Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays
On fairness, full cooperation, and quantum game with incomplete information
Analytical model of tilted driver-pickup coils for eddy current nondestructive evaluation
Separability criteria based on Heisenberg-Weyl representation of density matrices
Effect of Raman-pulse duration related to the magnetic field gradient in high-precision atom gravimeters
The effect of the Raman-pulse duration related to the magnetic field gradient, as a systematic error, is playing an important role on evaluating the performance of high-precision atomic gravimeters. We study this effect with a simplified theoretical model of the time-propagation operator. According to the typical parameters, we find that this effect should be taken into account when the gravimeter reaches an accuracy of 10-10g, and the larger the pulse duration is, the more obvious the systematic effect will be. Finally, we make a simple discussion on the possibility of testing this effect.
The global monopole spacetime and its topological charge
Effects of intrinsic and extrinsic noises on transposons kinetics
The absolute concentration robustness (ACR) steady state of a biochemical system can protect against changing a large concentration of the system's components. In this paper, a minimal model of autonomous-nonautonomous transposons driven by intrinsic and extrinsic noises is investigated. The effects of intrinsic and extrinsic noises on ACR steady state of the transposons kinetics are studied by numerical simulations. It is found that the predator-prey-like oscillations around the ACR steady state are induced by the intrinsic or extrinsic noises. Comparing with the case of intrinsic noises, the extrinsic noises can inhibit the amplitude of oscillations of transposon kinetics. To characterize the predator-prey-like oscillations, we calculate the probability distributions and the normalized correlation functions of a system in the stability domain. With the increasing of noise intensity, the peak of the probability distribution is shifted from the ACR steady state to the trivial steady state. The normalized autocorrelation and cross-correlation functions indicate that the state of the predator-prey oscillator is transmitted to 50 successive generations at least.
Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem
Reconstruction of dynamic structures of experimental setups based on measurable experimental data only
Nowadays, massive amounts of data have been accumulated in various and wide fields, it has become today one of the central issues in interdisciplinary fields to analyze existing data and extract as much useful information as possible from data. It is often that the output data of systems are measurable while dynamic structures producing these data are hidden, and thus studies to reveal system structures by analyzing available data, i.e., reconstructions of systems become one of the most important tasks of information extractions. In the past, most of the works in this respect were based on theoretical analyses and numerical verifications. Direct analyses of experimental data are very rare. In physical science, most of the analyses of experimental setups were based on the first principles of physics laws, i.e., so-called top-down analyses. In this paper, we conducted an experiment of “Boer resonant instrument for forced vibration” (BRIFV) and inferred the dynamic structure of the experimental set purely from the analysis of the measurable experimental data, i.e., by applying the bottom-up strategy. Dynamics of the experimental set is strongly nonlinear and chaotic, and it's subjects to inevitable noises. We proposed to use high-order correlation computations to treat nonlinear dynamics; use two-time correlations to treat noise effects. By applying these approaches, we have successfully reconstructed the structure of the experimental setup, and the dynamic system reconstructed with the measured data reproduces good experimental results in a wide range of parameters.
Soliton structures in the (1+1)-dimensional Ginzburg-Landau equation with a parity-time-symmetric potential in ultrafast optics
Hydrophobic nanochannel self-assembled by amphipathic Janus particles confined in aqueous nano-space
Hydrophobic nanochannel plays a significant role in many physical, biological, and geological phenomena and exhibits impressive applications due to both its ubiquitous distribution and great ability to transport hydrophobic molecules, including various oils and gases. Based on theoretical modeling, we herein reveal that the amphipathic Janus nanoparticles have a large probability to self-assemble into uninterrupted hydrophobic nanochannels inside the aqueous nano-space, although there are large portions of the Janus nanoparticles to be hydrophilic. The key to this observation is the attractions between the hydrophobic regimes on neighboring amphipathic Janus particles through hydrophobic interaction in aqueous nano-space. More surprisingly, the permeation efficiency of hydrophobic molecules through the uninterrupted hydrophobic channel in Janus particles aggregate is even higher than that in the aggregate of hydrophobic particles. We note that the proposed amphipathic Janus particles can be transported to the appropriate positions by the water since the hydrophilic regimes still remain a strong particle-water interaction. We also note that most natural subsurface rocks are not completely hydrophobic or hydrophilic but have complex surfaces with inhomogeneous wetting property. Our work therefore provides a detailed molecular level understanding of the formation of underground strata as well as the new insight for constructing the artificial hydrophobic channels for various applications, such as the design of proppants to enhance the recovery of the unconventional oil/gas.
