Explicit Numerical Simulations Research Articles

Anomalous Crystalline-Electromagnetic Responses in Semimetals

We present a unifying framework that allows us to study the mixed crystalline-electromagnetic responses of topological semimetals in spatial dimensions up to D=3 through dimensional augmentation and reduction procedures. We show how this framework illuminates relations between the previously known topological semimetals and use it to identify a new class of quadrupolar nodal line semimetals for which we construct a lattice tight-binding Hamiltonian. We further utilize this framework to quantify a variety of mixed crystalline-electromagnetic responses, including several that have not previously been explored in existing literature, and show that the corresponding coefficients are universally proportional to weighted momentum-energy multipole moments of the nodal points (or lines) of the semimetal. We introduce lattice gauge fields that couple to the crystal momentum and describe how tools including the gradient expansion procedure, dimensional reduction, compactification, and the Kubo formula can be used to systematically derive these responses and their coefficients. We further substantiate these findings through analytical physical arguments, microscopic calculations, and explicit numerical simulations employing tight-binding models. Published by the American Physical Society 2024

UAV Wing leading edge crashworthiness behaviour under bird strike events: The added value of CF/PA additive solutions versus traditional metallic wing structures

In recent years, an increasing interest in innovative solutions design of aircraft structural components has been raised through both research and industrial fields, aimed at optimising weight and enhancing the ability to withstand both static and dynamic loads. This study compares the structural response to a bird strike phenomenon of a vertical tail of a UAV in standard metallic configuration with the one obtained from an innovative solution, equal in volume but with an internally designed architecture for an additive approach and manufactured by employing a carbon fibre reinforced filament engineered for metal replacement applications (carbon fibre, CF/polyamide, PA). The additive solution proposes the use of a 10 % infill and a lattice structure that completely replaces the traditional aircraft structure concept. This approach leads to a significant weight reduction, approximately 45 % compared to the traditional metallic configuration. The investigation was conducted through explicit numerical simulations considering different impact angles. The numerical model of the bird strike has been assessed by numerical-experimental comparison, simulating the impact of a bird with a flat plate. For this study, the Coupled Eulerian-Lagrangian (CEL) approach has been adopted to perform the simulation. The results were compared in terms of stress distribution, failure analysis, displacements, and energy-time and force-time diagrams. The work demonstrated that using innovative manufacturing processes, such as additive manufacturing, can significantly improve the bird strike resistance of aerospace structures. This improvement is achieved though the production of lighter, structurally collaborative geometries, by reducing the load transferred to the rest of the UAV by about 47 % and decreasing the displacement on the impact area by 53 %.

General bubble expansion at strong coupling

The strongly coupled system like the quark-hadron transition (if it is of first order) is becoming an active play yard for the physics of cosmological first-order phase transitions. However, the traditional field theoretic approach to strongly coupled first-order phase transitions is of great challenge, driving recent efforts from holographic dual theories with explicit numerical simulations. These holographic numerical simulations have revealed an intriguing linear correlation between the phase pressure difference (pressure difference away from the wall) to the nonrelativistic terminal velocity of an expanding planar wall, which has been reproduced analytically alongside both cylindrical and spherical walls from perfect-fluid hydrodynamics in our previous study but only for a bag equation of state. We also found, in our previous study, a universal quadratic correlation between the wall pressure difference (pressure difference near the bubble wall) to the nonrelativistic terminal wall velocity regardless of wall geometries. In this paper, we will generalize these analytic relations between the phase/wall pressure difference and terminal wall velocity into a more realistic equation of state beyond the simple bag model, providing the most general predictions so far for future tests from holographic numerical simulations of strongly coupled first-order phase transitions. Published by the American Physical Society 2024

Analysis of the mechanical response of solid rocket engine propellant under acceleration shock

