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This paper presents a method for generating dynamic caustic patterns by utilising dual-optimised holographic fields with Phased Array Transducer (PAT). Building on previous research in static caustic optimisation and ultrasonic manipulation, this approach employs computational techniques to dynamically shape fluid surfaces, thereby creating controllable and real-time caustic images. The system employs a Digital Twin framework, which enables iterative feedback and refinement, thereby improving the accuracy and quality of the caustic patterns produced. This paper extends the foundational work in caustic generation by integrating liquid surfaces as refractive media. This concept has previously been explored in simulations but not fully realised in practical applications. The utilisation of ultrasound to directly manipulate these surfaces enables the generation of dynamic caustics with a high degree of flexibility. The Digital Twin approach further enhances this process by allowing for precise adjustments and optimisation based on real-time feedback. Experimental results demonstrate the technique’s capacity to generate continuous animations and complex caustic patterns at high frequencies. Although there are limitations in contrast and resolution compared to solid-surface methods, this approach offers advantages in terms of real-time adaptability and scalability. This technique has the potential to be applied in a number of areas, including interactive displays, artistic installations and educational tools. This research builds upon the work of previous researchers in the fields of caustics optimisation, ultrasonic manipulation, and computational displays. Future research will concentrate on enhancing the resolution and intricacy of the generated patterns.

The demand for controlled blasting technology is increasing and the employment of slotted cartridges becomes prevalent. To investigate the influence of slot width on the patterns of crack expansion (crack refers to the sudden and violent fracture that occurs during blasting), five sets of model experiments were performed utilizing the dynamic caustics test system, with the slot width ranging from 0.50 to 1.50 mm. Upon this, numerical simulation was performed using the LS-DYNA finite element software to scrutinize the stress propagation process, and analyze the peak Von Mises stress at diverse monitoring points surrounding the borehole. It indicates that the angle (θ) of the primary crack at the slot is affected by the slot width (B), and their relationship agrees with an inverse tangent function. The angle (θ) gradually increases with the augmentation of the slot width (B). Furthermore, the average peaks of burst primary crack expansion velocity and dynamic stress intensity factor are affected by the slot width. The former experiences a reduction of 38%, while the latter undergoes a decline of 42% across the spectrum of slot width from 0.50 to 1.50 mm. The numerical simulation results indicate a close alignment between the crack expansion pattern and the observations from dynamic caustics experiments. The Von Mises stress primarily concentrates in the normal direction of the slot and at the tip of the crack. With the augmentation of slot width, the Von Mises stress at each monitoring point in the slot direction suddenly increase, and the time-course curve presents the more pronounced double peaks.HighlightsA variety of mini slot pipes were designed for indoor dynamic caustic test to study the effect of slot width in cartridge on the directional concentration energy.An inverse tangent function between the crack angle and the cartridge slot width sheds light on the structural dynamics of auxiliary materials.The consistency of theoretical formulas, dynamic caustic experiment results, and numerical simulation results enhances the credibility.The effects of slot width on crack propagation velocity, dynamic stress intensity factor, and spatial and temporal distribution of stress are studied.

To study the crack propagation characteristics of the V-shaped energy- accumulating charge at different angles, a new numerical laser caustics test system was used to observe the fracture process of the V-shaped energy-concentrating charge; the mechanical distribution mechanism around the blast hole of the energy-accumulating charge was analyzed, and fractal theory was used to evaluate the damage degree of the energy-accumulating charge. A series of caustics test results show that the main crack has a longer expansion length in the energy-concentrating direction, and the crack expansion length is shorter in the nonenergy-concentrating direction. The fractal damage results of the energy gathering perforating charge indicate that as the angle of the charge increases, the damage caused by energy gathering blasting gradually increases, the complexity of crack propagation increases, and the main crack follows the direction of energy accumulation. The directivity becomes increasingly less obvious. When the energy gathering angle is 120°, the main crack propagation process is similar to that of the circular charge (control group). The shaped charge can be used for directional fracture control blasting, which helps to control the direction and number of cracks and improve the blasting effect.

