Contour Shape Research Articles

Innovative and diverse soliton solutions of the dual core optical fiber nonlinear models via two competent techniques

It becomes an interesting part for the researchers to analyze the dynamical behavior of soliton propagation in optical fibers for trans-oceanic and trans-continental distances. In this paper, we desire to retrieve distinct and innovative accurate wave solutions to the dual core optical fiber nonlinear equations by adopting the improved tanh method and the rational [Formula: see text]-expansion method. Consequently, a bundle of accurate wave solutions is achieved in diverse sense. The acquired solutions are made visible in the profiles of three-dimensional (3D), two-dimensional (2D) and contour shapes. The effects of the wave speed in soliton transmission are highlighted by plotting different 2D outlines in a single diagram for some obtained solutions. The employed techniques perform as before to unravel the suggested governing models for appropriate wave solutions and hence deserve to contribute in further research.

PAEDID: Patch Autoencoder-based Deep Image Decomposition for pixel-level defective region segmentation

Unsupervised pixel-level defective region segmentation is an important task in image-based anomaly detection for various industrial applications. The state-of-the-art methods have their own advantages and limitations: matrix-decomposition-based methods are robust to noise, but lack complex background image modeling capability; representation-based methods are good at defective region localization, but lack accuracy in defective region shape contour extraction; reconstruction-based methods detected defective region match well with the ground truth defective region shape contour, but are noisy. To combine the best of both worlds, we present an unsupervised Patch AutoEncoder-based Deep Image Decomposition (PAEDID) method for defective region segmentation. In the training stage, we learn the common background as a deep image prior by a patch autoencoder network. In the inference stage, we formulate anomaly detection as an image decomposition problem with the deep image prior and sparsity regularizations. By adopting the proposed approach, the defective regions in the image can be accurately extracted in an unsupervised fashion. We demonstrate the effectiveness of the PAEDID method in simulation studies and an industrial dataset in the case study.

Mechanism of ceramic slurry light scattering affecting contour accuracy and method of projection plane correction

Digital light processing (DLP) is a relatively mature ceramic additive manufacturing technology widely applied in medical bone implantation, electronic communication, and other fields. However, the size error caused by the light scattering from the complex contour can seriously affect the precision and forming quality of the printed green body. This paper studied the scattering behavior of complex structure ceramics under different exposure energies through two structural parameters: exposure width and contour shape. A formula for excess cure width is presented. The formula will be then applied to simplify the machine learning algorithms. Finally, by inverse compensation for the complex contour, we optimized some pore structures and complex shapes to greatly improve the fidelity of the structure.

Perspective method for construction of drying and watering network for growing potatoes

In the Central region of the Russian Federation, precipitation is uneven both during the growing season of plants and during the calendar year. Therefore, to obtain sustainable yields and ensure the optimal water-air balance of the soil, agro-reclamation measures are required, including the organization of additional irrigation. During the winter period, a significant amount of snow accumulates, which during the melting period does not have time to soak into the soil, forming surface runoff. The construction of a drainage and water supply network will make it possible to accumulate excess moisture in reservoirs to moisten the soil during the rainless period. The joint use of the drainage network and the drip irrigation system is recommended. Using such a system will allow at the estimated time to supply or divert water to a specific area, removing excess moisture from the soil by drainage to storage tanks and then directing irrigation water to the drip irrigation system during the dry period. The calculation of the irrigation rate, taking into account the semi-elliptical shape of the humidification contour, showed that the required volume of water could be accumulated in special storage tanks. Drip tape laying can be carried out mechanized using a special stacker based on a ridge former.

