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Yu Xie

Publications and source records attributed to Yu Xie.

At least 109 records · Page 6Linked to original sources

On-the-Fly Active Learning of Interpretable Bayesian Force Fields for Atomistic Rare Events

Machine learned force fields typically require manual construction of training sets consisting of thousands of first principles calculations, which can result in low training efficiency and unpredictable errors when applied to structures not represented in the training set of the model. This severely limits the practical application of these models in systems with dynamics governed by important rare events, such as chemical reactions and diffusion. We present an adaptive Bayesian inference method for automating the training of interpretable, low-dimensional, and multi-element interatomic force fields using structures drawn on the fly from molecular dynamics simulations. Within an active learning framework, the internal uncertainty of a Gaussian process regression model is used to decide whether to accept the model prediction or to perform a first principles calculation to augment the training set of the model. The method is applied to a range of single- and multi-element systems and shown to achieve a favorable balance of accuracy and computational efficiency, while requiring a minimal amount of ab initio training data. We provide a fully open-source implementation of our method, as well as a procedure to map trained models to computationally efficient tabulated force fields.

physics.comp-ph↗

Diabatic Hamiltonian Construction in van der Waals heterostructure complexes

A diabatization method is developed for the approximated description of the photoinduced charge separation/transfer processes in the van der Waals (vdW) heterostructure complex, which is based on the wavefunction projection approach using a plane wave basis set in the framework of the single-particle picture. We build the diabatic Hamiltonian for the description of the interlayer photoinduced hole-transfer process of the two-dimensional vdW MoS2/WS2 heterostructure complexes. The diabatic Hamiltonian gives the energies of the localized valence band states (located at MoS2 and valence band states (located at WS2), as well as the couplings between them. The wavefunction projection method provides a practical and reasonable approach to construct the diabatic model in the description of photoinduced charge transfer processes in the vdW heterostructure complexes.

physics.chem-ph↗

Initial Sampling in Symmetrical Quasiclassical Dynamics Based on Li-Miller Mapping Hamiltonian

A symmetrical quasiclassical (SQC) dynamics approach based on the Li-Miller (LM) mapping Hamiltonian (SQC-LM) was employed to describe nonadiabatic dynamics. In principle, the different initial sampling procedures may be applied in the SQC-LM dynamics, and the results may be dependent on the initial sampling. We provided various initial sampling approaches and checked their influence. We selected two groups of models including site-exciton models for exciton dynamics and linear vibronic coupling models for conical intersections to test the performance of SQC-LM dynamics with the different initial sampling methods. The results were examined with respect to those of the accurate multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) quantum dynamics. For both two models, the SQC-LM method more-or-less gives a reasonable description of the population dynamics, while the influence of the initial sampling approaches on the final results is noticeable. It seems that the proper initial sampling methods should be determined by the system under study. This indicates that the combination of the SQC-LM method with a suitable sampling approach may be a potential method in the description of nonadiabatic dynamics.

physics.chem-ph↗

On the containment problem for fat points ideals

In this note we show that Harbourne's conjecture is true for symbolic powers of ideals of points, we check that the stable version of this conjecture is valid for ideals of very general points (resp. generic points) in $\mathbb P_{\mathbb K}^N$ (resp. $\mathbb P_{\mathbb K(\underline{z})}^N$). We also show that this conjecture and the Harbourne-Huneke conjecture are true for a class of ideals $I$ defining fat points obtained from line arrangements in $\mathbb P_{\mathbb K}^2$.

math.AC↗

Performance of trajectory surface hopping method in the treatment of ultrafast intersystem crossing dynamics

We carried out extensive studies to examine the performance of the fewest-switches surface hopping method in the description of the ultrafast intersystem crossing dynamic of various singlet-triplet (S-T) models by comparison with the results of the exact full quantum dynamics. Different implementation details and some derivative approaches were examined. As expected, it is better to perform the trajectory surface hopping calculations in the spin-adiabatic representation or by the local diabatization approach, instead of in the spin-diabatic representation. The surface hopping method provides reasonable results for the short-time dynamics in the S-T model with weak spin-orbital coupling (diabatic coupling), although it does not perform well in the models with strong spin-orbital coupling (diabatic coupling). When the system accesses the S-T potential energy crossing with rather high kinetic energy, the trajectory surface hopping method tends to produce the good description of the nonadiabatic intersystem crossing dynamics. The impact of the decoherence correction on the performance of the trajectory surface hopping is system dependent. It improves the result accuracy in many cases, while its influence may also be minor for other cases.

