Simple Description Research Articles

On Solutions of Some Functional Equations of Radical Type

Many authors have studied various functional equations of forms patterned on the equation expressed as ga2+b2=g(a)+g(b), which can be considered, e.g., for real functions. Such equations are usually referred to as radical functional equations or of the radical type. Authors mainly study the so-called Ulam stability of such equations, i.e., they investigate how much the mappings satisfying the equations approximately (in a sense) differ from the exact solutions of these equations. Quite often, information about the solutions of these equations is also provided, but unfortunately, sometimes, such information is given in a misleading or incomplete way. It seems, therefore, that there is a need for a publication containing simple descriptions of such solutions (with appropriate examples), which would help in easy correction of such information and avoidance of similar problems for future authors. This is the main motivation for this expository paper. We present a general approach to the topic and consider two general forms of such equations. Moreover, the results presented in this paper show significant symmetry between the solutions of numerous functional equations and the solutions of equations of the radical type that correspond to them. To make this publication accessible to a wider audience, we omit various related information, avoid advanced generalizations, and present several simple examples.

Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission

We consider the motion of a circularly moving perturber in a self-gravitating, collisional system with a spherically symmetric density profile. We concentrate on the singular isothermal sphere, which, despite its pathological features, admits a simple polarization function in linear response theory. This allows us to solve for the acoustic wake trailing the perturber and the resulting dynamical friction, in the limit where the self-gravity of the response can be ignored. In a steady state and for subsonic velocities v p < c s , the dynamical friction torque Fφ∝vp3 is suppressed for perturbers orbiting in an isothermal sphere relative to the infinite, homogeneous medium expectation F φ ∝ v p . For highly supersonic motions, both expectations agree and are consistent with a local approximation to the gravitational torque. At fixed resolution (a given Coulomb logarithm), the response of the system is maximal for Mach numbers near the constant circular velocity of the singular isothermal profile. This resonance maximizes the gravitational-wave (GW) emission produced by the trailing acoustic wake. For an inspiral around a massive black hole of mass 106 M ⊙ located at the center of a (truncated) isothermal sphere, this GW signal could be comparable to the vacuum GW emission of a black hole binary at subnanohertz frequencies when the small black hole enters the Bondi sphere of the massive one. The exact magnitude of this effect depends on departures from hydrostatic equilibrium and on the viscosity present in any realistic astrophysical fluid, which are not included in our simplified description.

Physical Models for the Astrophysical Population of Black Holes: Application to the Bump in the Mass Distribution of Gravitational-wave Sources

Abstract Gravitational-wave observations of binary black holes have revealed unexpected structure in the black hole mass distribution. Previous studies employ physically motivated phenomenological models and infer the parameters that control the features of the mass distribution that are allowed in their model, associating the constraints on those parameters with their physical motivations a posteriori. In this work, we take an alternative approach in which we introduce a model parameterizing the underlying stellar and core-collapse physics and obtaining the remnant black hole distribution as a derived by-product. In doing so, we constrain the stellar physics necessary to explain the astrophysical distribution of black hole properties under a given model. We apply this to the mapping between initial mass and remnant black hole mass, accounting for mass-dependent mass loss using a simple parameterized description. Allowing the parameters of the initial mass–remnant mass relationship to evolve with redshift permits correlated and physically reasonable changes to features in the mass function. We find that the current data are consistent with no redshift evolution in the core–remnant mass relationship, but place only weak constraints on the change of these parameters. This procedure can be applied to modeling any physical process underlying the astrophysical distribution. We illustrate this by applying our model to the pulsational pair instability supernova (PPISN) process, previously proposed as an explanation for the observed excess of black holes at ∼35 M ⊙. Placing constraints on the reaction rates necessary to explain the PPISN parameters, we concur with previous results in the literature that the peak observed at ∼35 M ⊙ is unlikely to be a signature from the PPISN process as presently understood.

