Focusing Phenomenon Research Articles

Development of the full Lagrangian approach for modeling dilute dispersed media flows (a review)

Continuum models of media with zero pressure are widely used in various branches of physics and mechanics, including studies of a dilute dispersed phase in multiphase flows. In zero-pressure media, the particle trajectories may intersect, “folds” and “puckers” of the phase volume may arise, and “caustics” (the envelopes of particle trajectories) may appear, near which the density of the medium sharply increases. In recent decades, the phenomena of clustering and aerodynamic focusing of inertial admixture in gas and liquid flows have attracted increasing attention of researchers. This is due to the importance of taking into account the inhomogeneities in the impurity concentration when describing the transport of aerosol pollutants in the environment, the mechanisms of droplet growth in rain clouds, scattering of radiation by dispersed inclusions, initiation of detonation in two-phase mixtures, as well as when solving problems of two-phase aerodynamics, interpretation of measurements obtained by LDV or PIV methods, and in many other applications. These problems gave an impetus to a significant increase in the number of publications devoted to the processes of accumulation and clustering of inertial particles in gas and liquid flows. Within the framework of classical two-fluid models and standard Eulerian approaches assuming single-valuedness of continuum parameters of the media, it turns out impossible to describe zones of multi-valued velocity fields and density singularities in flows with crossing particle trajectories. One of the alternatives is the full Lagrangian approach proposed by the author earlier. In recent years, this approach has been further developed in combination with averaged Eulerian and Lagrangian (vortex-blob method) methods for describing the dynamics of the carrier phase. Such combined approaches made it possible to study the structure of local zones of accumulation of inertial particles in vortex, transient, and turbulent flows. This article describes the basic ideas of the full Lagrangian approach, provides examples of the most significant results which illustrate the unique capabilities of the method, and gives an overview of the main directions of further development of the method as applied to transient, vortex, and turbulent flows of “gas-particle” media. Some of the ideas discussed and the results presented below are of a more general interest, since they are also applicable to other models of zero-pressure media.

An Inclusional-Dialogic Approach to Qualitative Inquiry

My research looks into collaborative learning and co-creativity in educational contexts. This paper presents my research trajectory towards inclusional-dialogic perception, discernment, and expression. I understand this phenomenon as thinking from presence: a natural inquiry process that is immersive, dialogic, and inherently embodied; a creative dialogue between self and habitat. I combine Natural Inclusionality and dialogism as my philosophical foundations. Importantly, I extend the notion of thinking from presence to the research inquiry itself, broadening the scope of scientific explorations of experience. Thus, the inquiry becomes a dance in between extraspection (outward perception) and introspection (inward sensing), brought together in an empathic second perspective. The natural inclusional approach entails a move away from the logic and language of definition into the logic and language of flow. This article discusses how fluid logic has shaped my research approach and my writing, with three emergent features. First, the inquiry and its documentation constitute an open-ended and serendipitous dialogue with the phenomena in focus. Second, research analysis and writing moves away from the predominance of the textual, recognizing that the translation of the experience into language is not an unavoidable necessity. It also underlines the significance of the visual and poetic expression of philosophy, methods, and findings, fusing science and art into partnership. Third, the disseminative writing is immersive. It openly brings forth an interplay between subjective and objective. My own lived, personal experience of the researched phenomena is a central layer of experiential meaning making, affording contemplative insight. Centering my research approach around the notion of thinking from presence is not a purely epistemological issue. It speaks to the nature of reality and captures the overarching desire to contribute to a deeper human understanding of the self in the context of its natural neighborhood.

Optimizing microwave heating with slotted metal tubes for cylindrical loads

Cylindrical loads are commonly encountered in microwave heating and often suffer from uneven thermal distribution. Within certain radius and dielectric parameter ranges, cylindrical loads may exhibit central thermal focusing. This paper proposes a novel microwave heating method employing a slotted metal tube (SMT) to encase the cylindrical materials. The SMT alters the electric field distribution and enhances the coupling of microwave energy, thereby improving the heating uniformity and efficiency. We first developed a simulation model for microwave heating, analyzing how permittivity and dimensions affect the thermal focus of cylindrical materials. By optimizing the slot dimensions and positions, we overcome the thermal focusing phenomenon. Then, we conducted microwave heating experiments with mashed potatoes, showing that the use of SMT improved the temperature uniformity by 38 % and increased the microwave energy conversion efficiency by 48 %. Furthermore, we applied SMT to a more challenging scenario, involving the heating of cylindrical canned foods with metal lids, using a dual-source heating setup. The experimental results indicated that SMT remained effective in enhancing heating uniformity and efficiency. This method contributes to the development of microwave energy industrial applications, providing innovative solutions for cylindrical load heating.

