A finite element method of the self-consistent field theory on general curved surfaces

Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory (SCFT) has been proven to be a powerful tool for studying the equilibrium ordered structures. Many numerical methods have been developed to solve the SCFT model. However, most of these focus on the bulk systems, and little work on the confined systems, especially on general curved surfaces. In this work, we developed a linear surface finite element method, which has a rigorous mathematical theory to guarantee numerical precsion, to study the self-assembled phases of block copolymers on general curved surfaces based on the SCFT. Furthermore, to capture the consistent surface for a given self-assembled pattern, an adaptive approach to optimize the size of the general curved surface has been proposed. To demonstrate the power of this approach, we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces, including five closed surfaces and an unclosed surface. Numerical results illustrate the efficiency of the proposed method. The obtained ordered structures are consistent with the previous results on standard surfaces, such as sphere and torus. Certainly, the proposed numerical framework has the capability of studying the phase behaviors on general surfaces precisely

Decoherence and Energy Relaxation in the Quantum-Classical Dynamics for Charge Transport in Organic Semiconducting Crystals: an Instantaneous Decoherence Correction Approach

We explore an instantaneous decoherence correction (IDC) approach for the decoherence and energy relaxation in the quantum-classical dynamics of charge transport in organic semiconducting crystals. These effects, originating from environmental fluctuations, are essential ingredients of the carrier dynamics. The IDC is carried out by measurement-like operations in the adiabatic representation. While decoherence is inherent in the IDC, energy relaxation is taken into account by considering the detailed balance through the introduction of energy-dependent reweighing factors, which could be either Boltzmann (IDC-BM) or Miller-Abrahams (IDC-MA) type. For a non-diagonal electron-phonon coupling model, it is shown that the IDC tends to enhance diffusion while energy relaxation weakens this enhancement. As expected, both the IDC-BM and IDC-MA achieve a near-equilibrium distribution at finite temperatures in the diffusion process, while the Ehrenfest dynamics renders system tending to infinite temperature limit. The resulting energy relaxation times with the two kinds of factors lie in different regimes and exhibit different dependence on temperature, decoherence time and electron-phonon coupling strength, due to different dominant relaxation process.Comment: 8 pages, 4 figure

A New Kind of Deformed Hermite Polynomials and Its Applications

A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating function, orthonormality, differential and integral representaions, and recursion relations are also discussed in this paper. As its applications, we calculate explicit forms of parabose squeezed number states, derive a particularly simple subset of minimum uncertainty states for parabose amplitude-squared squeezing, and discuss their basic squeezing behaviours.Comment: 18 pages, LaTe

Graded Lie Algebra Generating of Parastatistical Algebraic Structure

A new kind of graded Lie algebra (we call it $Z_{2,2}$ graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable bose subspace of the $Z_{2,2}$ graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics.Comment: 8 pages, LaTe

Space Structure for the Simplest Parasupersymmetric System

Structure of the state-vector space for a system consisting of one mode parabose and one mode parafermi degree of freedom with the same parastatistics order $p$ is studied and a complete, orthonormal set of basis vectors in this space is constructed. There is an intrinsic double degeneracy for state vectors with $m$ parabosons and $n$ parafermions, where $m \not= 0$, $n \not= 0$, and $n \not= p$. It is also shown that the degeneracy plays a key role in realization of exact supersymmetry for such a system

Hybrid-BCP: A Robust Load Balancing and Routing Protocol for Intra-Car Wired/Wireless Networks

With the emergence of connected and autonomous vehicles, sensors are increasingly deployed within cars to support new functionalities. Traffic generated by these sensors congest traditional intra-car networks, such as CAN buses. Furthermore, the large amount of wires needed to connect sensors makes it harder to design cars in a modular way. To alleviate these limitations, we propose, simulate, and implement a hybrid wired/wireless architecture, in which each node is connected to either a wired interface or a wireless interface or both. Specifically, we propose a new protocol, called Hybrid-Backpressure Collection Protocol (Hybrid-BCP), to efficiently collect data from sensors in intra-car networks. Hybrid-BCP is backward-compatible with the CAN bus technology, and builds on the BCP protocol, designed for wireless sensor networks. Hybrid-BCP achieves high throughput and shows resilience to dynamic network conditions, including adversarial interferences. Our testbed implementation, based on CAN and ZigBee transceivers, demonstrates the load balancing and routing functionalities of Hybrid-BCP and its resilience to DoS attacks. We further provide simulation results, obtained with the ns-3 simulator and based on real intra-car RSSI traces, that compare between the performance of Hybrid-BCP and a tree-based collection protocol. Notably, the simulations show that Hybrid-BCP can achieve the same performance as the tree-based protocol while reducing the radio transmission power by a factor of 10

