Energy Conservation Criterion Research Articles

Activated Singlet Fission Dictated by Anti-Kasha Property in a Rylene Imide Dye.

A key challenge in the search of new materials capable of singlet fission (SF) arises from the primary energy conservation criterion, i.e., the energy of the triplet exciton has to be half that of the singlet (E(S1) ≥ 2E(T1)), which excludes most photostable organic materials from consideration and confines the design strategy to materials with low energy triplet states. One potential way to overcome this energy requirement and improve the triplet energy is to enable a SF channel from higher energy ("hot") excitonic states (Sn) in a process called activated SF. Herein, we demonstrate that efficient activated SF is achieved in a rylene imide-based derivative acenaphth[l, 2-a]acenaphthylene diimide (AADI). This process is enabled by an increase in the energy gap to greater than 1.0 eV between the S3 and S1 states due to the incorporation of an antiaromatic pentalene unit, which leads to the emergence of anti-Kasha properties in the isolated molecule. Transient spectroscopy studies show that AADI undergoes ultrafast SF from higher singlet excited states in thin film, with excitation wavelength-dependent SF yields. The SF yield of ∼200% is observed upon higher energy excitation, and long-lived free triplets persist on the μs time scale suggesting that AADI can be used in SF-enhanced devices. Our results suggest that enlarging the Sn-S1 energy gap is an effective way to turn on the activated SF channel and shed light on the development of novel, stable SF materials with high triplet energies.

Energy equality of weak solutions of the Navier–Stokes–Fourier equations allowing vacuum

In this paper, we are concerned with the conservation of energy criterion of the weak solutions to the Navier–Stokes–Fourier equations on the torus allowing vacuum. We establish the energy conservation criteria via the gradient of velocity for the weak solutions of this system, which generalizes the corresponding recent energy conservation criteria in terms of the velocity obtained by Aoki and Iwabuchi in Aoki and Iwabuchi (2022). Moreover, sufficient conditions for weak solutions keeping the energy balance allowing vacuum are shown for the full Navier–Stokes equations.

Multi-mode microcavity frequency engineering through a shifted grating in a photonic crystal ring.

Frequency engineering of whispering-gallery resonances is essential in microcavity nonlinear optics. The key is to control the frequencies of the cavity modes involved in the underlying nonlinear optical process to satisfy its energy conservation criterion. Compared to the conventional method that tailors dispersion by cross-sectional geometry, thereby impacting all cavity mode frequencies, grating-assisted microring cavities, often termed as photonic crystal microrings, provide more enabling capabilities through mode-selective frequency control. For example, a simple single period grating added to a microring has been used for single frequency engineering in Kerr optical parametric oscillation (OPO) and frequency combs. Recently, this approach has been extended to multi-frequency engineering by using multi-period grating functions, but at the cost of increasingly complex grating profiles that require challenging fabrication. Here, we demonstrate a simple approach, which we term as shifted grating multiple mode splitting (SGMMS), where spatial displacement of a single period grating imprinted on the inner boundary of the microring creates a rotational asymmetry that frequency splits multiple adjacent cavity modes. This approach is easy to implement and presents no additional fabrication challenges compared to an unshifted grating, and yet is very powerful in providing multi-frequency engineering functionality for nonlinear optics. We showcase an example where SGMMS enables OPO across a wide range of pump wavelengths in a normal-dispersion device that otherwise would not support OPO.