Inertial particle focusing in fluid flow through spiral ducts: dynamics, tipping phenomena and particle separation

Small finite-size particles suspended in fluid flow through an enclosed curved duct can focus to points or periodic orbits in the two-dimensional duct cross-section. This particle focusing is due to a balance between inertial lift forces arising from axial flow and drag forces arising from cross-sectional vortices. The inertial particle focusing phenomenon has been exploited in various industrial and medical applications to passively separate particles by size using purely hydrodynamic effects. A fixed size particle in a circular duct with a uniform rectangular cross-section can have a variety of particle attractors, such as stable nodes/spirals or limit cycles, depending on the radius of curvature of the duct. Bifurcations occur at different radii of curvature, such as pitchfork, saddle-node and saddle-node infinite period (SNIPER), which result in variations in the location, number and nature of these particle attractors. By using a quasi-steady approximation, we extend the theoretical model of Harding et al. (J. Fluid Mech., vol. 875, 2019, pp. 1–43) developed for the particle dynamics in circular ducts to spiral duct geometries with slowly varying curvature, and numerically explore the particle dynamics within. Bifurcations of particle attractors with respect to radius of curvature can be traversed within spiral ducts and give rise to a rich nonlinear particle dynamics and various types of tipping phenomena, such as bifurcation-induced tipping (B-tipping), rate-induced tipping (R-tipping) and a combination of both, which we explore in detail. We discuss implications of these unsteady dynamical behaviours for particle separation and propose novel mechanisms to separate particles by size in a non-equilibrium manner.

Optimizing solar powered electrokinetic remediation of chromium contaminated groundwater: One step closer to a sustainable solution

Electrokinetic remediation (EKR) presents a promising solution for addressing soil and groundwater contamination challenges. However, practical viability is hindered by significant energy consumption and related expenses, necessitating a comprehensive sustainability approach beyond solely adopting renewable energy and low-carbon sources. This study aims to merge innovative solar-powered systems with a risk-based evaluation strategy for tackling chromium-contaminated groundwater, providing valuable insights into EKR economically viable and applicable approaches. Through the integration of environmental and electrical engineering expertise, this study introduces the Continuous Solar-powered Electrokinetic Remediation (CSER) system and risk-based energy efficiency (REF) evaluation approach, addressing intermittency issues while optimizing energy generation and minimizing costs. Experimental results demonstrate removal efficiencies ranging from 29.85% to 84.26%, highlighting the impact of intermittent current, voltage boosters, and electrolyte selection on risk reduction and energy consumption. While intermittent current intensifies the focusing phenomenon and reduces contaminant migration, it may offer promising results in specific cases, such as observed in the EK2 experiment. Conversely, the EK3 results reveal that the integration of conventional solar power with a voltage booster may enhance removal rates but often leads to unfavorable outcomes in risk reduction considering related higher energy consumption. However, CSER, with its utilization of constant current, proves more efficient in power generation, risk reduction, and energy usage compared to other systems. Integration of such a system with cost-effective and environmentally friendly chemical agents could significantly increase the REF index while minimizing related costs, thereby shifting EKR remediation techniques towards sustainable solutions for contaminated groundwater worldwide.

Role of Allee and Fear for Controlling Chaos in a Predator–Prey System with Circulation of Disease in Predator