Photonic generation of RF and microwave signal with relative frequency instability of 10-15 Hot!
We demonstrate the ultra-stable frequency sources aiming to improve the short-time instability of primary frequency standards. These sources are realized by using photonic generation approach, and composed of ultra-stable lasers, optical-frequency-combs, optical signal detecting parts, and synthesizers. Preliminary evaluation shows that the sources produce fixed-frequency at 9.54(/9.63) GHz, 10 MHz, and tunable-frequency around 9.192 GHz with relative frequency instability of 10-15 for short terms.
4.3 THz quantum-well photodetectors with high detection sensitivity Hot!
We demonstrate a high performance GaAs/AlGaAs-based quantum-well photodetector (QWP) device with a peak response frequency of 4.3 THz. The negative differential resistance (NDR) phenomenon is found in the dark current-voltage (I-V) curve in the current sweeping measurement mode, from which the breakdown voltage is determined. The photocurrent spectra and blackbody current responsivities at different voltages are measured. Based on the experimental data, the peak responsivity of 0.3 A/W (at 0.15 V, 8 K) is derived, and the detection sensitivity is higher than 1011 Jones, which is in the similar level as that of the commercialized liquid-helium-cooled silicon bolometers. We attribute the high detection performance of the device to the small ohmic contact resistance of ~2Ω and the big breakdown bias.
Weak wide-band signal detection method based on small-scale periodic state of Duffing oscillator
Demonstration of multi-Watt all-fiber superfluorescent source operating near 980 nm
Ab-initio calculations of structural, electronic, and optical properties of Zn3(VO4)2
Exploration of strong-field double ionization of C3H6 with the structures of propene and cyclopropane in intense laser fields
By using classical ensemble method, we investigate the double ionization of C3H6 molecule with different structures (propene and cyclopropane) in intense laser fields. The numerical results show that the non-sequential double ionization occurs in propene molecule rather than cyclopropane molecule in 1200 nm laser field. To further explain this interesting phenomenon, the momentum distribution of double ionized electrons is presented and the result presents the “finger-like” structure at about 30 TW/cm2 of propene molecule, and this structure is more obvious than that in cyclopropane molecule. The above phenomena are also demonstrated by analysing the energy distributions of double-ionized electrons versus time. Moreover, we also investigated the angular distribution at the end of pulse, which is different between propene and cyclopropane.
Influence factor analysis of field-free molecular orientation
Solvent effects and potential of mean force study of the SN2 reaction of CH3F+CN- in water
We used a combined quantum mechanics and molecular mechanics (QM/MM) method to investigate the solvent effects and potential of mean force of the CH3F+CN- reaction in water. Comparing to gas phase, the water solution substantially affects the structures of the stationary points along the reaction path. We quantitatively obtained the solvent effects' contributions to the reaction:1.7 kcal/mol to the activation barrier and -26.0 kcal/mol to the reaction free energy. The potential mean of force calculated with the density functional theory/MM theory has a barrier height at 19.7 kcal/mol, consistent with the experimental result at 23.0 kcal/mol; the calculated reaction free energy at -43.5 kcal/mol is also consistent with the one estimated based on the gas-phase data at -39.7 kcal/mol.