Геометрия контуров капельного увлажнения почв

Purpose: to determine dependencies and develop a methodology for calculating the geometric dimensions and constructing the outline of local moisture contours formed in the soil space during drip irrigation. Materials and methods. The factual basis of the development was the data of full-scale (field) measurements of the contours of the drip-moistened soil space and their office processing. The studies were carried out on experimental sites with different soil cover, represented by steppe, dry steppe and steppe-desert soil types: chernozems (ordinary and southern) and chestnut soils with a wide range of granulometric texture, water-physical properties and with different levels of pre-irrigation moisture, when ir-rigated with emitters productivity from 1,0 to 6,0 l/h. Results and discussion. During the study, the following things were considered as determining the process of contour formation and the contour geometry: soil conditions characterized by the physical clay content, the min-imum water capacity, bulk density and the level of pre-irrigation moisture; technological pa-rameters determined by the level of post-irrigation moisture, the given depth of soil moisture, the flow rate of drip micro-water outlets and the volume of water supply. Empirical depend-ences that allow determination of the linear dimensions, the wetted area dimensions and the volumes of moisture contours are obtained according to the given values: the physical clay content in soil within 18.0–77.0 % of the dry soil mass (DSM), the lowest moisture capacity in the range 16.5–32 % DSM, wetting depth from 0.5 to 1.2 m, additional irrigation moisture from 60 to 80 % of the level of the minimum water capacity, emitter flow from 1.0 to 6.0 l/h. Conclusion. A system of empirical dependencies has been obtained, and methods for predict-ing the external shape, linear, areal and volumetric dimensions of local moisture contours formed in the soil space during drip irrigation have been developed.

Капельное орошение молодых плантаций виноградников в условиях Республики Крым

Purpose: to determine elements of irrigation technology for young vineyard plantations using the drip irrigation method on various types of soil in the Republic of Crimea and test them under the conditions of this region. Materials and methods. The research was carried out in the village of Pavlovka, Belogorsky district of the Republic of Crimea. The establishment of field experiments and observations were carried out using generally accepted methods for setting up and conducting field experiments. Results. As a result of the research, the water-physical properties of soils of the Republic of Crimea were analyzed and rational elements of the technology for irrigating young vineyard plantations using drip irrigation on various types of soils (limits of optimal soil moisture, dripper consumption, wetted depth, irrigation period and water application rate) were calculated. When calculating the irrigation regime for the drip irrigation method, it is necessary to take into account the wetted layer depth, the physical properties of soil, the planting pattern, the moisture contour shape, the dripper flow rate and pre-irrigation soil moisture. The elements of irrigation technology for young vineyard plantations vary significantly, for example, the recommended flow rate of drippers varies from 2–4 l/h on chernozems to 6–8 l/h on light chestnut soils and steppe solonetzes, while the duration of irrigation varies from 2–3 h on light chestnut soils up to 6–9 h on ordinary chernozems. Conclusions. When testing the results, it was found that the drip irrigation method has a positive effect on the survival rate of table grape cuttings. On average, this indicator for varieties was 98.8%. For soil and climatic conditions of the Republic of Crimea, the varieties Sport, Podarok to Irina, Baikonur and Zabava turned out to be the most responsive in terms of their morphological characteristics. During the growing season of the first year young table grapes (in a medium-dry year), 16 irrigations of 30 cubic m/ha with an irrigation rate of 480 cubic m/ha were carried out, while the total water consumption excluding the use of moisture from soil was 3740 cubic m/ha.

Slope gradient impacts on rill morphological characteristics: Using indoor simulation experiment on loamy clay under certain rainfall intensity

In the present study, the rill morphological parameters and their spatial distributions were investigated using indoor rainfall simulation experiments in combination with 3D terrestrial laser scanning technique. Moreover, the optimal rill morphological indicators for rill erosion evaluation were selected based on the relationship of rill morphological parameters and erosion amount. The results showed that total rill length (L), rill density (ρ), maximum width (Wmax), the degree of contour line departure (μ) and shape ratio (η) increased with the increase of slope gradient, whilst the mean rill depth (Dmean), mean rill width (Wmean) and width/depth ratio (W/D) decreased with the increase of slope gradient. The spatial distribution pattern of each rill morphology parameter was also changed with slope gradient, showing differences in upper slope, central slope and lower slope. Most of rill morphological parameters were highly correlated with rill erosion amount, except the mean rill width (Wmean), degree of contour line departure (μ), and rill density (ρ). The plane area of rill (Parea) or the degree of rill dissection (δ) was selected as the optimal morphological parameter to predict rill erosion amount, followed by the maximum area of cross section (CSmax), the maximum rill depth (Dmax), and the mean rill depth (Dmean). In particular, the parameters of CSmax and Dmax are recommended for rill erosion estimation based on the convenience and ease of data acquisition.

Intact Chorionic Vesicle in Very Early Products of Conception Specimens: Clinicopathologic Features of 26 Cases That May Mimic Complete Hydatidiform Mole.