Modeling the viscoelastic-viscoplastic behavior of glassy polymer membrane with consideration of non-uniform sub-chains in entangled networks

Glassy polymers are common engineering materials and usually work in a linear elastic stage. However, some functional glassy polymers, such as perfluorinated sulfonic acid (PFSA) membranes, face more complicated working conditions: varied temperature, humidity, and long-term loading, where the viscoelastic behavior has a huge impact on their durability. The early studies on the constitutive model of glassy polymers focus on the elastic–plastic behavior, especially yielding and strain hardening, while showing limitations in predicting the time-dependent viscoelastic response of the PFSA membrane at complex conditions. This paper establishes a viscoelastic-viscoplastic (VE-VP) constitutive model of glassy polymers based on the non-uniform length distribution of entangled molecular chains. During loading, heating and hydration, the prior activation of short entangled chains is the precondition of the viscoelastic response of the material in the small deformation stage. To distinguish activated molecular chains from others, a calculation method of chain activation is established based on the energy conservation criterion and applied to monitor the activation state of the entangled chain network. For the verification of the model, uniaxial tensile, stress relaxation, and dynamic thermomechanical tests are conducted. The present model shows great accuracy in predicting the VE-VP behavior of the PFSA membrane, with the error less than 8% in the stress relaxation tests, providing a new perspective of constitutive modeling for glassy polymers.

The role of density in the energy conservation for the isentropic compressible Euler equations

In this paper, we study Onsager’s conjecture on the energy conservation for the isentropic compressible Euler equations via establishing the energy conservation criterion involving the density ϱ∈Lk(0,T;Ll(Td)). The motivation is to analyze the role of the integrability of density in energy conservation of weak solutions in this system, since almost all known corresponding results require ϱ∈L∞(0,T;L∞(Td)). Our results imply that the lower integrability of density ϱ means that more integrability of the velocity v is necessary in energy conservation. The proof relies on the Constantin–Weinan–Titi type and Lions type commutators on the mollifying kernel.

On the viability of f(Q) gravity models

In general relativity, the contracted Bianchi identity makes the field equation compatible with the energy conservation, likewise in f(R) theories of gravity. We show that this classical phenomenon is not guaranteed in the symmetric teleparallel theory, and rather generally f(Q) model specific. We further prove that the energy conservation criterion is equivalent to the affine connection’s field equation of f(Q) theory, and except the model, the non-linear f(Q) models do not satisfy the energy conservation or, equivalently the second field equation in every spacetime geometry; unless Q itself is a constant. So the problem is deep-rooted in the theory, several physically motivated examples are provided in the support.

Variable discrete ordinates method for radiation transfer in concentric spherical variable index media

Radiation heat transfer in participating concentric spherical media with variable refractive index along the radial direction is solved by the variable discrete ordinates method. The radiative properties, including refractive index, are assumed to be constant in each volume element, such that a radiative ray travels along straight line in each volume element, and redirects by passing the interface of volume elements according to Snell's law of refraction, or specularly reflects back into the volume element. The radiative transfer equation in spherical coordinates system is solved for different number and direction of ordinates in each volume element. The performance of the present method is examined for two cases with medium's specified temperature and radiative equilibrium with continuous linear, continuous non-linear, and discontinuous profiles of refractive index. The accuracy of the present method is checked by comparing with benchmark solutions. For the cases where the exact solution is not available, the energy conservation criterion is used to validate the solution method. The effects of radiative properties, such as wall emissivities, optical thickness, single scattering albedo, and anisotropy factor are examined by some example problems.

Energy equality for the tropical climate models

In this paper, we derive several new energy conservation criterion of weak solutions for both the inviscid primitive tropical climate model and the tropical climate model with partial or full diffusion. For the inviscid primitive tropical climate model, we first establish a Onsager-type sufficient condition on the regularity of the weak solutions to guarantee conservation the total energy, where, the regularity of the weak solutions are measured in terms of the Triebel–Lizorkin type of norms, Ḟp,qs and Besov norms, Ḃp,qs. This result can be understood as a generalization of the notable work of Chae (2006). And than, for the dissipative models, we provide a Shinbrot-type sufficient condition on the weak solutions to ensure the energy conservation. In addition, without the condition of Leray–Hopf class, the energy equality holds if a solution (u,v,θ) to the tropical climate model belongs to L4L4. The result can be regarded as a corresponding extension with different approach in Galdi (2019). To the best of our knowledge, this is the first energy conservation criterion of distributional solutions for this model.