This paper explores a predator–prey system featuring fear and disease within the predator population,utilizing the Rosenzweig–MacArthur model with Holling type-II functional response. The primary focus lies in investigating the impact of a fear factor, wherein the prey’s growth rate is hindered due to predator-induced fear. Additionally, the model accounts for the spread of disease among predators,leading to a division between susceptible and infected predator subpopulations. The inclusion of an Allee effect in the susceptible predator further enriches the model. The study involves a thorough examination, encompassing local and global stability analysis as well as Hopf bifurcation analysis around the interior equilibrium point. Numerical simulations underscore a noteworthy observation: an escalation in interaction force propels the system into chaotic dynamics,marked by stable focus, limit cycles and period-doubling phenomena. A noteworthy finding pertains to the influence of the Allee parameter ([Formula: see text]) on chaotic dynamics. As the Allee parameter values increase, the system tends to stable focus through a sequence of chaotic states, period-doubling and limit cycles. Subsequently, the paper introduces the role of another pivotal parameter, the fear factor, into the chaotic dynamics. Intriguingly, chaos transforms into stable focus through diverse nonlinear phenomena, including period-doubling and limit cycles. This nuanced exploration of parameters sheds light on the intricate dynamics governing the predator–prey system, offering a comprehensive understanding of the interplay between fear, disease and ecological factors. So our observation throughout this paper that how chaos behaves here after one by one injection of our new features: fear factor and Allee parameter?

Floating quantifiers, specificity and focus in Lalo Yi

Lalo Yi presents a distribution of numeral-classifier pairs that appears to be the complete inverse of the norm found in other numeral-classifier languages. With many numerically-quantified, discourse-new referents, Lalo Yi permits only the use of a floated pattern, and it is not possible to combine numerals and classifiers with NPs as in other numeral-classifier languages. This patterning presents a clear challenge to the oft-adopted assumption that floating quantifiers are derived from non-floated forms by applications of movement (stranding), and potentially favors a base-generation/adverbial approach. A broader consideration of Lalo Yi, however, leads to the proposal that the occurrence of the floating pattern results from a combination of two occurrences of movement—DP movement to a low focus position/FocP, followed by NP-raising to a higher case position. Obligatory stranding of the DP remnant containing numeral-classifier pairs is suggested to result from the FocP being a (low) criterial position in the sense of Rizzi (in: Cheng and Corver (eds) Wh-movement: moving on, MIT Press, Cambridge, pp 97–134, 2006), requiring freezing-realization of the DP in SpecFocP but permitting sub-extraction of NP to satisfy case requirements licensed by a higher functional head. Quite generally, it is suggested that the paradigm in Lalo Yi demonstrates the grammaticalization of an optional tendency found elsewhere in numeral-classifier languages to use special forms for the specific and non-specific indefinite interpretations of numerically-quantified nominals. Additionally, the paper contributes to the growing description and typology of low focus phenomena across languages and observations of variation in the ways that focus may be realized in different languages.

Focusing of weakly nonlinear inertial waves by a vertically oscillating annular forcing

We investigate the focusing phenomenon of inertial waves generated by a vertically oscillating slender torus in a uniformly rotating fluid. Building on the previous research on linear aspects of inertial wave focusing by Liu et al. [“Focusing of inertial waves by a vertically annular forcing,” Phys. Fluids 34, 086601 (2022)], we analyze the focusing phenomenon in a fluid with a small Rossby number using the perturbation method. Our analytical solution to the weakly nonlinear problem reveals that, in addition to the primary inertial waves predicted by the linear theory, secondary inertial waves (SIW) are excited due to wave interaction if the forcing frequency is lower than the fluid rotation rate. Particularly, in our case, the SIWs induced directly by the oscillating torus form a relatively weak secondary focal area on the rotation axis below the primary focal point. The rays of the SIWs form a new double cone with a different angle than the primary cone. In addition, the SIWs are also excited at the primary focal point with a much stronger effect than that generated by the oscillating torus in an inviscid limit, but significantly suppressed even in low-viscosity fluids. A fully nonlinear analysis, especially in the primary focal zone, is necessary for further study.

The meaning and feeling of the time and space between psychotherapy sessions and everyday life: Client experiences of transitions

Objective To explore how clients in psychodynamic or psychoanalytic psychotherapy, conducted in the traditional in-person setting, experience the transitions in time and space between psychotherapy sessions and everyday life. Method Twelve semi-structured interviews were analyzed with inductive experiential thematic analysis, focusing on how the participants experience and make sense of the phenomenon in focus. Results The participants described therapy as a sheltered space where they could be open, vulnerable, receptive, and present. Approaching and leaving psychotherapy sessions, the participants established different behavioral patterns and routines dealing with their anxieties and resistances. In this in-between area, the participants could handle interconnections and differences between therapy and everyday life. Participants stressed the clinical impact of transitions: transitions affect both therapy and everyday life; disturbed transitions have an adverse impact; transitions are insufficiently addressed in therapy. Conclusion Transitions between therapy and life appear to be an essential but seldom recognized part of the therapy process beyond the borders of therapy sessions. Implications of these findings for psychotherapy training and practice are discussed, and a tentative transtheoretical framework for further research is proposed.