Among the morphologic mimics of hydatidiform moles, the chorionic vesicle of early first-trimester pregnancy has received scant attention. The chorionic vesicle is the stage of the implanted blastocyst in which the cytotrophoblastic shell is circumferentially lined by primary and secondary villi and envelops the notochord stage embryo, yolk sac, and amniotic sac, ∼5 to 6 weeks since the last menstrual period. Miscarriage specimens at this early gestational age that contain an intact chorionic vesicle may be misinterpreted as a complete hydatidiform mole because of its large size, cistern-like cavity, and circumferentially radiating villi and trophoblast, particularly so when embryonic tissue is absent. We present the clinicopathologic features of 26 products of conception specimens containing a chorionic vesicle, some of which were submitted for consultation as a possible complete mole. The median gestational age was 6 weeks. The majority were free-floating in the specimen, unattached to endometrium. The median diameter was 6.3mm and ranged up to 11.3mm. The embryo was absent in 81% of cases, leaving an empty cavity resembling the cistern of a complete mole in all but 2 cases. Most cases exhibited circumferential villi and variable degrees of proliferating polarized villous trophoblast and extravillous trophoblast but trophoblast atypia was absent. Villous stromal karyorrhexis and blue-gray myxoid extracellular stromal matrix were observed in the majority of cases. A minority exhibited focal abnormal villous morphology concerning for early molar pregnancy, including irregular projections (27%), invaginations (12%), or bulbous shapes (4%) of the villous contours and trophoblast pseudoinclusions (15%). In contrast, orderly hierarchical branching of the secondary villi occurred in 31%. p57 immunoexpression was intact in all 25 cases tested. Short tandem repeat genotype testing confirmed a biparental diploid genotype in both of 2 cases tested. Although uncommonly observed in early first-trimester products of conception specimens, the normal chorionic vesicle merits awareness as a potential diagnostic pitfall. While some morphologic features resemble those of a well-developed complete mole, at this early gestational age such features are not expected in a very early complete mole. Attention to the reported gestational age, if available, and presence of embryonic tissues will mitigate against misclassification as complete mole. As with the workup of any potential gestational trophoblastic disease, partnering the clinical and morphologic evaluation with molecular evaluation (intact p57 immunoexpression and lack of any of the characteristic molar genotypes) offers the most precise classification.

Dosimetric variability across a library of computational tumor phantoms.

In radiopharmaceutical therapy, dosimetry-based treatment planning and response evaluation require accurate tumor absorbed dose estimates. Tumor dose estimates are routinely derived using simplistic spherical models, despite the well-established influence of tumor geometry on the dosimetry. Moreover, the degree of disease invasiveness correlates with departure from ideal geometry; malignant lesions often possess lobular, spiculated, or otherwise irregular margins in contrast to the commonly regular/smooth contours characteristic of benign lesions. To assess the effects of tumor shape, size, and margin contour on absorbed dose, an array of tumor geometries was modeled using computer-aided design software and the models used to calculate absorbed dose per unit time-integrated activity (i.e., S-values) for several clinically used therapeutic radionuclides, ⁹⁰Y, ¹³¹I, ¹⁷⁷Lu, ²¹¹At, ²²⁵Ac, ²¹³Bi, and ²²³Ra. <b>Methods:</b> 3D tumor models of several different shape classifications were generated using Blender software. Ovoid shapes were generated using axial scaling. Lobulated, spiculated, and irregular contours were generated using noise-based mesh deformation. The meshes were rigidly scaled to different volumes, and S-values were then computed using PARaDIM software. Radiomic features were extracted for each shape and the impact on S-values was examined. Finally, estimates of the systematic error present in dose calculations which model complex tumor shapes versus equivalent-mass spheres were determined. <b>Results:</b> The dependence of the tumor S-values on shape was largest for extreme departures from spherical geometry and for long-range beta emissions (e.g., ⁹⁰Y beta emissions). S-values for spheres agreed reasonably well with lobulated, spiculated, or irregular contours if the displacement scalar L was small. For marked deviations from spherical shape and small volumes, the systematic error of the equivalent-sphere approximation increased to 30-75% depending on radionuclide. The largest errors were observed for shapes with many long spicules and for spherical shells where the thickness was less than or comparable to the particle range in tissue. <b>Conclusion:</b> Variability in tumor S-values as a function of tumor shape and margin contour was observed, suggesting usage of contour-matched phantoms to improve accuracy of tumor dosimetry in organ-level dosimetry paradigms. Implementing a library of tumor phantoms in organ-level dosimetry software may facilitate optimization strategies for personalized radionuclide therapies.