A general sufficient criterion for energy conservation in the Navier–Stokes system

In this paper, we derive an energy conservation criterion based on a combination of velocity and its gradient for the weak solutions of both the homogeneous incompressible Navier–Stokes equations and the general compressible Navier–Stokes equations. For the incompressible case, this class implies almost known corresponding results on periodic domain via either the velocity or its gradient including the famous Lions' energy conservation criterion obtained in [1, Rend. Semin. Mat. Univ. Padova, 30 (1960)]. For the compressible case, this helps us to extend the previously known criteria for the energy conservation of weak solutions from the incompressible fluid to compressible flow and improve the recent results due to Nguyen‐Nguyen‐Tang in [26, Nonlinearity, 32 (2019)] and Liang in [27, Proc. Roy. Soc. Edinburgh Sect. A, (2020)].

Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system

Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system

Global energy conservation for distributional solutions to incompressible Hall-MHD equations without resistivity

This paper concerns the global energy conservation for distributional solutions to incompressible Hall-MHD equations without resistivity. Motivated by the works of Tan and Wu in [arXiv:2111.13547v2] and Wu in [J. Math. Fluid Mech. 24, 111 (2022)], we establish the energy balance for a distributional solution in whole spaces Rd(d ? 2) provided that u, b ? L4L4 and ?b ? L8/3 L8/3. Moreover, as a corollary, we also obtain the energy conservation criterion for a Leray-Hopf weak solution.

Application of Lifting Wavelet Packet Decomposing Algorithm in EMC Simulation of Automobile

The purpose of this paper is to extract data features and denoise the interference excitation source in vehicle electromagnetic compatibility test. The lifting wavelet packet algorithm inherits the multi-resolution characteristics of the classic (first generation) wavelet transform. The transform is only carried out in the time domain, which can achieve in situ operation. It has the advantages of small space occupation, fast transformation speed, easy inversion, etc. It can use energy conservation criteria to extract characteristic energy to identify the conducted interference sources in the vehicle, and the obtained characteristic spectrum is used as the modulation array of the excitation source of the vehicle numerical simulation. In this paper, the collected interference signals are decomposed into lifting wavelet packets, and then the characteristic energy is extracted to identify the conducted interference sources in the vehicle. Signal to noise ratio (SNR), root mean square error (RMSE) and peak error (PE) are used to verify the consistency between the simulation signal and the original signal. The results show that the lifting wavelet packet algorithm has a strong ability to identify the conducted interference sources in the vehicle.

Vectorial discrete ray tracing approach for solving radiative transfer in irregular variable index media via discrete transfer method

A novel vectorial discrete ray tracing approach is applied for tracking the curve paths of radiative beams through the variable index media with complex geometries. In this approach, the irregular solution domain is discretized by a boundary-fitted grid, where the radiative properties, including the refractive index, are considered to be constant for each control volume and control surface. Radiative beams travel along straight lines through each volume element until they hit the interfaces between adjacent volume elements, where the direction of rays changes according to the Snell's law of refraction. The radiation heat transfer in absorbing, emitting, and isotropically scattering media is solved by the discrete transfer method. The problem is solved for one-, two-, and three-dimensional media. Axisymmetric media are simulated by detaching a sector with specular sidewalls. Verification is done by comparing the results with available benchmark solutions in literature. For the cases where the data is not available, the accuracy is proved by satisfaction the energy conservation criterion.