physics.chem-ph↗

Performance Evaluation of the Symmetrical Quasi-Classical Dynamics Method based on Meyer-Miller Mapping Hamiltonian in the Treatment of Site-Exciton Models

The symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC) shows the great potential in the treatment of the nonadiabatic dynamics of complex systems. We performed the comprehensive benchmark calculations to evaluate the performance of the MM-SQC method in various site-exciton models with respect to the accurate results of quantum dynamics method multilayer multiconfigurational time-dependent Hartree (ML-MCTDH). The parameters of the site-exciton models are chosen to represent a few of prototypes used in the description of photoinduced excitonic dynamics processes in photoharvesting systems and organic solar cells, which include the rather board situations with the fast or slow bath and different system-bath couplings. When the characteristic frequency of the bath is low, the MM-SQC method performs extremely well, and it gives almost the identical results to those of ML-MCTDH. When the fast bath is considered, the deviations exist between the MM-SQC and ML-MCTDH results if the high-frequency bath modes are improperly treated by the classical manner. When the so-called adiabatic renormalization was employed to construct the reduced Hamiltonian by freezing high-frequency modes, the MM-SQC dynamics can give the results comparable to the ML-MCTDH ones. Thus, the MM-SQC method itself provide reasonable results in all test site-exciton models, while the proper treatments of the bath modes must be employed. The possible dependence of the MM-SQC dynamics on the different initial sampling methods for the nuclear degrees of freedom is also discussed.

physics.chem-ph↗

Analysis of Trajectory Similarity and Configuration Similarity in On-the-Fly Surface-Hopping Simulation on Multi-Channel Nonadiabatic Photoisomerization Dynamics

We propose an 'automatic' approach to analyze the results of the on-the-fly trajectory surface hopping simulation on the multi-channel nonadiabatic photoisomerization dynamics by considering the trajectory similarity and the configuration similarity. We choose a representative system phytochromobilin chromophore model to illustrate the analysis protocol. After a large number of trajectories are obtained, it is possible to define the similarity of different trajectories by the Fréchet distance and to employ the trajectory clustering analysis to divide all trajectories into several clusters. Each cluster in principle represents a photoinduced isomerization reaction channel. This idea provides an effective approach to understand the branching ratio of the multi-channel photoisomerization dynamics. For each cluster the dimensionality reduction is employed to understand the configuration similarity in the trajectory propagation, which provides the understanding of the major geometry evolution features in each reaction channel. The results show that this analysis protocol not only assigns all trajectories into different photoisomerization reaction channels, but also extracts the major molecular motion without the requirement of the pre-known knowledge of the active photoisomerization site. As a side product of this analysis tool, we can also easily to find the so-called 'typical' or 'representative' trajectory for each reaction channel.

physics.chem-ph↗

Inclusion of machine learning kernel ridge regression potential energy surfaces in on-the-fly nonadiabatic molecular dynamics simulation

We discuss a theoretical approach that employs machine learning potential energy surfaces (ML-PESs) in the nonadiabatic dynamics simulation of polyatomic systems by taking 6-aminopyrimidine as a typical example. The Zhu-Nakamura theory is employed in the surface hopping dynamics, which does not require the calculation of the nonadiabatic coupling vectors. The kernel ridge regression is used in the construction of the adiabatic PESs. In the nonadiabatic dynamics simulation, we use ML-PESs for most geometries and switch back to the electronic structure calculations for a few geometries either near the S1/S0 conical intersections or in the out-of-confidence regions. The dynamics results based on ML-PESs are consistent with those based on CASSCF PESs. The ML-PESs are further used to achieve the highly efficient massive dynamics simulations with a large number of trajectories. This work displays the powerful role of ML methods in the nonadiabatic dynamics simulation of polyatomic systems.

physics.chem-ph↗

Chudnovsky's Conjecture for very general points in $\mathbb{P}_k^{N}$

We prove a long-standing conjecture of Chudnovsky for very general and generic points in $\mathbb{P}_k^N$, where $k$ is an algebraically closed field of characteristic zero, and for any finite set of points lying on a quadric, without any assumptions on $k$. We also prove that for any homogeneous ideal $I$ in the homogeneous coordinate ring $R=k[x_0, \ldots, x_N]$, Chudnovsky's conjecture holds for large enough symbolic powers of $I$.

math.AC↗

Technical Report: A Methodology for Studying 802.11p VANET Broadcasting Performance with Practical Vehicle Distribution