Mетод визначення зміни просторового положення об'єкта орбітального сервісу з невідомою формою

This paper presents a method for determining the pose of an on-orbit service object (target) with an unknown surface shape based on processing target surface point clouds. It is assumed that a point cloud is obtained using a sensor in the form of a lidar-based system onboard the service spacecraft. The algorithm of the method operates with a simplified description of the cloud; it uses only the coordinates of the cloud points without identifying any surface features. The idea of the method is as follows. From all cloud points obtained at a certain time instant, select points that are close to a certain degree to a given set of planes arranged in space in a certain way. From the point cloud corresponding to the next time instant, select points that are close to the same set of planes, but moved in space in a known way. By convention, let the arrangement of the projections of the selected cloud points onto the given planes be called a pattern of the intersection of the point clouds with the planes. By varying the displacement of the set of planes, maximize the coincidence of the intersection patterns of the first and second clouds of points. The degree of coincidence of the intersection patterns is characterized by a specified objective function whose arguments are target pose parameters. The target displacement parameters are found as the arguments of the objective function that maximize it. A variant of the objective function is proposed. A test example of the application of the proposed method is considered. A global optimization method known as the direct search method was used to find the arguments of the objective function. Test calculations were performed, and they confirmed the workability of the algorithm and determined its scope of applicability. The computational burden was not considered: the goal was to verify the workability of the method in principle. The advantage of the proposed method is its ability to determine a change in the pose of an object with an unknown surface shape. The proposed method may be considered as a source of observation data for a filtering procedure when estimating the parameters of the relative motion of a target with an unknown surface shape.

Egg-shaped sections of fluid structures around black holes

Astrophysical fluids subjected to the strong gravity of black holes can form rotating toroidal-like structures known as thick accretion discs. In order to facilitate the study of such structures, we introduce approximate empirical formulae for a relatively simple analytical description of their poloidal cross-sections that are usually described only numerically. Our comparisons of the approximate and exact descriptions of the cross-sections of the structures rotating around Schwarzschild and Kerr central black holes, together with the determination of the associated total masses of these structure, indicate a high degree of accuracy for these introduced formulae.

Realizing multiband states with ultracold dipolar quantum simulators

The manipulation of dipolar interactions within ultracold molecular ensembles represents a pivotal advancement in experimental physics, aiming at the emulation of quantum phenomena unattainable through mere contact interactions. Our study uncovers regimes of multiband occupation which allow to probe more realistic, complex long-range interacting lattice models with ultracold dipolar simulators. By mapping out experimentally relevant ranges of potential depths, interaction strengths, particle fillings, and geometric configurations, we calculate the agreement between the state prepared in the quantum simulator and a target lattice state. We do so by separately calculating numerically exact many-body wave functions in the continuous space and single- or multiband lattice representations, and building their many-body state overlaps. Our findings reveal that for shallow lattices and stronger interactions above half filling, multiband population increases, resulting in fundamentally different ground states than the ones observed in simple lowest-band descriptions, e.g., striped vs checkerboard states. A wide range of probed parameter regimes in its turn provides a systematic and quantitative blueprint for realizing multiband states with two-dimensional quantum simulators employing ultracold dipolar molecules. Published by the American Physical Society 2024

A global–land snow scheme (GLASS) v1.0 for the GFDL Earth System Model: formulation and evaluation at instrumented sites

Abstract. Snowpacks modulate water storage over extended land regions and at the same time play a central role in the surface albedo feedback, impacting the climate system energy balance. Despite the complexity of snow processes and their importance for both land hydrology and global climate, several state-of-the-art land surface models and Earth System Models still employ relatively simple descriptions of the snowpack dynamics. In this study we present a newly-developed snow scheme tailored to the Geophysical Fluid Dynamics Laboratory (GFDL) land model version 4.1. This new snowpack model, named GLASS (Global LAnd–Snow Scheme), includes a refined and dynamical vertical-layering snow structure that allows us to track the temporal evolution of snow grain properties in each snow layer, while at the same time limiting the model computational expense, as is necessary for a model suited to global-scale climate simulations. In GLASS, the evolution of snow grain size and shape is explicitly resolved, with implications for predicted bulk snow properties, as they directly impact snow depth, snow thermal conductivity, and optical properties. Here we describe the physical processes in GLASS and their implementation, as well as the interactions with other surface processes and the land–atmosphere coupling in the GFDL Earth System Model. The performance of GLASS is tested over 10 experimental sites, where in situ observations allow for a comprehensive model evaluation. We find that when compared to the current GFDL snow model, GLASS improves predictions of seasonal snow water equivalent, primarily as a consequence of improved snow albedo. The simulated soil temperature under the snowpack also improves by about 1.5 K on average across the sites, while a negative bias of about 1 K in snow surface temperature is observed.