Three‐dimensional shaped and contour pattern synthesis with multiple beam approach

AbstractA multiple‐beam synthesis method is proposed to generate three‐dimensional (3D) shaped and contour patterns from a planar phased array antenna. Three‐dimensional radiation patterns are synthesized primarily with optimum beam positions and variable mainbeam power levels of multiple beams, followed by calculating the resultant element weights. Contour patterns are synthesized from multiple beam peaks by mapping the individual beam power levels to their corresponding 3 dB beamwidth coverage areas at each designated location on the contour. The far‐field contour shape affected by the influence of the element pattern, mutual coupling, and scan loss is compensated by the peak power of the scanned beam patterns. The proposed synthesis supports dynamically changeable contour shapes. Flat‐topped, stepped 3D patterns and arbitrary contour shapes with shaped null zones inside the contour are simulated and implemented on a 16 × 16 element 5G mmWave planar phased array. Measured radiation patterns are compared with simulations and presented.

Performance on a Contour Integration task as a function of Contour Shapes: A comparison study between individuals with schizophrenia and Neurotypical Individuals

Performance on a Contour Integration task as a function of Contour Shapes: A comparison study between individuals with schizophrenia and Neurotypical Individuals

Aesthetic shape generation system based on novelty and complexity

Increasing the aesthetic quality of a shape is an important objective for enhancing the attractiveness of a product. Many studies on shape generation systems are based on the user’s emotion as a means of supporting the ideas of product designers. However, most of the proposed systems are unsuitable for extrapolation of shapes because they rely on the subjective evaluation of the user to determine the shape of an object. Experimental aesthetics theory suggests that a moderate level of novelty and complexity yields pleasant feelings. Furthermore, a mathematical model has been proposed for this theory that focuses on the sum of the information content induced by the novelty and complexity of an object. In this study, we formulated the novelty and complexity of contoured shapes and developed a system that generates a variety of shapes with the given novelty and complexity parameters. We conducted experiments using the generated butterfly and automobile shapes. The results indicate that the system can independently manipulate the novelty and complexity of a shape and affect its interestingness. The system may support the evaluation and further investigation of the most acceptable level of novelty and complexity with respect to the product shape.

Multi-objective optimization of the ORC axial turbine for a waste heat recovery system working in two modes: cogeneration and condensation

Due to the demand of the district heating network and electric power grid ORC turbines can operate in the condensation and cogeneration modes. This approach requires the design of an expander which is characterized by high efficiency in each mode of operation. The paper is devoted to a multi-objective efficiency optimization of a one stage axial ORC turbine working on MM (Hexamethyldisiloxane). An Implicit Filtering algorithm (IF) is used to find a flowpath with maximum efficiency. During the optimization the rotor profiles (at the hub and shroud) and the shape of endwall contours of the rotor domain are changed. Five optimization tasks are carried out with different weights of the efficiency of both modes of operation. Pareto fronts are obtained and a decision-making method is used to select an optimum solution. The optimization of the rotor row allows for significant efficiency improvements in two regimes of operation, with respect to a baseline geometric configuration designed with the help of classical methods.

Perception and Quantization Model for Periodic Contour Modifications.

Periodic, wave-like modifications of 2D shape contours are often applied to convey quantitative data via images. However, to the best of our knowledge, there has been no in-depth investigation of the perceptual uniformity and legibility of these kind of approaches. In this paper, we design and perform a user study to evaluate the perception of periodic contour modifications related to their geometry and colour. Based on the study results, we statistically derive a perceptual model, which demonstrates a mainly linear stimulus-to-perception relationship for geometric and colour amplitude and a close-to-quadratic relationship for the respective frequencies, with a rather negligible dependency on the waveform. Furthermore, analyzing the distribution of perceived magnitudes and the overlapping of the respective 50% confidence intervals, we extract distinguishable, visually equidistant quantization levels for each contour-related visual variable. Moreover, we give first insights into the perceptual dependency between amplitude and frequency, and propose a scheme for transferring our model to glyphs with different size, which preserves the distinguishability and the visual equidistance. This work is seen as a first step towards a comprehensive understanding of the perception of periodic contour modifications in image-based visualizations.