Further analysis of scintillation index for a laser beam propagating through moderate-to-strong non-Kolmogorov turbulence based on generalized effective atmospheric spectral model
Optical encryption of multiple three-dimensional objects based on multiple interferences and single-pixel digital holography
Implication of two-coupled tri-stable stochastic resonance in weak signal detection
Multi-window transparency and fast-slow light switching in a quadratically coupled optomechanical system assisted with three-level atoms
Optomechanically induced transparency with Bose–Einstein condensate in double-cavity optomechanical system
We propose a novel technique of generating multiple optomechanically induced transparency (OMIT) of a weak probe field in hybrid optomechanical system. This system consists of a cigar-shaped Bose-Einstein condensate (BEC), trapped inside each high finesse Fabry-Pérot cavity. In the resolved sideband regime, the analytic solutions of the absorption and the dispersion spectrum are given. The tunneling strength of the two resonators and the coupling parameters of the each BEC in combination with the cavity field have the appearance of three distinct OMIT windows in the absorption spectrum. Furthermore, whether there is BEC in each cavity is a key factor in the number of OMIT windows determination. The technique presented may have potential applications in quantum engineering and quantum information networks.
Effect of multiple rescattering processes on harmonic emission in spatially inhomogeneous field
Enhanced second harmonic generation in a two-dimensional optical micro-cavity
We introduce a two-dimensional Bose-Einstein condensation model consisting of massive photon and photon-pair. Based on the new nonlinear model, the traditional process of second harmonics generation is reinvestigated. In order to describe the process, a new quantum phase, the harmonic phase, is introduced. The order parameter of the new physical phase is also given in this paper.
Random phase screen influence of the inhomogeneous tissue layer on the generation of acoustic vortices
The influence of the inhomogeneous tissue layer on the generation of acoustic vortices (AV) is studied theoretically and experimentally based on the phase screen model. By considering the time-shift of a random phase screen, the formula of acoustic pressure for the AV beam generated by a circular array of eight planar piston sources is derived. With the actual correlation length of the abdominal wall, numerical simulations before and after the insertion of the inhomogeneous tissue layer are conducted, and also demonstrated by experimental measurements. It is proved that, when the thickness variation of the phase screen is less than one wavelength, no significant influence on the generation of AVs can be produced. The variations of vortex nodes and antinodes in terms of the location, shape, and size of AVs are not obvious. Although the circular pressure distribution might be deformed by the phase interference with a larger thickness variation, AVs can still be generated around the center axis with perfect phase spirals in a reduced effective radius. The favorable results provide the feasibility of AV generation inside the human body and suggest the application potential of AVs in object manipulation for biomedical engineering.
Acoustic radiation force on a multilayered sphere in a Gaussian standing field
Numerical analysis of plasma arc physical characteristics under additional constraint of keyhole
Laser-driven relativistic electron dynamics in a cylindrical plasma channel
Areal density and spatial resolution of high energy electron radiography
Experimental investigation on electrical characteristics and ignition performance of multichannel plasma igniter
Relighting of jet engines at high altitudes is very difficult because of the high velocity, low pressure, and low temperature of the inlet airflow. Successful ignition needs sufficient ignition energy to generate a spark kernel to induce a so-called critical flame initiation radius. However, at high altitudes with high-speed inlet airflow, the critical flame initiation radius becomes larger; therefore, traditional ignition technologies such as a semiconductor igniter (SI) become infeasible for use in high-altitude relighting of jet engines. In this study, to generate a large spark kernel to achieve successful ignition with high-speed inlet airflow, a new type of multichannel plasma igniter (MCPI) is proposed. Experiments on the electrical characteristics of the MCPI and SI were conducted under normal and sub-atmospheric pressures (P=10-100 kPa). Ignition experiments for the MCPI and SI with a kerosene/air mixture in a triple-swirler combustor under different velocities of inlet airflow (60-110 m/s), with a temperature of 473 K at standard atmospheric pressure, were investigated. Results show that the MCPI generates much more arc discharge energy than the SI under a constant pressure; for example, the MCPI generated 6.93% and 16.05% more arc discharge energy than that of the SI at 30 kPa and 50 kPa, respectively. Compared to the SI, the MCPI generates a larger area and height of plasma heating zone, and induces a much larger initial spark kernel. Furthermore, the lean ignition limit of the MCPI and SI decreases with an increase in the velocity of the inlet airflow, and the maximum velocity of inlet airflow where the SI and MCPI can achieve successful and reliable ignition is 88.7 m/s and 102.2 m/s, respectively. Therefore, the MCPI has the advantage of achieving successful ignition with high-speed inlet airflow and extends the average ignition speed boundary of the kerosene/air mixture by 15.2%.