Study on Cu- and Pb-contaminated loess remediation using electrokinetic technology coupled with biological permeable reactive barrier

Although the electrokinetic (EK) remediation has drawn great attention because of its good maneuverability, the focusing phenomenon near the cathode and low removal efficiency remain to be addressed. In this study, a novel EK reactor was proposed to remediate Cu and Pb contaminated loess where a biological permeable reactive barrier (bio-PRB) was deployed to the middle of the EK reactor. For comparison, three test configurations, namely, CG, TG-1, and TG-2, were available. CG considered the multiple enzyme-induced carbonate precipitation (EICP) treatments, while TG-1 considered both the multiple EICP treatments and pH regulation. TG-2 further considered NH4+ recovery based on TG-1. CG not only improved Cu and Pb removals by the bio-PRB but also depressed the focusing phenomenon. TG-1 causes more Cu2+ and Pb2+ to migrate toward the bio-PRB and aggravates Cu and Pb removals by the bio-PRB, depressing the focusing phenomenon. TG-2 depressed the focusing phenomenon the most because Cu2+ and Pb2+ can combine with not only CO32− but PO43−. The removal efficiency of Cu and Pb is 34% and 36%, respectively. A NH4+ recovery of about 100% is attained.

Dual-wavelength dielectric metasurface for full-space light manipulations

Dielectric metasurfaces have been credited for their salient capability in manipulating visible light with high efficiency, yet their operations are usually specified to the transmission space with limited functionality at a specified single wavelength. In this work, we show that dielectric metasurface can also be considered as an effective platform to independently control transmitted and reflected light wavefronts with high efficiency at two distinct wavelengths. In specific, silicon meta-atoms allowing high transmission and reflection of orthogonally linear-polarized light at wavelengths of 690 nm and 750 nm along with independent 2π phase modulations are successfully established. The first demonstrated dual-functional metasurface can transform incident plane wave into focused point beam spot and focused vortex beam in transmission and reflection spaces, respectively. The spatial multiplexing strategy is further considered to enrich the functionality diversity of a single meta-device, on which two off-axis light focusing phenomena and focused vortex beams carrying opposite topological charges in either transmission or reflection spaces with reduced crosstalk are successfully witnessed. Lastly, the metasurface enabling broadband anomalous deflection further demonstrates that the device’s efficiency can be further improved with densely packed meta-atoms. Our study provides a new thought in light control, which can be further considered in the development of multi-wavelength and full-space meta-devices.

On‐Demand Subwavelength‐Scale Light Sculpting Using Nanometric Holograms

AbstractSpatially or temporally structured light has attracted considerable attention for its intriguing beam characteristics, which have found extensive applications in classical and quantum optics. Extending structured light from macroscale and microscale to nanometricscale brings more prospects both for fundamental and applied science. However, sculpting light at the subwavelength scale remains a challenge since its transverse structure is fragile in the nanometric scale. Here a novelholography for arbitrary light sculpting at the subwavelength scale is demonstrated. A wave phenomenon of diffractive focusing from an amplitude‐only nanometric (50‐nm‐thick) film is introduced, and use of the induced high‐spatial‐frequency waves as carriers to encode information of an object is considered. Using this technique, nanometric holograms are designed and fabricated for generating the well‐defined eigen modes including the zero‐order Bessel beam, vortex beam, vector beam, Airy beam, as well as an arbitrary light pattern, with feature sizes on the deep‐subwavelength scale. The broadband performance of the hologram is examined, and a white‐light nondiffracting beam at the deep‐subwavelength scale is realized. This demonstration paves a way toward on‐demand light sculpting at the nanometric scale, which may find applications such as optical super‐resolution imaging, nanoparticle manipulation, and precise measurements.