In a Vehicular Ad-hoc Network (VANET), the performance of the communication protocol is influenced heavily by the vehicular density dynamics. However, most of the previous works on VANET performance modeling paid little attention to vehicle distribution, or simply assumed homogeneous car distribution. It is obvious that vehicles are distributed non-homogeneously along a road segment due to traffic signals and speed limits at different portions of the road, as well as vehicle interactions that are significant on busy streets. In light of the inadequacy, we present in this paper an original methodology to study the broadcasting performance of 802.11p VANETs with practical vehicle distribution in urban environments. Firstly, we adopt the empirically verified stochastic traffic models, which incorporates the effect of urban settings (such as traffic lights and vehicle interactions) on car distribution and generates practical vehicular density profiles. Corresponding 802.11p protocol and performance models are then developed. When coupled with the traffic models, they can predict broadcasting efficiency, delay, as well as throughput performance of 802.11p VANETs based on the knowledge of car density at each location on the road. Extensive simulation is conducted to verify the accuracy of the developed mathematical models with the consideration of vehicle interaction. In general, our results demonstrate the applicability of the proposed methodology on modeling protocol performance in practical signalized road networks, and shed insights into the design and development of future communication protocols and networking functions for VANETs.

cs.NI↗

Symmetry relations revealed in Mueller Matrix hemispherical maps

The hemispherical Mueller matrix map for light reflected from a plane-parallel planetary atmosphere is shown to obey several symmetry properties that provide a straightforward method to check their physical realizability. The mirror scattering relation and the reciprocity relation are employed to support the symmetry rules for hemispherical Mueller matrix maps. Additionally, two classes of experiments are identified in which the symmetry rules can be applied, namely, when the incident beam is at zenith and off- zenith angles and the scattering particles are spheres and randomly oriented hexagonal particles.

physics.optics↗

Generalized stretched ideals and Sally Conjecture

We introduce the concept of $j$-stretched ideals in a Noetherian local ring. This notion generalizes to arbitrary ideals the classical notion of stretched $\mathfrak{m}$-primary ideals of Sally and Rossi-Valla, as well as the concept of ideals of minimal and almost minimal $j$-multiplicity introduced by Polini-Xie. One of our main theorems states that, for a $j$-stretched ideal, the associated graded ring is Cohen-Macaulay if and only if two classical invariants of the ideal, the reduction number and the index of nilpotency, are equal. Our second main theorem, presenting numerical conditions which ensure the almost Cohen-Macaulayness of the associated graded ring of a $j$-stretched ideal, provides a generalized version of Sally's conjecture. This work, which also holds for modules, unifies the approaches of Rossi-Valla and Polini-Xie and generalizes simultaneously results on the Cohen-Macaulayness or almost Cohen-Macaulayness of the associated graded module by several authors, including Sally, Rossi-Valla, Wang, Elias, Corso-Polini-Vaz Pinto, Huckaba, Marley and Polini-Xie.

math.AC↗

Generalized Hilbert coefficients and Northcott's inequality

Let $R$ be a Cohen-Macaulay local ring of dimension $d$ with infinite residue field. Let $I$ be an $R$-ideal that has analytic spread $\ell(I)=d$, $G_d$ condition and the Artin-Nagata property $AN^-_{d-2}$. We provide a formula relating the length $λ(I^{n+1}/JI^{n})$ to the difference $P_I(n)-H_I(n)$, where $J$ is a general minimal reduction of $I$, $P_I(n)$ and $H_I(n)$ are the generalized Hilbert-Samuel polynomial and the generalized Hilbert-Samuel function in the sense of C. Polini and Y. Xie. We then use it to establish formulas to compute the higher generalized Hilbert coefficients of $I$. As an application, we extend Northcott's inequality to non $\mathfrak{m}$-primary ideals. When equality holds in the generalized Northcott's inequality, the ideal $I$ enjoys nice properties. Indeed, in this case, we prove that the reduction number of $I$ is at most one and the associated graded ring of $I$ is Cohen-Macaulay. We also recover results of G. Colom$\acute{\rm e}$-Nin, C. Polini, B. Ulrich and Y. Xie on the positivity of the generalized first Hilbert coefficient $j_1(I)$. Our work extends that of S. Huckaba, C. Huneke and A. Ooishi to ideals that are not necessarily $\mathfrak{m}$-primary.

math.AC↗

Hybrid Density Functional Study of Structural and Electronic Properties of Functionalized \ce{Ti_{n+1}X_n} (X= C, N) monolayers