The increased-range solid rocket engine of new ammunition often needs to withstand extremely high acceleration overload, leading to damage to the propellant’s structural integrity. To address this issue, this paper constructs a nonlinear viscoelastic constitutive model for the CMDB propellant by using low- and high-strain rate mechanical property tests. Combined with the secondary development of explicit dynamics and numerical simulation technology, the mechanical response of a certain type of solid rocket propellant under different acceleration impacts is analyzed. The results show that under acceleration impact loads, the propellant will compress, rebound, and recover over time, continuously cycling. Its axial displacement, maximum equivalent stress, and maximum equivalent strain exhibit irregular sinusoidal wave-like periodic cycles. Looking at the time when the peaks appear, the time when the maximum equivalent stress appears always lags behind the time when the maximum axial displacement peak appears. Due to the viscous effect of the viscoelastic material of the propellant, the time when the equivalent strain peak appears will lag behind the equivalent stress. Because of the material’s damping effect, both the peak values of the maximum equivalent stress and equivalent strain decrease over time. Under continuous high acceleration impact loads, this viscous damping phenomenon continuously diminishes, and the peak value of the propellant’s axial displacement gradually increases.

A simulation modeling methodology considering random multiple shots for shot peening process

Abstract Shot peening (SP) process is a typical surface strengthening process for metal and metal matrix composites, which can significantly improve the fatigue life and strength. The traditional SP simulation model falls short as it only takes into account one or a few shots, proving insufficient for accurately simulating the entire impact process involving hundreds of shots. In this study, a random multiple shots simulation modeling methodology with hundreds of random shots is proposed to simulate the impact process of SP. In order to reduce the simulation error, the random function Rand of MATLAB is used to generate the shot distributions many times, and the shot distribution closest to the average number is selected and the three-dimension parametric explicit dynamics numerical simulation model is built using ABAQUS software. Orthogonal experiments are carried out to investigate the influences of shot diameter, incident impact velocity, and angle on the residual stress distribution, roughness, and specimen deformation. Results showed that the average relative errors of maximum residual compressive stress, roughness, and deformation of specimen between simulation model and experimental value are 30.99, 16.14, and 16.73%, respectively. The primary factors affecting residual stress and deformation is shot diameter, and the main factor affecting roughness is impact velocity.

On Finite-Time Blow-Up Problem for Nonlinear Fractional Reaction Diffusion Equation: Analytical Results and Numerical Simulations

The study of the blow-up phenomenon for fractional reaction–diffusion problems is generally deemed of great importance in dealing with several situations that impact our daily lives, and it is applied in many areas such as finance and economics. In this article, we expand on some previous blow-up results for the explicit values and numerical simulation of finite-time blow-up solutions for a semilinear fractional partial differential problem involving a positive power of the solution. We show the behavior solution of the fractional problem, and the numerical solution of the finite-time blow-up solution is also considered. Finally, some illustrative examples and comparisons with the classical problem with integer order are presented, and the validity of the results is demonstrated.

Residual load-carrying performance of CFRP strengthened RC beam after drop hammer impact

Carbon fiber reinforced polymer (CFRP) external bonding is a common approach to strengthen the bearing capacity of the reinforced concrete (RC) members. In this study, two types of RC beams, i.e., CFRP strengthened beam and conventional RC beam, were tested under drop hammer impact and subsequent quasi-static loading. The strengthening effect of the CFRP on the dynamic responses, failure modes and residual load-carrying performance of the RC beams were fully investigated. Then, a high-resolution explicit numerical simulation was conducted to further investigate the residual load-carrying mechanism of the CFRP strengthened beam. The experimental results demonstrate that even though the CFRP sheet peels off from the soffit of the investigated beam instantaneously upon impact, which provides a little contribution to the impact damage elimination in the mid-span of the beam, the oblique cracks within the flexure-shear zone were reduced moderately. Further, the bonded CFRP sheet can effectively reduce the maximum and residual displacement of the beam and improve the recovery performance of deformation. In addition, the residual resistance, residual stiffness and post-impact energy absorption capacity of the beams with CFRP are shown to be higher than those of the unstrengthened ones. The experimental and numerical results both show that the effective anchoring approach has an important effect on the residual loading performance enhancement. Larger impact energy and more significant impact dynamic effect tend to degrade the bearing performance of the beam more.