Crack patterns in masonry structures using phase field method

This work aims to study the crack pattern in masonry-like structures by a simplified description of the mediumusing a variational damage model. In literature, when modeling fractures in masonry structures, capturingboth fracture types, cracks in units, and cracks at the interface simultaneously, usually requires a complicated scheme. The phase-field method has been widely used recently because of its robustness in capturing variousfracture types. In this work, we consider the mortar and the interface (between the mortar and units) as a thickinterface layer with pseudo-material properties. We conduct numerical tests on a bending beam and a tensilewall using strategies of material properties with a phase field model. As it is not distinguished the crack in themortar and the brick-mortar interface, it is shown in this work that both types of fracture, in the thick interfacelayer and the unit, can be captured just using the phase field method and the simplified micro model.

Two‐phase flows simulations in a space‐time framework for injection molding applications: Comparison with experimental results

AbstractHigh‐resolution numerical simulations of the injection molding process are crucial for precise process and part behavior prediction and tool fabrication. However, the complex flow behavior with high shear rates, rapid cooling as well as the nonlinear material properties post many challenges, and efficient high‐resolution numerical analysis is still subject to research. This study presents a simplified numerical description of the polymer flow and cooling during the injection phase, aiming for efficient and yet accurate simulations of the process. The in‐house finite‐element solver XNS is used to simulate the polymer and air flows, as a two‐phase flow, using the level‐set method. The injected polymer is characterized as a shear‐thinning flow using the non‐Newtonian Cross‐Williams‐Landel‐Ferry rheology model. To reduce the computational time, other polymer model effects such as a precise crystallization kinetics model during the injection phase have been neglected as a result of the findings of a previous study. Heading towards more efficient computations, we use a space‐time discretization, which has a higher convergence rate than commonly used time discretizations and can allow future mesh refinement in time, particularly convenient for our application. The results of the simulation are compared to the propagation of the flow front in an injection molding process of a plate part. The flow front is traced in‐situ by three aligned infrared sensors that detect the temperature increase from the mold wall. The time of flow front propagation between two sensors is in good agreement with experimental results. The peak temperature is calculated lower as compared to the experiment; however the temperature gradients are in good agreement validating the numerical model presented here.

An integrated framework for the study of exercise across the postdiagnosis cancer continuum.

Exercise plays many important roles across the entire cancer continuum that have been described in previous frameworks. These frameworks, however, have generally provided a simplified description of the roles of exercise postdiagnosis. The modern cancer treatment landscape has become complex and often consists of multiple lines of multimodal treatments combined concurrently and/or sequentially and delivered over many months or years. This complexity requires a more multifaceted and targeted approach to the study of exercise after a cancer diagnosis. Here, we propose a new integrated framework-Exercise Across the Postdiagnosis Cancer Continuum (EPiCC)-that highlights the distinct roles of exercise for disease treatment and supportive care from diagnosis until death. We also propose new terminology to clarify the distinct roles of exercise that emerge in the context of the modern cancer treatment landscape. The EPiCC Framework is structured around multiple sequential cancer treatments that highlight six distinct cancer treatment-related time periods for exercise-before treatments, during treatments, between treatments, immediately after successful treatments, during longer term survivorship after successful treatments, and during end of life after unsuccessful treatments. The EPiCC Framework proposes that the specific roles of exercise as a disease treatment and supportive care intervention will vary depending on its positioning within different cancer treatment combinations. As a cancer treatment, exercise may serve as a "priming therapy", primary therapy, neoadjuvant therapy, induction therapy, "bridging therapy", adjuvant therapy, consolidation therapy, maintenance therapy, and/or salvage therapy. As a supportive care intervention, exercise may serve as prehabilitation, intrahabilitation, interhabilitation, rehabilitation, "perihabilitation", health promotion/disease prevention, and/or palliation. To date, exercise has been studied during all of the cancer treatment-related time periods but only in relation to some cancer treatments and combinations. Moreover, fewer studies have examined exercise across multiple cancer treatment-related time periods within any cancer treatment combination. Future research is needed to study exercise as a disease treatment and supportive care intervention within and across the distinct cancer treatment-related time periods contained within different cancer treatment combinations. The aim of the EPiCC Framework is to stimulate a more targeted, integrated, and clinically-informed approach to the study of exercise after a cancer diagnosis.