Density functional theory simulations with conventional (PBE) and hybrid (HSE06) functionals were performed to investigate the structural and electronic properties of MXene monolayers, \ce{Ti_{n+1}C_n} and \ce{Ti_{n+1}N_n} ($n$ = 1--9) with surfaces terminated by O, F, H, and OH groups. We find that PBE and HSE06 give similar results. Without functional groups, MXenes have magnetically ordered ground states. All the studied materials are metallic except for \ce{Ti_{2}CO_{2}}, which we predict to be semiconducting. The calculated density of states at the Fermi level of the thicker MXenes ($n$ $\geqslant$ 5) is much higher than for thin MXenes, indicating that properties such as electronic conductivity and surface chemistry will be different. In general, the carbides and nitrides behave differently with the same functional groups.

cond-mat.mtrl-sci↗

Generalized Hilbert Functions

Let $M$ be a finite module and let $I$ be an arbitrary ideal over a Noetherian local ring. We define the generalized Hilbert function of $I$ on $M$ using the 0th local cohomology functor. We show that our definition re-conciliates with that of Ciuperc$\breve{\rm a}$. By generalizing Singh's formula (which holds in the case of $λ(M/IM)<\infty$), we prove that the generalized Hilbert coefficients $j_0,..., j_{d-2}$ are preserved under a general hyperplane section, where $d={\rm dim}\,M$. We also keep track of the behavior of $j_{d-1}$. Then we apply these results to study the generalized Hilbert function for ideals that have minimal $j$-multiplicity or almost minimal $j$-multiplicity. We provide counterexamples to show that the generalized Hilbert series of ideals having minimal or almost minimal $j$-multiplicity does not have the `expected' shape described in the case where $λ(M/IM)<\infty$. Finally we give a sufficient condition such that the generalized Hilbert series has the desired shape.

math.AC↗

Generalized stretched ideals and Sally's Conjecture

Given a finite module $M$ over a Noetherian local ring $(R, \m)$, we introduce the concept of $j$-stretched ideals on $M$. Thanks to a crucial specialization lemma, we show that this notion greatly generalizes (to arbitrary ideals, and with respect to modules) the classical definition of stretched $\m$-primary ideals of Sally and Rossi-Valla, as well as the notion of minimal and almost minimal $j$-multiplicity given recently by Polini-Xie. For $j$-stretched ideals $I$ on a Cohen-Macaulay module $M$, we show that ${\rm gr}_I(M)$ is Cohen-Macaulay if and only if two classical invariants of $I$, the reduction number and the index of nilpotency, are equal. Moreover, for the same class of ideals, we provide a generalized version of Sally's conjecture (proving the almost Cohen-Macaulayness of associated graded rings). Our work unifies the approaches of Rossi-Valla and Polini-Xie and generalizes simultaneously results on the (almost) Cohen-Macaulayness %and almost Cohen-Macaulayness of associated graded modules by several authors, including Sally, Rossi-Valla, Wang, Elias, Rossi, Corso-Polini-Vaz Pinto, Huckaba and Polini-Xie.

math.AC↗

On the Cohen-Macaulayness of the conormal module of an ideal

In the present paper we investigate a question stemming from a long-standing conjecture of Vasconcelos: given a generically a complete intersection perfect ideal I in a regular local ring R, is it true that if I/I^2 (or R/I^2) is Cohen-Macaulay then R/I is Gorenstein? Huneke and Ulrich, Minh and Trung, Trung and Tuan and - very recently - Rinaldo Terai and Yoshida, already considered this question and gave a positive answer for special classes of ideals. We give a positive answer for some classes of ideals, however, we also exhibit prime ideals in regular local rings and homogeneous level ideals in polynomial rings showing that in general the answer is negative. The homogeneous examples have been found thanks to the help of J. C. Migliore. Furthermore, the counterexamples show the sharpness of our main result. As a by-product, we exhibit several classes of Cohen-Macaulay ideals whose square is not Cohen-Macaulay. Our methods work both in the homogeneous and in the local settings.

math.AC↗

Formulas for the multiplicity of graded algebras

Let $R$ be a standard graded Noetherian algebra over an Artinian local ring. Motivated by the work of Achilles and Manaresi in intersection theory, we first express the multiplicity of $R$ by means of local $j$-multiplicities of various hyperplane sections. When applied to a homogeneous inclusion $A\subseteq B$ of standard graded Noetherian algebras over an Artinian local ring, this formula yields the multiplicity of $A$ in terms of that of $B$ and of local $j$-multiplicities of hyperplane sections along ${\rm Proj}\,(B)$. Our formulas can be used to find the multiplicity of special fiber rings and to obtain the degree of dual varieties for any hypersurface. In particular, it gives a generalization of Teissier's Plücker formula to hypersurfaces with non-isolated singularities. Our work generalizes results by Simis, Ulrich and Vasconcelos on homogeneous embeddings of graded algebras.

math.AC↗