Vorticity, Gyroscopic precession, and Spin-Curvature Force

In investigating the relation between vorticity and gyroscopic precession, we calculate the vorticity vector in Godel, Kerr, Lewis, Schwarzschild, Minkowski metric and find out the vorticity vector of the specific observers is the angular velocity of gyroscopic precession. Furthermore, considering space-time torsion will flip the vorticity and spin-curvature force to opposite sign. This result is very similar to the behavior of positive and negative helicity of quantum spin in Stern-Gerlach force. It implies that the inclusion of torsion will lead to analogous property of quantum spin even in classical treatment

A New Parameter Estimation Algorithm Based on Sub-band Dual Frequency Conjugate LVT

A new parameter estimation algorithm, known as Sub-band Dual Frequency Conjugate LVT (SDFC-LVT), is proposed for the ground moving targets. This algorithm first constructs two sub-band signals with different central frequencies. After that, the two signals are shifted by different values in frequency domain and a new signal is constructed by multiplying one with the conjugate of the other. Finally, Keystone transform and LVT operation are performed on the constructed signal to attain the estimates. The cross-term and the performance of the proposed method are analyzed in detail. Since the equivalent carrier frequency is reduced greatly, the proposed method is capable of obtaining the accurate parameter estimates and resolving the problem of ambiguity which invalidates Keystone transform. It is search-free and can compensate the range walk of multiple targets simultaneously, thereby reducing the computational burden. The effectiveness of the proposed method is demonstrated by both simulated and real data.Comment: 27 pages, 7 figure

Drift of Charge Carriers in Crystalline Organic Semiconductors

We investigate the direct-current response of crystalline organic semiconductors in the presence of finite external electric fields by the quantum-classical Ehrenfest dynamics complemented with instantaneous decoherence corrections (IDC). The IDC is carried out in the real-space representation with the energy-dependent reweighing factors to account for both intermolecular decoherence and energy relaxation by which conduction occurs. In this way, both the diffusion and drift motion of charge carriers are described in a unified framework. Based on an off-diagonal electron-phonon coupling model for pentacene, we find that the drift velocity initially increases with the electric field and then decreases at higher fields due to the Wannier-Stark localization, and a negative electric-field dependence of mobility is observed. The Einstein relation, which is a manifestation of the fluctuation-dissipation theorem, is found to be restored in electric fields up to ~$10^5$ V/cm for a wide temperature region studied. Furthermore, we show that the incorporated decoherence and energy relaxation could explain the large discrepancy between the mobilities calculated by the Ehrenfest dynamics and the full quantum methods, which proves the effectiveness of our approach to take back these missing processes.Comment: 8 pages, 5 figure

Parameter Estimation of Ground Moving Targets Based on SKT-DLVT Processing

It is well known that the motion of a ground moving target may induce the range cell migration, spectrum spread and velocity ambiguity during the imaging time, which makes the image smeared. To eliminate the influence of these factors on image focusing, a novel method for parameter estimation of ground moving targets, known as SKT-DLVT, is proposed in this paper. In this method, the segmental keystone transform (SKT) is used to correct the range walk of targets simultaneously, and a new transform, namely, Doppler Lv's transform (LVT) is applied on the azimuth signal to estimate the parameters. Theoretical analysis confirms that no interpolation is needed for the proposed method and the targets can be well focused within limited searching range of the ambiguity number. The proposed method is capable of obtaining the accurate parameter estimates efficiently in the low signal-to-noise ratio (SNR) scenario with low computational burden and memory cost, making it suitable to be applied in memory-limited and real-time processing systems. The effectiveness of the proposed method is demonstrated by both simulated and real data.Comment: 39 pages, 9 figure