dynamics and thermodynamics using the Adam-Gibbs (AG) relation and the random first order transition (RFOT) theory. Using two model glass-forming liquids, we find that even after removing the effect of long wavelength fluctuations, the AG relation breaks down in two dimensions. Next, we consider the effect of anharmonicity of vibrational entropy-a second factor that affects the thermodynamics but not dynamics. Using the potential energy landscape formalism, we explicitly compute the configurational entropy, both with and without the anharmonic correction. We show that even with both the corrections, the AG relation still breaks down in 2D. The extent of deviation from the AG relation crucially depends on the attractive vs repulsive nature of interparticle interactions, choice of representative timescale (diffusion coefficient vs α-relaxation time), and implies that the RFOT scaling exponents also depend on these factors. Thus, our results suggest that some differences in the nature of glassy dynamics between 2D and 3D remain that are not explained by long wavelength fluctuations.

The simplified energy landscape of the φ 4 model and the phase transition

The on-lattice φ 4 model is a paradigmatic example of a continuous real-variable model undergoing a continuous symmetry-breaking phase transition (SBPT). Here, we study the Z2 -symmetric mean-field case without the quadratic term in the local potential. We show that the Z2 -SBPT is not affected by the quadratic term and that the potential energy landscape is greatly simplified from a geometric–topological viewpoint. In particular, only three critical points exist to confront, with a number growing as eN (N is the number of degrees of freedom) of the model with a negative quadratic term. We focus on the properties of the equipotential surfaces with the aim to deepen the link between SBPTs and the essential properties of a potential that is capable of entailing them. The results are interpreted in view of of some recent achievements regarding rigorous necessary and sufficient conditions for a Z2 -SBPT.

Effects of nonlinearities and geometric imperfections on multistability and deformation localization in wrinkling films on planar substrates

Compressed elastic films on soft substrates release part of their strain energy by wrinkling, which represents a loss of symmetry, characterized by a pitchfork bifurcation. Its development is well understood at the onset of supercritical bifurcation, but not beyond, or in the case of subcritical bifurcation. This is mainly due to nonlinearities and the extreme imperfection sensitivity. In both types of bifurcations, the energy–displacement diagrams that can characterize an energy landscape are non-convex, which is notoriously difficult to determine numerically or experimentally, let alone analytically. To gain an elementary understanding of such potential energy landscapes, we take a thin beam theory suitable for analyzing large displacements under small strains and significantly reduce its complexity by reformulating it in terms of the tangent rotation angle. This enables a comprehensive analytical and numerical analysis of wrinkling elastic films on planar substrates, which are effective stiffening and/or softening due to either geometric or material nonlinearities. We also validate our findings experimentally. We explicitly show how effective stiffening nonlinear behavior (e.g., due to substrate or membrane deformations) leads to a supercritical post-bifurcation response, makes the energy landscape non-convex through energy barriers causing multistability, which is extremely problematic for numerical computation. Moreover, this type of nonlinearity promotes uni-modal, uniformly distributed, periodic deformation patterns. In contrast, nonlinear effective softening behavior leads to subcritical post-bifurcation behavior, similarly divides the energy landscape by energy barriers and conversely promotes localization of deformations. With our theoretical model we can thus explain an experimentally observed phenomenon that in structures with effective softening followed by an effective stiffening behavior, the symmetry is initially broken by localizing the deformation and later restored by forming periodic, distributed deformation patterns as the load is increased. Finally, we show that initial imperfections can significantly alter the local or global energy-minimizing deformation pattern and completely remove some energy barriers. We envision that this knowledge can be extrapolated and exploited to convexify extremely divergent energy landscapes of more sophisticated systems, such as wrinkling compressed films on curved substrates (e.g., on cylinders and spheres) and that it will enable elementary analysis and the development of specialized numerical tools.

Accelerating structure search using atomistic graph-based classifiers.

We introduce an atomistic classifier based on a combination of spectral graph theory and a Voronoi tessellation method. This classifier allows for the discrimination between structures from different minima of a potential energy surface, making it a useful tool for sorting through large datasets of atomic systems. We incorporate the classifier as a filtering method in the Global Optimization with First-principles Energy Expressions (GOFEE) algorithm. Here, it is used to filter out structures from exploited regions of the potential energy landscape, whereby the risk of stagnation during the searches is lowered. We demonstrate the usefulness of the classifier by solving the global optimization problem of two-dimensional pyroxene, three-dimensional olivine, Au12, and Lennard-Jones LJ55 and LJ75 nanoparticles.