Predicting nonsmooth chaotic dynamics by reservoir computing.

Reservoir computing (RC) has been widely applied to predict the chaotic dynamics in many systems. Yet much broader areas related to nonsmooth dynamics have seldom been touched by the RC community which have great theoretical and practical importance. The generalization of RC to this kind of system is reported in this paper. The numerical work shows that the conventional RC with a hyperbolic tangent activation function is not able to predict the dynamics of nonsmooth systems very well, especially when reconstructing attractors (long-term prediction). A nonsmooth activation function with a piecewise nature is proposed. A kind of physics-informed RC scheme is established based on this activation function. The feasibility of this scheme has been proven by its successful application to the predictions of the short- and long-term (reconstructing chaotic attractor) dynamics of four nonsmooth systems with different complexity, including the tent map, piecewise linear map with a gap, both noninvertible and discontinuous compound circle maps, and Lozi map. The results show that RC with the new activation function is efficient and easy to run. It can make perfectly both short- and long-term predictions. The precision of reconstructing attractors depends on their complexity. This work reveals that, to make efficient predictions, the activation function of an RC approach should match the smooth or nonsmooth nature of the dynamical systems.

Localized vibrational characteristics of biphenylene strips resulting in length-dependent Raman spectra.

The length dependence of the Raman spectra and vibrational properties of biphenylene strips are explored using density functional theory. The Raman intensity of two bands increases and decreases with length due to the enlarging and shrinking of the proportion of effective vibrating units. The red shift of vibrational modes is observed with the increase in length, owing to the various vibrational characteristics of the effective vibrating units. More importantly, a linear relationship between the energy gap and the wavenumber of the shifting Raman bands is obtained. The results allow us to interpret the length-dependence of the Raman spectra from the perspective of localized vibrational characteristics and suggest that Raman spectroscopy can be used as a convenient method to determine the energy gap of nanomaterials.

Size-tunable energy gaps of hydrogen-terminated biphenylene segments.

The electronic properties of hydrogen-terminated biphenylene (BP) segments of different sizes on the sub-nanoscale are explored using density functional theory, and the size dependence of the energy gap is evaluated using a structural parameter as a function of the bond lengths and the electronic density contributions. More importantly, the energy gap is observed to decrease linearly with the reduced hydrogen-to-carbon ratio of the corresponding structures, while the decrease-rate undergoes a diminution of four times at a gap of 0.5 eV due to the transformed distribution of the lowest unoccupied molecular orbital. The results give a deep insight into the size-tunable energy gaps of BPs and provide a possibility for the preparation of hydrogen-terminated carbon materials with a desirable energy gap.

Plasmon-Mediated Hydrogen Dissociation with Symmetry Tunability.

The atomic-scale mechanism of plasmon-mediated H2 dissociation on gold nanoclusters is investigated using time-dependent density functional theory. The position relationship between the nanocluster and H2 has a strong influence on the reaction rate. When the hydrogen molecule is located in the interstitial center of the plasmonic dimer, the hot spot here has a great field enhancement, which can promote dissociation effectively. The change in the molecular position results in symmetry breaking, and the molecular dissociation is inhibited. For the asymmetric structure, direct charge transfer from the gold cluster to the antibonding state of the hydrogen molecule by plasmon decay makes a prominent contribution to the reaction. The results provide deep insights into the influence of structural symmetry on plasmon-assisted photocatalysis in the quantum regime.

Cerebral cortical regions always connect with each other via the shortest paths.

In human society, the choice of transportation mode between two cities is largely influenced by the distance between the regions. Similarly, when neurons communicate with each other within the cerebral cortex, do they establish their connections based on their physical distance? In this study, we employed a data-driven approach to explore the relationships between fiber length and corresponding geodesic distance between the fiber's two endpoints on brain surface. Diffusion-MRI-derived fiber streamlines were used to represent extra-cortical axonal connections between neurons or cortical regions, while geodesic paths between cortical points were employed to simulate intra-cortical connections. The results demonstrated that the geodesic distance between two cortical regions connected by a fiber streamline was greater than the fiber length most of the time, indicating that cortical regions tend to choose the shortest path for connection; whether it be an intra-cortical or extra-cortical route, especially when intra-cortical routes within cortical regions are longer than potential extrinsic fiber routes, there is an increased probability to establish fiber routes to connect the both regions. These findings were validated in a group of human brains and may provide insights into the underlying mechanisms of neuronal growth, connection, and wiring.

Selective Raman Enhancement with Electronic Sensitivity in Tip-Enhanced Raman Spectroscopy.

Chemical interaction between the tips and molecules is one of the main contributing mechanisms to tip-enhanced Raman spectroscopy (TERS). In this work, we calculate the TERS spectra of the biphenylene (BP) dimer at 13 nonequivalent tip sites by means of density functional theory and explore the influence of the TERS tip on vibrational mode characters and Raman intensity. The Raman intensity of the vibrational mode involving the antisymmetric stretching of tetra-rings is found to be specifically enhanced. We attribute this specific enhancement to the electronic sensitive atom vibrational character of the mode and infer that the vibrational strength of atoms can be tuned by the TERS tip. The results provide an intuitive interpretation on the effects of tip-induced electronic redistributions on specific vibrational modes in TERS and indicate the possibility to further improve the TERS resolution.

Synchronous slowing down in coupled logistic maps via random network topology.

The speed and paths of synchronization play a key role in the function of a system, which has not received enough attention up to now. In this work, we study the synchronization process of coupled logistic maps that reveals the common features of low-dimensional dissipative systems. A slowing down of synchronization process is observed, which is a novel phenomenon. The result shows that there are two typical kinds of transient process before the system reaches complete synchronization, which is demonstrated by both the coupled multiple-period maps and the coupled multiple-band chaotic maps. When the coupling is weak, the evolution of the system is governed mainly by the local dynamic, i.e., the node states are attracted by the stable orbits or chaotic attractors of the single map and evolve toward the synchronized orbit in a less coherent way. When the coupling is strong, the node states evolve in a high coherent way toward the stable orbit on the synchronized manifold, where the collective dynamics dominates the evolution. In a mediate coupling strength, the interplay between the two paths is responsible for the slowing down. The existence of different synchronization paths is also proven by the finite-time Lyapunov exponent and its distribution.