FICE: Text-conditioned fashion-image editing with guided GAN inversion

Fashion-image editing is a challenging computer-vision task where the goal is to incorporate selected apparel into a given input image. Most existing techniques, known as Virtual Try-On methods, deal with this task by first selecting an example image of the desired apparel and then transferring the clothing onto the target person. Conversely, in this paper, we consider editing fashion images with text descriptions. Such an approach has several advantages over example-based virtual try-on techniques: (i) it does not require an image of the target fashion item, and (ii) it allows the expression of a wide variety of visual concepts through the use of natural language. Existing image-editing methods that work with language inputs are heavily constrained by their requirement for training sets with rich attribute annotations or they are only able to handle simple text descriptions. We address these constraints by proposing a novel text-conditioned editing model called FICE (Fashion Image CLIP Editing) that is capable of handling a wide variety of diverse text descriptions to guide the editing procedure. Specifically, with FICE, we extend the common GAN-inversion process by including semantic, pose-related, and image-level constraints when generating images. We leverage the capabilities of the CLIP model to enforce the text-provided semantics, due to its impressive image–text association capabilities. We furthermore propose a latent-code regularization technique that provides the means to better control the fidelity of the synthesized images. We validate the FICE through rigorous experiments on a combination of VITON images and Fashion-Gen text descriptions and in comparison with several state-of-the-art, text-conditioned, image-editing approaches. Experimental results demonstrate that the FICE generates very realistic fashion images and leads to better editing than existing, competing approaches. The source code is publicly available from: https://github.com/MartinPernus/FICE.

Analysis of Glucose Responsive Glucagon Therapeutics using Computational Models of the Glucoregulatory System.

Glucose-responsive glucagon (GRG) therapeutics are a promising technology for reducing the risk of severe hypoglycemia as a complication of diabetes mellitus. Herein, the performance of candidate GRGs in the literature by modeling the kinetics of activation and connecting them as input into physiological glucoregulatory models is evaluated and projected the two distinct GRG designs, experimental results reported in Wu etal. (GRG-I) and Webber etal. (GRG-II) is considered. Both are evaluated using a multi-compartmental glucoregulatory model (IMPACT) and used to compare in-vivo experimental data of therapeutic performance in rats and mice. For GRG-I and GRG-II, the total integrated glucose material balances are overestimated by 41.5% ± 14% and underestimated by 24.8% ± 16% compared to in-vivo time-course data, respectively. These large differences to the relatively simple computational descriptions of glucagon dynamics in the model, which underscores the urgent need for improved glucagon models is attributed. Additionally, therapeutic insulin and glucagon infusion pumps are modeled for type 1 diabetes mellitus (T1DM) human subjects to extend the results to additional datasets. These observations suggest that both the representative physiological and non-physiological models considered in this work require additional refinement to successfully describe clinical data that involve simultaneous, coupled insulin, glucose, and glucagon dynamics.

Addressing type Ia supernova color variability with a linear spectral template

Type Ia Supernovae (SNeIa) provided the first evidence of an accelerated expansion of the universe and remain a valuable probe to cosmology. They are deemed standardizable candles due to the observed correlations between their luminosity and photometric quantities. This characteristic can be exploited to estimate cosmological distances after accounting for the observed variations. There is however a remaining dispersion unaccounted for in the current state-of-the-art standardization methods. In an attempt to explore this issue, we propose a simple linear 3-component rest-frame flux description for a light-curve fitter. Since SNIa intrinsic color index variations are expected to be time-dependent, our description builds upon the mathematical expression of the well-known Spectral Adaptive Light Curve Template 2 (SALT2) for rest-frame flux, whilst we drop the exponential factor and add an extra model component with time and wavelength dependencies. The model components are obtained by performing either Principal Component Analysis (PCA) or Factor Analysis (FA) onto a representative training set. The constraining power of the model dubbed Pure Expansion Template for Supernovae (PETS) is evaluated and we found compatible results with SALT2 for Ωm0 and ΩΛ0 within 68% uncertainty between the two models, with PETS’ fit parameters exhibiting non-negligible linear correlations with SALT2’ parameters. For both PCA and FA model versions we verified that the first component mainly describes color index variations, proving it is a dominant effect on SNIa spectra. The model nuisance parameter which multiplies the color index variation-like fit parameter shows evolution with redshift in an initial binned cosmology analysis. This behavior can be due to selection effects and should be further investigated with higher redshift SNeIa samples. Overall, our model shows promise, as there are still a few aspects to be refined; however, it still falls short in reducing the unaccounted dispersion.

Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity

Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells. Starting from a bar and hinge model for the elastic energy of a generic four parallelogram panel origami pattern, we derive a complete set of geometric compatibility conditions identifying the pattern’s soft modes in this limit. The compatibility equations form a system of partial differential equations constraining the actuation of the origami’s creases (a scalar angle field) and the relative rotations of its unit cells (a pair of skew tensor fields). We show that every solution of the compatibility equations is the limit of a sequence of soft modes — origami deformations with finite bending energy and negligible stretching. Using these sequences, we derive a plate-like theory for parallelogram origami patterns with an explicit coarse-grained quadratic energy depending on the gradient of the crease-actuation and the relative rotations of the cells. Finally, we illustrate our theory in the context of two well-known origami designs: the Miura and Eggbox patterns. Though these patterns are distinguished in their anticlastic and synclastic bending responses, they show a universal twisting response. General soft modes captured by our theory involve a rich nonlinear interplay between actuation, bending and twisting, determined by the underlying crease geometry.

Empirical approaches for non-linear site response: results for the ESG6-blind test

As a contribution to step 3 of the ESG6 blind prediction exercise, we present an application of two different, purely empirical approaches to estimate the strong ground motion at a soft site ("KUMA") from the observed ground motion at a reference rock site ("SEVO") for the two largest shocks of the Kumamoto 2016 sequence. The two methods estimate the non-linear transfer function between a reference rock and a sedimentary site by modifying the linear transfer function derived from weak motion recordings. The modification is based either on a machine learning tool based on a wide collection of Japanese weak and strong motion recordings and the associated site metadata (method 1), or on an estimate of a site-specific parameter related to an average non-linear site response (method 2). The acceleration time series are then derived at the sedimentary site of interest using an estimation of the time delay between wave arrivals at the rock and site stations, and a minimum phase assumption for the site transfer function. These predictions were made blindly, but after the ESG6 conference they could be compared both with the actual ground motion recorded at KUMA during the two shocks, and the average and range of all other predictions preformed for this benchmark. Both of these purely empirical methods provide an honorable prediction of usual engineering ground motion parameters of the two target events. The performance of these two purely empirical approaches is at least comparable to those of the numerical simulation methods for the foreshock—if not better—and slightly worse for the (largest) mainshock. As the methods required only recordings of weak motions at the target and a referent sites and very simple description of the soil profile. The use of moderate motions to constrain the frequency shift prediction for the second method and the consideration of an alternative phase modification are possible ways to improvement.Graphical

Dual digraphs of finite meet-distributive and modular lattices

We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and Haviar (2015). These digraphs, known as TiRS digraphs, have their origins in the dual representations of lattices by Urquhart (1978) and Ploščica (1995). We describe two properties of finite lattices which are weakenings of (upper) semimodularity and lower semimodularity respectively, and then show how these properties have a simple description in the dual digraphs. Combined with previous work in this journal on dual digraphs of semidistributive lattices (2022), it leads to a dual representation of finite meet-distributive lattices. This provides a natural link to finite convex geometries. In addition, we present two sufficient conditions on a finite TiRS digraph for its dual lattice to be modular. We close by posing three open problems.

Somewhere between the Nahḍa and the Nadal: toward a rhizomatic cartography of Hispanophone Moroccan literature

The great variety of Hispanophone Moroccan literature evades facile categorization and breaks down identity qualifiers. It exists, yet it refuses to be easily categorized: is it a Moroccan literature that just happens to be expressed in Spanish? Or is it a peripheral Spanish literature that has grown out of the historical proximity and connections between the Iberian Peninsula and the Maghreb? This long, shared history complicates a simple description of these works as “postcolonial literature,” and suggests what Deleuze and Guattari call a rhizomatic literary cartography. This project seeks to engage with these questions of literary identity in Hispanophone Moroccan literature in order to consider the competing factors contributing to this unique literary phenomenon. My thesis is that Hispanophone Moroccan literature must be understood as a rhizomatic cartography. If it is considered as a peripheral Spanish or postcolonial literature, we risk overlooking many of its valuable contributions to the Hispanophone literary canon.