An Effective Field Theory for large oscillons

We consider oscillons — localized, quasiperiodic, and extremely long-living classical solutions in models with real scalar fields. We develop their effective description in the limit of large size at finite field strength. Namely, we note that nonlinear long-range field configurations can be described by an effective complex field ψ(t,x) which is related to the original fields by a canonical transformation. The action for ψ has the form of a systematic gradient expansion. At every order of the expansion, such an effective theory has a global U(1) symmetry and hence a family of stationary nontopological solitons — oscillons. The decay of the latter objects is a nonperturbative process from the viewpoint of the effective theory. Our approach gives an intuitive understanding of oscillons in full nonlinearity and explains their longevity. Importantly, it also provides reliable selection criteria for models with long-lived oscillons. This technique is more precise in the nonrelativistic limit, in the notable cases of nonlinear, extremely long-lived, and large objects, and also in lower spatial dimensions. We test the effective theory by performing explicit numerical simulations of a (d + 1)-dimensional scalar field with a plateau potential.

Dynamical free energy based model for quantum decision making

We propose a quantum-mechanical framework to describe the dynamics of human decision making, where the interactions between the open quantum system of decision makers and its surrounding environment at given temperature are relevantly taken into account. The temporal evolution of quantum system is described in terms of the time-dependent density matrix, from which we can evaluate those thermodynamic functions such as internal energy, (von Neumann) entropy and (Helmholtz) free energy. In this study we rely on the symmetrical quasi-classical (SQC) windowing approach to numerically solve the non-adiabatic quantum dynamics. We then consider the Hamiltonians to formulate the Prisoner’s Dilemma (PD) problem and calculate the population dynamics of the quantum states of two players’ decisions, where some quantum coherence or interference effects are observed. The evaluated free energy tends to decrease toward the thermodynamic equilibrium value, thus driving the dynamics of quantum system between the Nash equilibrium and Pareto optimum states. The calculated entropy often shows a tendency of temporal decrease, thus indicating the emergence of order in the quantum system. We have also applied the present scheme to the issue of the violation of the sure thing principle and found its occurrence through explicit numerical simulations for the PD problem. The present study may provide a theoretical basis to connect the dynamics of quantum decision making to the free energy principle in cognitive science.

General analytical conditions for inflaton fragmentation: Quick and easy tests for its occurrence

Understanding the physics of inflaton condensate fragmentation in the early Universe is crucial as the existence of fragments in the form of non-topological solitons (oscillons or Q-balls) may potentially modify the evolution of the post-inflation Universe. Furthermore, such fragments may evolve into primordial black holes and form dark matter, or emit gravitational waves. Due to the non-perturbative and non-linear nature of the dynamics, most of the studies rely on numerical lattice simulations. Numerical simulations of condensate fragmentation are, however, challenging and, without knowing where to look in the parameter space, they are likely to be time-consuming as well. In this paper, we provide generic analytical conditions for the perturbations of an inflaton condensate to undergo growth to non-linearity in the cases of both symmetric and asymmetric inflaton potentials. We apply the conditions to various inflation models and demonstrate that our results are in good agreement with explicit numerical simulations. Our analytical conditions are easy to use and may be utilised in order to quickly identify models that may undergo fragmentation and determine the conditions under which they do so, which can guide subsequent in-depth numerical analyses.

Fast and robust implementation of quantum gates by transitionless quantum driving

As a basic operation in quantum computers, quantum logic gates and particularly controlled NOT (CNOT) gates are important in quantum information processing. In this paper, we propose a one-step scheme to generate a CNOT gate via transitionless quantum driving. In this scheme, an effective Hamiltonian is obtained based on quantum Zeno dynamics to drive the system to evolve into the target state when the parameters are reasonably set. The results of explicit numerical simulations indicate that the proposed scheme is robust against instability related to variation in experimental parameters and decoherence. The scheme can also be extended to generate a Toffoli gate, which is useful for large-scale quantum computers. Moreover, the generation process involves only a single step, greatly simplifying its implementation.