To study the propagation law of the main crack in slot blasting through pre-cracks at different angles, a new type of digital laser dynamic caustics test system was utilized for the examination of the dynamic propagation process of burst cracks passing through 0, 30, 60, and 90° pre-cracks. The research results are presented as follows: (1) As the angle of the pre-crack increases, the length of main crack through the pre-crack and the forward propagation length decrease, and the main crack propagates forward through the pre-crack in the same direction as the slot direction; (2) in slotted hole blasting, the left side of the 0, 30, 60 pre-crack produced wing crack B under the action of the reflected stress wave, and the left side of the 90° pre-crack did not produce wing crack B, showing that the 90° pre-crack has a certain inhibitory effect on the reflected stretching wave; and (3) the pictures of the main crack in slot blasting are binarized through the pre-crack at different angles. The main crack is divided into M and N areas before and after the pre-crack. As the angle of the pre-crack increases, the box dimensions M and N first decrease and then increase, indicating that the crack propagation complexity before and after the main crack passes through the pre-crack decreases and then increases.

The drilling and blasting method remains fundamental to mining and tunneling projects, prized for its simplicity and economy. However, conventional techniques are increasingly challenged by modern safety and environmental standards, particularly in complex geological settings. Slotted charge blasting technology addresses these limitations by offering exceptional control over fracture propagation and damage. This paper provides a comprehensive review of the field, synthesizing global research on its theoretical foundations, advanced diagnostic methodologies, key performance parameters, and engineering applications. We critically analyze the current challenges facing the technology, particularly in weak rock conditions, where extensive plastic deformation and rapid energy dissipation often compromise directional control, and identify promising trends for its future development. Specifically, the integration of intelligent adaptive control and additive manufacturing is highlighted as a key direction. By mapping out a clear trajectory for future research, this work provides a scientific basis to advance the efficacy and safety of slotted charge blasting in demanding engineering environments.

An underground roadway usually contains defects of various types, and when the roadway is subjected to external loading, the locations of those defects influence the roadway by differing degrees. In this study, to study how the locations of defects affect crack propagation in a roadway, specimens with tunnel-type voids were made using polymethyl methacrylate, and the stress wave produced by a bullet impacting an incident rod was used as the impact load. Meanwhile, the variations in crack speed, displacement, and dynamic stress intensity factor during crack propagation were obtained using an experimental system of digital laser dynamic caustics, and the commercial software ABAQUS was used for numerical simulations. From the experiments and numerical simulations, the crack propagation path was verified and the impact fracture behavior of a semicircular-arch roadway with different defect positions was presented. The results show that when the pre-fabricated crack is on the central axis of the sample, the crack propagation is purely mode I; when the pre-fabricated crack is 5 mm from the central axis, the crack propagation alternates between mode I and a mixture of modes I and II; when the pre-fabricated crack is at the edge of the semicircular-arch roadway, the crack propagation follows the I–II mixed mode.

The damage to the surrounding rock under the adjacent explosive load generally manifests as fracture growth. In order to in-depth understand the fracture growth law and mechanism, fracture growth process in the surrounding rock with a nearby adjacent tunnel under the explosive load is studied using the dynamic caustics method. Test results indicate that the original fracture growth process can be divided into two stages, demarcated when the main fracture penetrates the original fracture. The original fracture grows in the vertical direction due to the free surface of the tunnel in the first stage. The main fracture from the explosive source plays a dominant role in the growth direction of the original fracture in the second stage, and the original fracture deflects and grows parallel to the main fracture. Based on kinematic and energy analysis, the penetration process is companied by energy transfer and superposition. The neglected back-facing side also contains fracture on the lower side. The fracture growth direction changes after the original fracture penetrates the free surface of tunnel under the combined effect of the original fracture and unloading wave.