Passive and active field theories for disease spreading

The worldwide COVID-19 pandemic has led to a significant growth of interest in the development of mathematical models that allow to describe effects such as social distancing measures, the development of vaccines, and mutations. Several of these models are based on concepts from soft matter theory. Considerably less well investigated is the reverse direction, i.e. how results from epidemiological research can be of interest for the physics of colloids and polymers. In this work, we consider the susceptible-infected-recovered (SIR)-dynamical density functional theory (DDFT) model, a combination of the SIR model from epidemiology with DDFT from nonequilibrium soft matter physics, which allows for an explicit modeling of social distancing. We extend the SIR-DDFT model both from an epidemiological perspective by incorporating vaccines, asymptomaticity, reinfections, and mutations, and from a soft matter perspective by incorporating noise and self-propulsion and by deriving a phase field crystal (PFC) model that allows for a simplified description. On this basis, we investigate via computer simulations how epidemiological models are affected by the presence of non-reciprocal interactions. This is done in a numerical study of a zombie outbreak.

Zero liquid discharge management: optimizing sustainable reverse osmosis desalination practices

This study introduces a Zero Liquid Discharge (ZLD) scheme for Reverse Osmosis (RO) desalination, integrating ultra-filtration pretreatment and Electrodialysis (ED) for brine concentration. The scheme divides brine reject into fractions, directing them to an electrolyser and evaporator powered by renewable energy sources. Notable findings include the treatment plant's capability to produce 792 cubic meters of fresh water daily, while decreasing salt concentration from 4,660 ppm to 30 ppm, showcasing efficient desalination. Additionally, recycling fractions of RO unit waste to various components enhances resource efficiency. The study highlights the daily production of 2,269.27 kg of hydrogen, coupled with minimal electricity consumption of 74,885.91 kWh, thereby improving overall energy efficiency. Furthermore, the utilization of solar energy significantly reduces reliance on fossil fuels, thereby promoting sustainability and mitigating the environmental impacts associated with traditional energy sources. Solar energy is a clean, renewable resource that helps decrease greenhouse gas emissions and other pollutants, contributing to cleaner air and a healthier planet. This shift towards renewable energy is crucial in addressing climate change and ensuring a sustainable future for generations to come. In the context of desalination, emphasizing environmental preservation and water security is paramount. Desalination processes, while providing essential fresh water in arid regions, often produce brine as a byproduct. The brine, with a high salt concentration of 13,648 ppm, poses a disposal challenge that can negatively impact marine ecosystems if not managed properly. This is where Zero Liquid Discharge (ZLD) systems come into play. With a ZLD index of 2.7%, these systems ensure that all wastewater is treated and reused, leaving no liquid waste behind. ZLD technology captures and recycles every drop of water, converting waste into reusable resources, thus minimizing environmental harm. The model showcased a significant decrease in brackish water extraction from 1,200 cubic meters per day to 871.52 cubic meters per day, marking a notable 27% reduction. These results highlight the promising effectiveness of the proposed ZLD scheme in enhancing the efficiency of brackish water treatment, demonstrating its potential to significantly reduce the demand for fresh water resources while achieving sustainable desalination practices. This article will present a detailed yet a simple description of reverse osmosis and ZLD, how do they correlate and how these two technologies represent the future of water treatment.

Auditory localization: a comprehensive practical review.

Auditory localization is a fundamental ability that allows to perceive the spatial location of a sound source in the environment. The present work aims to provide a comprehensive overview of the mechanisms and acoustic cues used by the human perceptual system to achieve such accurate auditory localization. Acoustic cues are derived from the physical properties of sound waves, and many factors allow and influence auditory localization abilities. This review presents the monaural and binaural perceptual mechanisms involved in auditory localization in the three dimensions. Besides the main mechanisms of Interaural Time Difference, Interaural Level Difference and Head Related Transfer Function, secondary important elements such as reverberation and motion, are also analyzed. For each mechanism, the perceptual limits of localization abilities are presented. A section is specifically devoted to reference systems in space, and to the pointing methods used in experimental research. Finally, some cases of misperception and auditory illusion are described. More than a simple description of the perceptual mechanisms underlying localization, this paper is intended to provide also practical information available for experiments and work in the auditory field.