Approximate reflection and transmission coefficients at an interface between two contrasting viscoelastic anisotropic half-spaces

SUMMARY We present and compare two new methods to calculate the reflection and transmission coefficients of qP, qSV and qSH waves at a flat interface between two contrasting viscoelastic anisotropic half-spaces. The first method is a new version of the real ray tracing method that extends the traditional real ray tracing method to tackle the triplications of the qSV wave. This new version is valid for computing the reflection and transmission coefficients of the qP and qSV waves for all pre- and post-critical angles of incidence, which cannot be handled by the previous approach. The second method employs the real slowness direction and Snell's law to provide approximate reflection and transmission coefficients for such wave modes. This approximate method has attractive advantages which are not only the avoidance of the searching process inherent in the real ray tracing method but also offers competitive economical solutions to the first method. Many viscoelastic VTI models are utilized to validate the two methods. The numerical results show that (1) the ray angles, ray velocities, ray Q-factors, and the magnitudes of the reflection and transmission coefficients obtained by the two methods closely agree with each other, except in the vicinity of the critical angles and (2) the phase angles of the reflected and transmitted waves exhibit complexities due to the existence of some reverse phenomena between the approximate and the real ray tracing solutions. However, such phase discrepancies do not affect the magnitudes of the reflection and transmission coefficients. Moreover, the energy ratios of the different wave modes satisfy the energy conservation criterion at the interface.

The Torsional Rigidity of a Rectangular Prism

Using the membrane analogy, in 1934 Timoshenko derived the torsional rigidity of a rectangular prism of isotropic material as a function of its material shear modulus, width and thickness. However, he did not consider the energy conservation criterion, as it could be either unnecessary or replaced by other criteria in Timoshenko’s process. To confirm the correctness of Timoshenko’s solution, this work re-derives the torsional rigidity by considering all the equilibrium conditions, boundary conditions, symmetric and anti-symmetric conditions of displacement and stress, the energy conservation criterion, and even the energy minimization criterion. Using the TSAI technique, exact solutions for the displacements, strains, stresses and the torsional rigidity are derived perfectly. The derived torsional rigidity is in a completely different form from that derived by Timoshenko and is numerically identical. Interestingly, the solutions derived in this work verify that, when the values of the width and thickness of the rectangular prism are swapped, the value of the torsional rigidity remains the same, which makes perfect sense physically but is not discussed in Timoshenko’s process or any other research. This work presents a procedure considering all the mathematical details and the results remain correct when the width and thickness of the prism swap. This fact makes perfect sense physically, though has never been expounded before in Timoshenko’s or other researchers’ solutions, either for torsional rigidity or for the induced shear stresses and displacements.

Quantitative evaluations of improved surface integrity in ultrasonic rolling process for selective laser melted in-situ TiB2/Al composite

The novel surface nano-crystallization ultrasonic rolling process (USRP) technology is used to improve the surface integrity of Al-based TiB2/Al composite and widen potential applicability in this work. Based on self-developed two generations of USRP devices, the basic attempts to processing parameters are conducted to qualitatively link up with the surface integrity indicators of roughness, hardness and residual compressive stress as well as the surface morphologies. G factor based on energy conservation criterion is proposed to quantitatively evaluate USRP strengthening effect on the surface integrity. What is more important is that it can standardize the processing parameters with different generations USRP facilities. The logarithmic responses of surface integrity indicators with regard to the G factor show that significant strengthening effectiveness is able to be produced by two-side USRP (TS-USRP) with less energy consumption, as compared to single-side USRP (SS-USRP). The effect of strengthening efficiency is also included from the determinations of Wp and Wr factors, which are the selection criterion on optimized processing parameters. The results show that TS-USRP specimens possess generally better comprehensive performance than SS-USRP do, and TS-2 (F = 120 N, v = 4 mm/s, d = 0.1 mm, n = 3) is the best-choice specimen among them. In addition, the potential strengthen mechanisms are further explored for this specimen based on advanced microstructural observations, where remarkable compaction of the printing powder and the crushing of original inclusions play an important role in it. This work provides an insight into how to provide a direct quantitative evaluation on strengthening effect, which is expected to promote in many processing and manufacturing fields.