Projected Climate Change Impacts on Hurricane Storm Surge Inundation in the Coastal United States

The properties of hurricanes directly influence storm surges; however, the implications of projected changes to the climate are unclear. Here, we simulate the storm surges of historical storms under present day and end of century climate scenarios to assess the impact of climate change on storm surge inundation. We simulate 21 storms that impacted the Gulf of Mexico and Atlantic Coasts of the continental U.S. from 2000 to 2013. We find that the volume of inundation increases for 14 storms and the average change for all storms is +36%. The extent of inundation increases for 13 storms, and the average change for all storms is +25%. Notable increases in inundation occur near Texas, Louisiana, Mississippi, the west coast of Florida, the Carolinas, and New Jersey. Our calculations of inundation volume and extent suggest that at the end of the century, we can expect hurricanes to produce larger storm surge magnitudes in concentrated areas, as opposed to surges with lower magnitudes that are widespread. We examine changes in maximum wind speed, minimum central pressure, translation speed, and radius of the 33 ms−1wind to assess the impacts of individual storm characteristics on storm surge. We find that there is no single storm characteristic that directly relates to storm surge inundation or its climate induced changes. Even when all the characteristics are considered together, the resulting influences are difficult to anticipate. This is likely due to the complexity of the hydrodynamics and interactions with local geography. This illustrates that even as climate change research advances and more is known about projected impacts to hurricanes, implications for storm surge will be difficult to predict without explicit numerical simulation.

One-step implementation of a robust Fredkin gate based on path engineering

In this paper, we propose a scheme to generate a Fredkin gate in a single step based on path engineering. The quantum Zeno dynamics is utilized to simplify the Hamiltonian. As a result, an effective Hamiltonian will be obtained to drive the system to evolve into the target state in a short time if reasonable parameters are set. In addition, the results of explicit numerical simulations indicate that the scheme is robust against the instability of experimental parameters and the decoherence arising from atomic spontaneous emission and cavity decay. Most importantly, our scheme is just a single step, which greatly simplifies actual operation.

Explicit solutions and numerical simulations for an asymptotic water waves model with surface tension

This paper deals with the water waves problem for uneven bottom under the influence of surface tension. We consider here an asymptotic limit for the Green–Naghdi equations in KdV scale, that is the Boussinesq system. The derivation of the KdV equation with uneven bottom under the influence of surface tension has been established. Indeed, this derivation is obtained in a formal way by using the Whitham technique, then the analytic solution to this equation has been obtained in case of flat bottom. However, in case of uneven bottom an $$H^s$$ -consistent solution has been obtained. Also, an $$H^s$$ -consistent solution for the Boussinesq system has been established, taking into consideration the influence of surface tension and uneven bottom. Finally, we confirmed the obtained theoretical results of this paper numerically, by devoting the last section to make a numerical validation. Moreover, analytic solutions to the KdV $$\sigma $$ and Boussinesq system were established in case of several bottom parametrization including the linear one.

Determining factors affecting sheet metal plastic wrinkling in response to nonuniform tension using wrinkling limit diagrams

Abstract In thin plate plastic forming, the efficient, accurate prediction and control of wrinkling is a basic requirement. Because there is no clear means of determining the main strain space curve (similar to the fracture forming limit diagram) when establishing the critical wrinkling state, this work used diagonal tensile plate tests to verify a numerical simulation of plastic wrinkling in thin plates. This model included a buckling mode obtained by an eigenvalue buckling analysis as the initial shape defect in a dynamic explicit numerical simulation of the plastic deformation of the test pieces. This permitted calculation of the true instability morphology of the test piece and avoided the difficulty associated with simulating plastic deformation wrinkling morphologies using existing static implicit or dynamic explicit numerical simulation algorithms. The morphology and characteristics of the critical wrinkling limit diagram (WLD) associated with nonuniform tension were investigated. The effect of the specimen thickness and boundary conditions on the WLD in the main strain space were also examined and the effects of various processing parameters on crease resistance were established. Finally, the effectiveness of the WLD established in this work was verified based on using non-contact full-field strain measurements to examine the plastic wrinkling of thin plates. This research provides a means of establishing the critical wrinkling line for various conditions.