Using the DEMATEL Method to Explore Influencing Factors for Video Communication and Visual Perceptions in Social Media

This study used expert interviews and the DEMATEL method to explore the influencing factors affecting the evaluation of the good and cognitive response of video communication and visual perception in social media and for the benefit of facilitation of the implementation in improving the overall video communication and visual quality in social media in the related fields of communication, advertising, and visual design. Correspondingly, it could provide educators and practitioners in the field with a foundation to maximize the effectiveness of allocating resources to these influencing factors. This study explored the influencing factors of video communication and visual perception in social media and evaluated the causality, relevance, and degree of materiality among different factors. The results of this study indicated that the six dimension factors, including like (X8), feeling satisfied (X9), feeling of attractiveness (X11), a good sense of shape contour (modeling) (X12), good visual characteristics (X13), and a good sense of color (X14), showed a high degree of connection (prominence) with other dimension factors. Improving the quality of these six factors could help solve the problem while promoting a good feeling about the other factors.

Local Three-Dimensional Characterization of Nonlinear Grain Boundary Length within Bulk ZnO Using Nanorobot in SEM

Aiming at the problems of lack of data on the nonlinear morphology to divide uneven grain boundary in bulk ceramics, a unique approach of nanorobot-based characterization of three-dimensional nonlinear structure length can be creatively proposed under scanning electron microscope to quantify the actual morphology of local micro-area grain boundary in bulk ZnO. Contour shapes of the targeted grain boundaries in plane X-Y can be imaged using SEM. Z-directional relative height differences at different positions can be sequentially probed by nanorobot. Experiments demonstrate that it is effective to characterize three-dimensional length structures of nonlinear grain boundaries in bulk materials. By quantifying Z-directional relative height differences, it can be verified to show that irregular characteristics exist in three-dimensional grain boundary length, which can extend the depth effect on nonlinear bulk conductance. Furthermore, this method can also obtain nonlinear quantitative topographies to divide grain boundaries to uneven structure in the analysis of bulk polycrystalline materials.

Morphologic, morphometric and contour shape variations of sagittal otoliths of Lepidorhombus spp. in the Aegean Sea.

Otoliths are calcareous anatomical structures in the inner ear of fishes, and they can be used in the discrimination of fish species and stocks due to their species-specific shape. Sagittal otoliths in the Lepidorhombus whiffiagonis and Lepidorhombus boscii, two flatfish species of the same genus distributed in the Aegean Sea, were compared using morphology, morphometry and contour shape analyses. Blind and eyed side otoliths of Lepidorhombus species were evaluated separately due to their morphological features and statistical differences in morphometric measurements (p < 0.05). Four analysis groups were formed: blind side otolith of L. whiffiagonis, eyed side otolith of L. whiffiagonis, blind side otolith of L. boscii and eyed side otolith of L. boscii. Morphometric differences in otolith shape were performed by canonical discriminant analysis, and the first discriminant axis explained 97.4% (Wilks λ=0.270) of the variance between the groups, and the second axis explained 2.3% (Wilks λ=0.620). Classification success between Lepidorhombus species based on CDA is 100%, and the overall CDA classification score between groups is 76.5%. The wavelet functions obtained in the contour analysis showed high variability in the anterior, posterior-dorsal, antero-dorsal and ventral regions of the otoliths among these four analysis groups. Consequently, it is thought that this study will contribute to the taxonomic classification of fish with the morphological and morphometric differences in the blind and eyed side otoliths and the analyses made with the high discrimination success obtained in Lepidorhombus species.

Association among the morphological characteristics of the human ear – An approach towards forensic identification