Generation of periodic evolution patterns by the interaction of pearcey-gaussian beams carrying sidelobe in parabolic potential

Based on the fractional Schrödinger equation, the propagation properties of the Pearcey-Gaussian beam with the sidelobe in the parabolic potential are studied by using the split-step Fourier numerical simulation method. The focusing phenomenon appears without the parabolic potential when Pearcey-Gaussian beam carries the sidelobe. In the case of the parabolic potential, the beam forms the bound state in the propagation process. The period of the bound state decreases as the parabolic potential coefficient increases. In addition, the interaction of two Pearcey-Gaussian beams with the sidelobe in the potential is investigated. The effect of Lévy index, interval parameter, initial phase factor and parabolic potential coefficient on the interaction of two Pearcey-Gaussian beams with sidelobe is considered.

Strategies For Safety: A Mixed Method Study of Communication, Teamwork and Health Professional Attitudes When Implementing Multidisciplinary Simulation in The Emergency Department

The Emergency Department (ED) team delivers care to critically unwell patients. Within this, there are a range of complexities and responsibilities identified. Technical skills can be taught in lectures and books; however, the newly evolving phenomenon of focusing on non-technical medical skills has advanced over time. Using non-technical skills, such as communication and human factors, can influence the team's functioning, which could potentially influence a positive outcome of a critical care event. This study explores whether multidisciplinary simulation training, focusing on non-technical skills, can improve participants’ communication and teamwork and if regular simulation practice can influence healthcare staff attitudes towards embedding a regular simulation program at a local site. A convergent mixed method approach was used to determine staff attitude towards a newly implemented simulation programin the hospital ED. Data was collected over six weeks. The quantitative component measured teamwork and communication with Guise’s validated and reliable tool, the Clinical Teamwork Scale (CTS). Further data using a developed evaluation survey provided participant feedback pre and post-simulation. Thirty-two participants, sixteen nurses and sixteen doctors, were surveyed. The results could suggest a trend of a positive outlook towards implementing a regular simulation practice. However, further analysis would be required. A common theme was participant confidence post-simulation practice and willingness to participate in future simulations. Baseline opinions from all participants were positive. The study has generated valuable insight towards staff attitudes toward MDT simulation in the ED setting. The evidence can further support the implementation of a regular simulation program.

A new approach to Negative Concord: Catalan as a case in point

In this paper, we revisit the phenomenon of Negative Concord focusing on the Strict vs. Non-Strict divide. With Catalan as a case in point, we show that Negative Concord Items (NCIs) are not negative quantifiers (NQs) or polarity items (PIs) but inherently negative indefinites by virtue of carrying a negative feature [neg] that contributes a negative semantics to the proposition and is subject to a syntax–phonology constraint that forces it to overtly c-command Tense in compliance with Jespersen’s NegFirst principle. We argue that to satisfy such constraint, [neg] can disembody from the NCI via overt Move F(eature) to adjoin at a pre-Infl(ection) position and be Spelled-Out homophonous to the negative marker. The Strict vs. Non-Strict contrast follows from whether [neg] always moves independently from the rest of the NCI via Move F (Strict Negative Concord) or predates, whenever possible, on another movement of the NCI that places [neg] in the required pre-Infl position (Non-Strict Negative Concord) thus not having to disembody.

No concept is an island: conceptualising (in) the industrial network approach

PurposeThe purpose of this paper is to inquire into how conceptualising is done in the industrial network approach (INA).Design/methodology/approachThe description and analysis of conceptualising is based on key INA references and an example illustrating the characteristics of conceptualising in individual studies.FindingsThe paper concludes that there is an open and interactive way of conceptualising in the INA. The empirical and theoretical grounding achieved through combining concepts in individual empirical studies interplays with conceptual development in the research community over time.Research limitations/implicationsThree paradoxes are suggested for further discussion of conceptualising as a key element in theorising in the INA community.Originality/valueBy explicating how INA researchers engage in conceptualising both in individual empirical studies and as a community, the authors identify characteristics similar to the empirical phenomena in focus of the research: interaction, combining and heterogeneity of concepts.