Simulation and Experimental Comparison of Laser Impact Welding with a Plasma Pressure Model

In this study, spatial and temporal profiles of an Nd-YAG laser beam pressure pulse are experimentally characterized and fully captured for use in numerical simulations of laser impact welding (LIW). Both axisymmetric, Arbitrary Lagrangian-Eulerian (ALE) and Eulerian dynamic explicit numerical simulations of the collision and deformation of the flyer and target foils are created. The effect of the standoff distance between the foils on impact angle, velocity distribution, springback, the overall shape of the deformed foils, and the weld strength in lap shear tests are investigated. In addition, the jetting phenomenon (separation and ejection of particles at very high velocities due to high-impact collision) and interlocking of the foils along the weld interface are simulated. Simulation results are compared to experiments, which exhibit very similar deformation and impact behaviors. In contrast to previous numerical studies that assume a pre-defined deformed flyer foil shape with uniform initial velocity, the research in this work shows that incorporation of the actual spatial and temporal profiles of the laser beam and modeling of the corresponding pressure pulse based on a laser shock peening approach provides a more realistic prediction of the LIW process mechanism.

Composite Geological Strength Index Approach with Application to Hydrothermal Vein Networks and Other Intrablock Structures in Complex Rockmasses

Conventional rockmass characterization and analysis methods for geotechnical assessment in mining, civil tunnelling, and other excavations consider only the intact rock properties and the discrete fractures that are present and form blocks within rockmasses. As modern underground excavations go deeper and enter into more high stress environments with complex excavation geometries and associated stress paths, healed structures within initially intact rock blocks such as hydrothermal veins, veinlets and stockwork (termed intrablock structures) are having an increasing influence on rockmass behaviour and should be included in modern geotechnical engineering design. Field observations indicate the conventional Geological Strength Index (GSI) does not accurately estimate rockmass strength and behaviour of complex rockmasses. A modified GSI chart to include intrablock structures and a new Composite Geological Strength Index (CGSI) methodology to combine multiple suites of rockmass structure using a weighted harmonic average are presented as tools to evaluate complex rockmasses that contain multiple suites of structure for application to geomechanical numerical models. CGSI is introduced and numerically validated using implicit and explicit finite element method numerical simulations of an underground excavation and a case study of field observations in an adit at the El Teniente mine in Chile. In both cases, the CGSI approach using the modified GSI chart results in an improved estimate of rockmass behaviour in implicit equivalent continuum numerical models when compared to a conventional GSI approach.

Estimating fluid flow rates through fracture networks using combinatorial optimization

To enable fast uncertainty quantification of fluid flow in a discrete fracture network (DFN), we present two approaches to quickly compute fluid flow in DFNs using combinatorial optimization algorithms. Specifically, the presented Hanan Shortest Path Maxflow (HSPM) and Intersection Shortest Path Maxflow (ISPM) methods translate DFN geometries and properties to a graph on which a max flow algorithm computes a combinatorial flow, from which an overall fluid flow rate is estimated using a shortest path decomposition of this flow. The two approaches are assessed by comparing their predictions with results from explicit numerical simulations of simple test cases as well as stochastic DFN realizations covering a range of fracture densities. Both methods have a high accuracy and very low computational cost, which can facilitate much-needed in-depth analyses of the propagation of uncertainty in fracture and fracture-network properties to fluid flow rates.

Nonlinear dynamics of a planar hinged-supported beam with one end spring system

Forced nonlinear oscillations of a planar, initially straight, Timoshenko beam are studied. The goal of this paper is to examine large amplitude vibrations of a hinged-simply supported beam with a linear axial spring on one end, allowing to consider the influence of varying axial boundary conditions. Influence of geometrical nonlinearity coming from very large deformations in axial, transversal and rotational directions on frequency response curves are presented for a wide spectrum of the spring stiffness. The complete frequency response curve is computed by a special pseudo continuation method of explicit numerical simulations. For selected cases, a jump phenomenon between branches and super/sub harmonic resonances have been observed.

New Saturated Delayed Control for a Chain of Integrators with Nonlinear Terms

AbstractThis paper investigates the saturated delayed stabilization of a chain of integrators with higher‐order nonlinear terms. With the aid of a recent state transformation, the system is transformed into a canonical form in which time delay appears in both input and states. As a result, natural cancellations can be fully used in the saturation reduction analysis, and fewer terms need to be estimated in the asymptotical stability analysis of the reduced system. In addition, a single tuneable parameter is introduced to the special state transformation, which facilitates compensating an arbitrarily large input‐delay. As an example, a simplified inertia wheel pendulum system is provided with an explicit controller and numerical simulations are given to demonstrate the effectiveness of the suggested controller.