Introduction and objectivesThe human external ear has intricate anatomy due to the presence of elevated and depressed structures which form the morphological characteristics of the external ear. It has been observed that they have some form of interdependence. Therefore, the present study is aimed to investigate the association amongst the morphological characteristics of the external ear and its feasibility for forensic identification. Material and methodsA cross-sectional sample of 497 participants (233 males and 264 females) aged 18–35 years (24.42 ± 5.17) was taken for the study. The data was collected from the district Solan of Himachal Pradesh, North India. Both the ears of the participants were examined for various morphological characteristics. The shape of the external ear, the contour shape of the supero-anterior, superior and supero-posterior helix, and other morphological characteristics were analyzed and classified based on the shape, rolling, contour shape, the strength of the elevated structures, and other factors. The associations between the morphological characteristics were investigated using chi-square and correspondence analysis, while Cramer’s V test was used to determine the strength of the association. ResultsA total number of 33 morphological characteristics were considered for the present study. Each morphological characteristic was compared with the other 32 parameters. Therefore, a total number of 1056 (33 ×32) pairs were examined, with only 587 pairs showing a statistically significant association. The shape of the external ear, for example, has a significant association with 25 out of 32 morphological characteristics, including rolling of the superior and posterior helix, the contour shape of the supero-anterior, superior, supero-posterior helix, etc. Moreover, all the statistically significant pairs were subjected to correspondence analysis to evaluate the measure of their association. Wide rolled superior helix, for example, is closely associated with a round-shaped external ear, implying that if a person has a wide rolled superior helix, he or she is more likely to have a round-shaped external ear. ConclusionThe present study has explored and developed the database of the association of the morphological characteristics of the external ear. The database may be useful in predicting the shape and size of the external ear from some of these characteristics. The findings could be utilized during facial reconstruction in forensic examinations and the reconstruction of deformed ears. This study, therefore, finds that the morphological features of the ear are an important addition to the arsenal of the forensic investigator.

Clinical and experimental study of a terahertz time-domain system for the determination of the pathological margins of laryngeal carcinoma

ObjectiveLaryngeal cancer is a common malignancy in otorhinolaryngological head and neck surgery, accounting for approximately one-third of all head and neck malignancies. Terahertz time-domain spectroscopy (THz-TDS) has recently been found to be useful for the detection of tumors. This study was conducted to investigate the application of THz-TDS in the diagnosis of pathological resection margins of laryngeal cancer.MethodsFresh laryngeal cancer tissues from 10 patients with laryngeal cancer were extracted, and after simultaneous HE staining and terahertz imaging, the tumor area, paracancerous area, and normal tissue area of each laryngeal cancer tissue sample were located under a microscope according to the pathological results of HE staining.ResultsThe shape contours of the tumor region revealed by terahertz imaging maps and HE staining were similar. In the terahertz spectrum in the frequency range of 0.5–1.9 THz, both the absorption coefficient and refractive index values followed the order tumor > para cancer > normal tissue, with statistically significant differences (P < 0.01). When the terahertz frequency was 1.5 THz, the absorption coefficient of terahertz light waves by laryngeal cancer tissue and the percentage of nuclei showed an extremely high positive correlation (P < 0.01, r = 0.971). In the frequency ranges of 0.5–1.2 THz and 1.6–1.9 THz, the absorption coefficients of the highly differentiated group were higher than those of the moderately differentiated group. In the frequency range of 1.2–1.6 THz, the results were reversed, with statistically significant differences (P < 0.05). In the frequency range of 0.5–1.9 THz, the highly differentiated group had a higher refractive index than the moderately differentiated group, with a statistically significant difference (P < 0.05).ConclusionsTHz-TDS can be used to determine the pathological margins of laryngeal cancer based on the absorption coefficient and refractive index, and the magnitudes of the absorption coefficient and refractive index are related to the percentage of nuclei. The degree of differentiation of laryngeal cancer tissue can be assessed by THz-TDS. The study shows that the terahertz time-domain system is promising for applications in the diagnosis of laryngeal cancer, especially for the more accurate identification of intraoperative margins.

Metamaterial-enabled asymmetric negative refraction of GHz mechanical waves

Wave refraction at an interface between different materials is a basic yet fundamental phenomenon, transversal to several scientific realms – electromagnetism, gas and fluid acoustics, solid mechanics, and possibly also matter waves. Under specific circumstances, mostly enabled by structuration below the wavelength scale, i.e., through the metamaterial approach, waves undergo negative refraction, eventually enabling superlensing and transformation optics. However, presently known negative refraction systems are symmetric, in that they cannot distinguish between positive and negative angles of incidence. Exploiting a metamaterial with an asymmetric unit cell, we demonstrate that the aforementioned symmetry can be broken, ultimately relying on the specific shape of the Bloch mode isofrequency curves. Our study specialized upon a mechanical metamaterial operating at GHz frequency, which is by itself a building block for advanced technologies such as chip-scale hybrid optomechanical and electromechanical devices. However, the phenomenon is based on general wave theory concepts, and it applies to any frequency and time scale for any kind of linear waves, provided that a suitable shaping of the isofrequency contours is implemented.