Structural phase transition, strength, and texture in vanadium at high pressure under nonhydrostatic compression
Estimation of enhanced low dose rate sensitivity mechanisms using temperature switching irradiation on gate-controlled lateral PNP transistor
First principles study of ceramic materials (IVB group carbides) under ultrafast laser irradiation
Power flow analysis in a hybrid phononic crystal structure
Phase diagram, correlations, and quantum critical point in the periodic Anderson model Hot!
Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matrix embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin-spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin-spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.
First-principles investigations of proton generation in α-quartz
Proton plays a key role in the interface-trap formation that is one of the primary reliability concerns, thus learning how it behaves is key to understand the radiation response of microelectronic devices. The first-principles calculations have been applied to explore the defects and their reactions associated with the proton release in α -quartz, the well-known crystalline isomer of amorphous silica. When a high concentration of molecular hydrogen (H2) is present, the proton generation can be enhanced by cracking the H2 molecules at the positively charged oxygen vacancies in dimer configuration. If the concentration of molecular hydrogen is low, the proton generation mainly depends on the proton dissociation of the doubly-hydrogenated defects. In particular, a fully passivated E'2 center can dissociate to release a proton barrierlessly by structure relaxation once trapping a hole. This research provides a microscopic insight into the proton release in silicon dioxide, the critical step associated with the interface-trap formation under radiation in microelectronic devices.
Magnetism, optical, and thermoelectric response of CdFe2O4 by using DFT scheme
Structural, electronic, elastic, and thermal properties of CaNiH3 perovskite obtained from first-principles calculations
A theoretical study of the structural, elastic, electronic, mechanical, and thermal properties of the perovskite-type hydride CaNiH3 is presented. This study is carried out via first-principles full potential (FP) linearized augmented plane wave plus local orbital (LAPW+lo) method designed within the density functional theory (DFT). To treat the exchange-correlation energy/potential for the total energy calculations, the local density approximation (LDA) of Perdew-Wang (PW) and the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) are used. The three independent elastic constants (C11, C12, and C44) are calculated from the direct computation of the stresses generated by small strains. Besides, we report the variation of the elastic constants as a function of pressure as well. From the calculated elastic constants, the mechanical character of CaNiH3 is predicted. Pertaining to the thermal properties, the Debye temperature is estimated from the average sound velocity. To further comprehend this compound, the quasi-harmonic Debye model is used to analyze the thermal properties. From the calculations, we find that the obtained results of the lattice constant (a0), bulk modulus (B0), and its pressure derivative (B'0) are in good agreement with the available theoretical as well as experimental results. Similarly, the obtained electronic band structure demonstrates the metallic character of this perovskite-type hydride.
Effect of P impurity on mechanical properties of NiAlΣ5 grain boundary: From perspectives of stress and energy
Spin flip in single quantum ring with Rashba spin-orbit interation
Spin-independent transparency of pure spin current at normal/ferromagnetic metal interface
The spin transparency at the normal/ferromagnetic metal (NM/FM) interface was studied in Pt/YIG/Cu/FM multilayers. The spin current generated by the spin Hall effect (SHE) in Pt flows into Cu/FM due to magnetic insulator YIG blocking charge current and transmitting spin current via the magnon current. Therefore, the nonlocal voltage induced by an inverse spin Hall effect (ISHE) in FM can be detected. With the magnetization of FM parallel or antiparallel to the spin polarization of pure spin currents (σsc), the spin-independent nonlocal voltage is induced. This indicates that the spin transparency at the Cu/FM interface is spin-independent, which demonstrates that the influence of spin-dependent electrochemical potential due to spin accumulation on the interfacial spin transparency is negligible. Furthermore, a larger spin Hall angle of Fe20Ni80 (Py) than that of Ni is obtained from the nonlocal voltage measurements.
Electro-statically controllable graphene local heater
We report on current-induced thermal power investigation of graphene nanostructure for potential local-heating applications. It is found that the efficiency of heating can be greatly improved if graphene is patterned into structures with narrow width and long channel. In a narrow graphene-ribbon, the Joule heating power exhibits an obvious dependence on the back-gate voltage. By monitoring Raman spectra, the temperature of graphene-ribbon can be determined. The temperature of graphene-ribbon is modulated by the electric field effect when the sample is sourced with a relatively high current.