Study on Engraving Resistance Characteristic of Band Based on Different Structure Parameters of Rifling

The gun barrel working in complex environments is prone to damage, including the wear and ablation of the bore in the gun barrel. These changes cause changes in the rifling structure, which in turn affects the combustion law of gunpowder gas, which affects the pressure in the bore and changes the internal ballistics of the gun performance. This article takes a large caliber howitzer as the research object, considers the frictional force change during high-speed and high-pressure sliding, and also considers the energy conservation criterion during the engraving process. The initial ballistic equations are established during the initial movement period and Coupled solution with band engraving process. Considering the large deformation, high strain rate, temperature softening effect and cumulative damage effect, an explicit dynamic algorithm is used to compare the differences of the elastic band engraving process under different rifling structure parameters. The influence of different rifling structure parameters on the force state of the belt is analyzed. The influence of the main structural parameters of the engraving system on the belt engraving process is obtained. It provides a useful reference for the integrated analysis of the ammunition and the gun and the optimization of the barrel structure.

A new model of acid fracturing based on boundary element method coupled with multi-field multi-phase process

In this research, the thermal-hydro-mechanical-chemistry coupling process involved in acid fracturing is simulated using 2D displacement discontinuity method combined with the finite volume method. Temperature field models, acid flow models, and acid rock reaction models are also established based on material conservation and energy conservation criteria. And the new acid fracturing method is used to solve the problem of rock deformation, fluid interference, fracture opening, temperature, acid rock reaction, multiphase flow, and carbon dioxide characteristics coupling. Simulations of larger scale acid fracturing are carried out to analyze the influence of injection rate, initial acid concentration, acid viscosity and initial reservoir temperature, and acid temperature on the bottom of the well on optimizing acidizing design. The results show: the acid rock reaction and its reaction product have a significant influence on the fracture extension. And the coupled process and the influence of carbon dioxide are necessary to be considered when studying the acid fracturing process. For obtaining as long as possible effective penetration distance of the acid, a larger injection rate can be selected, a larger initials acid concentration, a lower acid viscosity and a lower acid temperature at the bottom of the well.

Enhancement of toughness of Al-to-steel Friction Melt Bonded welds via metallic interlayers

The toughness of Al-to-steel welds decreases with increasing thickness of the intermetallic (IM) layer formed at the interface. Co plating has been added as interlayer in Al-to-steel Friction Melt Bonded (FMB) welds to control the nature and thickness of the IM layer. In comparison to a weld without interlayer, Co plating brings about a reduction of the thickness of the IM layer by 70%. The critical energy release rate of the crack propagating in the weld is used as an indicator of toughness. It is evaluated via an adapted crack propagation test using an energy conservation criterion. For a weld without interlayer, critical energy release rate is found to increase when the thickness of the intermetallic layer decreases. When the intermetallic layer is thick, the crack propagates in a brittle manner through the intermetallic whereas, at low layer thickness, the crack deviates and partially propagates through the Al plate, which causes an increase of toughness. The use of a Co interlayer brings about an increase of toughness by causing full deviation of the crack towards the Al plate.

New insights into the design of conjugated polymers for intramolecular singlet fission

Singlet fission (SF), a multiple exciton generation process that generates two triplet excitons after the absorption of one photon, can potentially enable more efficient solar cell designs by harvesting energy normally lost as heat. While low-bandgap conjugated polymers are highly promising candidates for efficient SF-based solar cells, few polymer materials capable of SF have been reported because the SF process in polymer chains is poorly understood. Using transient spectroscopy, we demonstrate a new, highly efficient (triplet yield of 160–200%) isoindigo-based donor–acceptor polymer and show that the triplet pairs are directly emissive and exhibit a time-dependent energy evolution. Importantly, aggregation in poor solvents and in films significantly lowers the singlet energy, suppressing triplet formation because the energy conservation criterion is no longer met. These results suggest a new design rule for developing intramolecular SF capable low-bandgap conjugated polymers, whereby inter-chain interactions must be carefully engineered.