Dynamic fracture behaviour of crack curving in bent beams has been investigated. In order to understand the propagation mechanism of such cracks under impact, an experimental method is used that combines dynamic photoelasticity with dynamic caustics to study the interaction of the flexural waves and the crack. From the state change of the transient stresses in polymer specimen, the curving fracture in the impulsively loaded beams is analyzed. The dynamic responses of crack tips are evaluated by the stress intensity factors for the cracks running in varying curvature paths under bending stress wave.

The Maxey–Riley equation has been extensively used by the fluid dynamics community to study the dynamics of small inertial particles in fluid flow. However, most often, the Basset history force in this equation is neglected. Analytical solutions have almost never been attempted because of the difficulty in handling an integro-differential equation of this type. Including the Basset force in numerical solutions of particulate flows involves storage requirements which rapidly increase in time. Thus the significance of the Basset history force in the dynamics has not been understood. In this paper, we show that the Maxey–Riley equation in its entirety can be exactly mapped as a forced, time-dependent Robin boundary condition of the one-dimensional diffusion equation, and solved using the unified transform method. We obtain the exact solution for a general homogeneous time-dependent flow field, and apply it to a range of physically relevant situations. In a particle coming to a halt in a quiescent environment, the Basset history force speeds up the decay as a stretched exponential at short time while slowing it down to a power-law relaxation, ${\\sim}t^{-3/2}$ , at long time. A particle settling under gravity is shown to relax even more slowly to its terminal velocity ( ${\\sim}t^{-1/2}$ ), whereas this relaxation would be expected to take place exponentially fast if the history term were to be neglected. An important mechanism for the growth of raindrops is by the gravitational settling of larger drops through an environment of smaller droplets, and repeatedly colliding and coalescing with them. Using our solution we estimate that the rate of growth rate of a raindrop can be grossly overestimated when history effects are not accounted for. We solve exactly for particle motion in a plane Couette flow and show that the location (and final velocity) to which a particle relaxes is different from that due to Stokes drag alone. For a general flow, our approach makes possible a numerical scheme for arbitrary but smooth flows without increasing memory demands and with spectral accuracy. We use our numerical scheme to solve an example spatially varying flow of inertial particles in the vicinity of a point vortex. We show that the critical radius for caustics formation shrinks slightly due to history effects. Our scheme opens up a method for future studies to include the Basset history term in their calculations to spectral accuracy, without astronomical storage costs. Moreover, our results indicate that the Basset history can affect dynamics significantly.

Novel Cyanoguanidine-modified chitosan (CCs) adsorbent was successfully prepared via a four-step procedure; first by protection of the amino groups of chitosan, second by insertion of epoxide rings, third by opening the latter with cyanoguanidine, and fourth by restoring the amino groups through elimination of the protection. Its structure and morphology were checked using Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. The adsorption capacity of CCs for Congo Red (CR) dye was studied under various conditions. It decreased significantly with the increase in the solution pH value and dye concentration, while it increased with increasing temperature. The adsorption fitted to the pseudo-second order kinetic model and Elovich model. The intraparticle diffusion model showed that the adsorption involved a multi-step process. The isotherm of CR dye adsorption by CCs conforms to the Langmuir isotherm model, indicating the monolayer nature of adsorption. The maximum monolayer coverage capacity, qmax, was 666.67 mg g−1. Studying the thermodynamic showed that the adsorption was endothermic as illustrated from the positive value of enthalpy (34.49 kJ mol−1). According to the values of ΔG°, the adsorption process was spontaneous at all selected temperatures. The value of ΔS° showed an increase in randomness for the adsorption process. The value of activation energy was 2.47 kJ mol−1. The desorption percentage reached to 58% after 5 cycles. This proved that CCs is an efficient and a promising adsorbent for the removal of CR dye from its aqueous solution.