Distinct edge states and optical conductivities in the zigzag and armchair silicene nanoribbons under exchange and electric fields
Distinctive distribution of defects in CdZnTe: In ingots and their effects on the photoelectric properties
Strong coupling between localized 5f moments and itinerant quasiparticles in the ferromagnetic superconductor UGe2
NMR evidence of charge fluctuations in multiferroic CuBr2 Hot!
We report combined magnetic susceptibility, dielectric constant, nuclear quadruple resonance (NQR), and zero-field nuclear magnetic resonance (NMR) measurements on single crystals of multiferroics CuBr2. High quality of the sample is demonstrated by the sharp magnetic and magnetic-driven ferroelectric transition at TN=TC≈ 74 K. The zero-field 79Br and 81Br NMR are resolved below TN. The spin-lattice relaxation rates reveal charge fluctuations when cooled below 60 K. Evidences of an increase of NMR linewidth, a reduction of dielectric constant, and an increase of magnetic susceptibility are also seen at low temperatures. These data suggest an emergent instability which competes with the spiral magnetic ordering and the ferroelectricity. Candidate mechanisms are discussed based on the quasi-one-dimensional nature of the magnetic system.
Formation of unusual Cr5+ charge state in CaCr0.5Fe0.5O3 perovskite Hot!
A new oxide CaCr0.5Fe0.5O3 was prepared under high pressure and temperature conditions. It crystallizes in a B-site disordered Pbnm perovskite structure. The charge combination is determined to be Cr5+/Fe3+ with the presence of unusual Cr5+ state in octahedral coordination, although Cr4+ and Fe4+ occur in the related perovskites CaCrO3 and CaFeO3. The randomly distributed Cr5+ and Fe3+ spins lead to short-range ferromagnetic coupling, whereas an antiferromagnetic phase transition takes place near 50 K due to the Fe3+-O-Fe3+ interaction. In spite of the B-site Cr5+/Fe3+ disorder, the compound exhibits electrical insulating behavior. First-principles calculations further demonstrate the formation of CaCr0.55+Fe0.53+O3 charge combination, and the electron correlation effect of Fe3+ plays an important role for the insulting ground state. CaCr0.5Fe0.5O3 provides the first Cr5+ perovskite system with octahedral coordination, opening a new avenue to explore novel transition-metal oxides with exotic charge states.
Magnetostructural transformation and magnetocaloric effect in Mn48-xVxNi42Sn10 ferromagnetic shape memory alloys
Calculation of electric field-temperature (E, T) phase diagram of a ferroelectric liquid crystal near the SmA-SmCα* transition
Particle swarm optimization and its application to the design of a compact tunable guided-mode resonant filter
Influence of fluorescence time characteristics on the spatial resolution of CW-stimulated emission depletion microscopy
High mobility ultrathin ZnO p-n homojunction modulated by Zn0.85Mg0.15O quantum barriers
The adding of ZnMgO asymmetric double barriers (ADB) in p-ZnO:(Li, N)/n-ZnO homojunction affects the p-n junction device performance prominently. Two different homojunctions are fabricated on Si (100) substrates by pulsed laser deposition; one is the traditional p-ZnO:(Li, N)/n-ZnO homojunction with different thicknesses named as S1 (250 nm) and S2 (500 nm), the other is the one with ADB embedded in the n-layer named as Q (265 nm). From the photoluminescence spectra, defect luminescence present in the S-series devices is effectively limited in the Q device. The current-voltage curve of the Q device shows Zener-diode rectification property because the two-dimensional electron gas tunnels through the narrow ZnMgO barrier under a reverse bias, thus decreasing the working p-n homojunction thickness from 500 nm to 265 nm. The ADB-modified homojunction shows higher carrier mobility in the Q device. The electroluminescence of the ZnO homojunction is improved in Q compared to S2, because the holes in p-type ZnO (Li, N) can cross the wide ZnMgO barrier under a forward bias voltage into the ZnO quantum well. Therefore, electron-hole recombination occurs in the narrow bandgap of n-type ZnO, creating an ultraviolet light-emitting diode using the ZnO homojunction.