Dynamics of Hydrogen Bond Breaking Induced by Outer-Valence Intermolecular Coulombic Decay

The photoexcitation of weakly bound complexes can lead to several decay pathways, depending on the nature of the potential energy surfaces. Upon excitation of a chromophore in a weakly bound complex, ionization of its neighbor upon energy transfer can occur due to a unique relaxation process known as intermolecular Coulombic decay (ICD), a phenomenon of renewed focus owing to its relevance in biological systems. Herein, we report the evidence for outer-valence ICD induced by multiphoton excitation by near-ultraviolet radiation of 4.4 eV photons, hitherto unknown in molecular systems. In the binary complexes of 2,6-difluorophenylacetylene with aliphatic amines, a resonant two-photon excitation localized on the 2,6-difluorophenylacetylene chromophore results in the formation of an amine cation following an outer-valence ICD process. The unique trends in experimentally observed translational energy distribution profiles of the amine cations following hydrogen bond dissociation, analyzed with the help of electronic structure and ab initio molecular dynamics calculations, revealed the presence of a delicate interplay of roaming dynamics, methyl-rotor dynamics, and binding energy.

Ground penetrating radar and magnetic gradient distribution approach for subsurface investigation of solution pipes in post-glacial settings

Abstract Solution pipes are an important geomorphological feature in carbonate rocks formed by the host rock’s dissolution due to water’s focused flow, indicating the phenomena of water focusing in particular areas. However, their visual exposures are often limited by sediment and vegetation cover, making it challenging to understand their spatial distribution and morphology. In this study, we used geophysical methods such as ground penetrating radar (GPR) and magnetic gradiometer to detect and estimate the spatial distribution of solution pipes in a freshly exposed quarry site in Smerdyna, Poland. Our results indicate that both GPR and magnetometric measurements effectively detect most of the solution pipes, particularly those filled with large amounts of clay and silt particles. The GPR method, in particular, proved to be convenient due to the high contrast of the dielectric constant. The information on the positions and shapes of the pipes obtained based on these methods is crucial in understanding the link between pipe morphology and the physical conditions at the time of their formation. Furthermore, our measurements provided quasi-spatial correlations between pipe positions, the distribution of inter-pipe distances, and the potential relationship between alignments of rock joints and pipe locations. Our study demonstrates the potential of geophysical methods in detecting and understanding solution pipes, which are essential from environmental and climatic perspectives. This information can be used for future studies on pipe formation and environmental impact.

Distinct separation of multiple CTCs using inertial focusing phenomena utilizing single-looped spiral microfluidic lab-on-chip

Looking towards the point-of-care diagnosis purposes, nowadays the most emerging method for separation of Circulating Tumor Cells (CTCs) from normal blood-cells is the inertial focusing phenomena utilizing microfluidic lab-on-chips. Keeping eye on the distinctly separating multiple CTCs from normal blood-cells, here we designed a single-looped spiral microfluidic lab-on-chip based on inertial focusing phenomena, which has been more efficient than double-looped and three-looped spirals. The performance of the device has been investigated using large MCF-7 (breast-cancer CTCs), PC3-9 (prostate-cancer CTCs) and normal blood-cells (white blood-cell, red blood-cell) and also larger multiple CTCs like largest MCF-7, PC3-9, A549 (lung-cancer CTCs) cells and normal blood-cells in three-dimensional numerical simulation utilizing COMSOL Multiphysics 5.4 software. In both cases the chip has accomplished efficient separation performance of nearly 100 % at the Reynolds number ranges from 55.9 - 65 (throughput 70 - 82 ml/h) and 114.74 (throughput of 147 ml/h) respectively in terms of cell separation purity and recovery.

Guided wave propagation and skew effects in anisotropic carbon fiber reinforced laminates

Guided ultrasonic waves provide a promising structural health monitoring (SHM) solution for composite structures as they are able to propagate relatively long distances with low attenuation. However, the material anisotropy results in directionally dependent phase and group velocities, in addition to energy focusing, wave skewing, and beam spreading phenomena. These effects could lead to inaccurate damage localization if not accounted for. In this contribution, the guided wave propagation behavior (A0 mode) for a highly anisotropic, unidirectional carbon fiber reinforced polymer laminate is systematically investigated through both finite element analysis and non-contact laser measurements and compared to theoretical predictions. The directional dependency of phase and group velocity measured for a point and line source shows good agreement with theoretical predictions, once a correction for wave skew effects is applied. Wave skew angles were evaluated from the experimental and numerical wave propagation in multiple directions and matched theoretical predictions based on the phase slowness curve. Significant guided wave beam spreading from a line source was observed and quantified from both experiments and simulations and compared with theoretical predictions using the anisotropy factor. The impact of anisotropic guided wave propagation behavior on SHM is discussed.