Thermomechanical response of aluminum alloys under the combined action of tensile loading and laser irradiations
Synthesis of strong SiV photoluminescent diamond particles on silica optical fiber by chemical vapor deposition
Quantitative deformation measurements and analysis of the ferrite-austenite banded structure in a 2205 duplex stainless steel at 250℃
Enhanced ionic conductivity in LAGP/LATP composite electrolyte
An improved secondary electrons energy spectrum model and its application in multipactor discharge
Factors influencing the performance of paintable carbon-based perovskite solar cells fabricated in ambient air
Analysis of multiple cell upset sensitivity in bulk CMOS SRAM after neutron irradiation
Simulation and experimental study of a novel bifacial structure of silicon heterojunction solar cell for high efficiency and low cost
A novel structure of Ag grid/SiNx/n+-c-Si/n-c-Si/i-a-Si:H/p+-a-Si:H/TCO/Ag grid was designed to increase the efficiency of bifacial amorphous/crystalline silicon-based solar cells and reduce the rear material consumption and production cost. The simulation results show that the new structure obtains higher efficiency compared with the typical bifacial amorphous/crystalline silicon-based solar cell because of an increase in the short-circuit current (Jsc), while retaining the advantages of a high open-circuit voltage, low temperature coefficient, and good weak-light performance. Moreover, real cells composed of the novel structure with dimensions of 75 mm×75 mm were fabricated by a special fabrication recipe based on industrial processes. Without parameter optimization, the cell efficiency reached 21.1% with the Jsc of 41.7 mA/cm2. In addition, the novel structure attained 28.55% potential conversion efficiency under an illumination of AM 1.5 G, 100 mW/cm2. We conclude that the configuration of the Ag grid/SiNx/n+-c-Si/n-c-Si/i-a-Si:H/p+-a-Si:H/TCO/Ag grid is a promising structure for high efficiency and low cost.
A novel knowledge-based potential for RNA 3D structure evaluation
Ribonucleic acids (RNAs) play a vital role in biology, and knowledge of their three-dimensional (3D) structure is required to understand their biological functions. Recently structural prediction methods have been developed to address this issue, but a series of RNA 3D structures are generally predicted by most existing methods. Therefore, the evaluation of the predicted structures is generally indispensable. Although several methods have been proposed to assess RNA 3D structures, the existing methods are not precise enough. In this work, a new all-atom knowledge-based potential is developed for more accurately evaluating RNA 3D structures. The potential not only includes local and nonlocal interactions but also fully considers the specificity of each RNA by introducing a retraining mechanism. Based on extensive test sets generated from independent methods, the proposed potential correctly distinguished the native state and ranked near-native conformations to effectively select the best. Furthermore, the proposed potential precisely captured RNA structural features such as base-stacking and base-pairing. Comparisons with existing potential methods show that the proposed potential is very reliable and accurate in RNA 3D structure evaluation.
A computational study of the chemokine receptor CXCR1 bound with interleukin-8
Molecular dynamics simulations of membrane deformation induced by amphiphilic helices of Epsin, Sar1p, and Arf1
The N-terminal amphiphilic helices of proteins Epsin,Sar1p,and Arf1 play a critical role in initiating membrane deformation.The interactions of these amphiphilic helices with the lipid membranes are investigated in this study by combining the all-atom and coarse-grained simulations.In the all-atom simulations,the amphiphilic helices of Epsin and Sar1p are found to have a shallower insertion depth into the membrane than the amphiphilic helix of Arf1,but remarkably, the amphiphilic helices of Epsin and Sar1p induce higher asymmetry in the lipid packing between the two monolayers of the membrane.The insertion depth of amphiphilic helix into the membrane is determined not only by the overall hydrophobicity but also by the specific distributions of polar and non-polar residues along the helix.To directly compare their ability to deform the membrane,the coarse-grained simulations are performed to investigate the membrane deformation under the insertion of multiple helices.
First integrals of the axisymmetric shape equation of lipid membranes
The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler-Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor.
Spatial memory enhances the evacuation efficiency of virtual pedestrians under poor visibility condition
Flowrate behavior and clustering of self-driven robots in a channel