Acoustic properties of microperforated panels and their optimizatión by simulated annealing

This thesis investigates the acoustic properties of microperforated panels as an alternative to passive noise control. The first chapters are devoted to the review of analytical models to obtain the acoustic impedance and absorption coefficient of perforated panels. The use of panels perforated with circular holes or with slits is discussed. The theoretical models are presented and some modifications are proposed to improve the modeling of the physical phenomena occurring at the perforations of the panels. The absorption band is widened through the use of multiple layer microperforated panels and/or the combination of a millimetric panel with a porous layer that can be a fibrous material or a nylon mesh. A commercial micrometric mesh downstream a millimetric panel is proposed as a very efficient and low cost solution for controlling noise in reduced spaces. The simulated annealing algorithm is used in order to optimize the panel construction to provide a maximum of absorption in a determined wide band frequency range. Experiments are carried out at normal sound incidence and plane waves. One example is shown for a double layer microperforated panel subjected to grazing flow. A good agreement is achieved between the theory and the experiments. RESUMEN En esta tesis se investigan las propiedades acústicas de paneles micro perforados como una alternativa al control pasivo del ruido. Los primeros capítulos están dedicados a la revisión de los modelos de análisis para obtener la impedancia acústica y el coeficiente de absorción de los paneles perforados. El uso de paneles perforados con agujeros circulares o con ranuras es discutido. Se presentan diferentes modelos y se proponen algunas modificaciones para mejorar la modelización de los fenómenos físicos que ocurren en las perforaciones. La banda de absorción se ensancha a través del uso de capas múltiples de paneles micro perforados y/o la combinación de un panel de perforaciones milimétricas combinado con una capa porosa que puede ser un material fibroso o una malla de nylon. Se propone el uso de una malla micrométrica detrás de un panel milimétrico como una solución económica y eficiente para el control del ruido en espacios reducidos. El algoritmo de recocido simulado se utiliza con el fin de optimizar la construcción de paneles micro perforados para proporcionar un máximo de absorción en una banda determinada frecuencias. Los experimentos se llevan a cabo en la incidencia normal de sonido y ondas planas. Se muestra un ejemplo de panel micro perforado de doble capa sometido a flujo rasante. Se consigue un buen acuerdo entre la teoría y los experimentos.

Estructuras espaciales desmontables y desplegables. Estudio de la obra del arquitecto Emilio Pérez Pinero.

La presente tesis estudia las realizaciones del arquitecto Emilio Pérez Pinero, todas dentro de las estructuras espaciales de barras desmontables y desplegables, elabora la documentación que hace transmisible su investigación y generaliza el estudio del comportamiento en la parcela de las desplegables. La obra de este arquitecto forma un conjunto original, atractivo y sin continuadores, y por otra parte, no abundan las" investigaciones sobre este tipo de estructuras ( mucho menos las realizaciones), en las que hay que resolver tanto su definición como su movilidad y comportamiento estructural. El contenido de la parte correspondiente a las estructuras desmontables se limita a las cúpulas reticuladas de una capa, con el sistema de reticulado y montaje ideado por Pinero, por considerar que se debe documentar su aportación pero no incidir mas en un campo de investigación que cuenta con abundantes estudios. Se aporta la solución matemática y un programa de ordenador para la definición geométrica completa del reticulado empleado. Las estructuras desplegables se caracterizan por el empleo de barras dispuestas en "x" en el espesor de la estructura, con generación de superficies tanto planas como curvas. En ambos casos se analiza la movilidad en fase de mecanismo, tanto a las soluciones de Pinero como a las complementarlas que se exponen. Se estudian las relaciones geométricas que deben de cumplirse para que sea posible el movimiento de las barras, relaciones particularmente complejas en las desplegables según superficies esféricas, y que determinan su definición geométrica. En la fase de estructura, además de analizar lo realizado por Pinero, documentando y definiendo sus componentes, se proponen varias estructuras posibles para cada mecanismo, y se desarrolla en detalle el tipo de los emparrillados de canto constante, donde se incluye un estudio comparativo de nueve variantes distintas. Se muestra el amplio campo de uso posible para estas estructuras. ABSTRACT The • present doctoral dissertation studies the work of de spanish architect Emilio Pérez Pinero, all of it within de field of spatial demountable and deployable structures. This contribution compiles the necessary documentation for research in this field and, besides, generalizes the theoretical background for the analysis of this type of structures. Pérez Pinero's contributions are original and attractive, but, so far, he has not any followers ; on the other hand research in this field is scarce (much less actual realizations). In the part corresponding to demountable structures the research is limited to reticulated domes of only one layer, following Pérez Pinero's sys~ tem, trying to give a comprehensive documentation of it. The mathematical solution is given and so is a computer program for the complete definition of the geometry of the structure. One characteristic of deployable structures is the use of struts placed - formix "X" in the thickness of the structure, making possible the generation of plañe as well as curved surfaces. In both cases, the operation in the phase of mechanism is studied, both fot Pinero's solution and for the other schemes presented. The geometrical relationships that must be maintained in order to guarantee strut's movements, are studied; these relationships are particularly complex in the case of spherical surfaces, and, in this last casey determine completely its geometrical definition. In regard of the structure behaviour, besides analysing Pinero's works, a variety of solutions are proposed for each mechanism. Particularly, the configuration for double layer grids of constant thickness is developed with great detall, and a comparative study of nine different solutions of this special case is included. A wide range of the possible applications of this structural type is shown.

Mutual coupling reduction using EBG in steering antennas

In this letter, a dual circular polarized steering antenna for satellite communications in X-band is presented. This antenna consists of printed elements grouped in an array, able to work from 7.25 up to 8.4 GHz in both polarizations: left-handed circular polarization (LHCP) and right-handed circular polarization (RHCP). The module antenna is compact, with narrow beamwidth, and reaches a gain of 16 dBi. It has the capability to steer in elevation to and electronically with a Butler matrix. In order to reduce the mutual coupling between adjacent patches, electromagnetic band-gap (EBG) structures are introduced. These EBGs combine double-layer and edge location via in order to reduce the size, without changing the low-permittivity substrate, and therefore maintaining the high radiation efficiency of the antenna.

EBG size reduction for low permittivity substrates

Double layer and edge-location via techniques are combined for electromagnetic band gap (EBG) size reduction. The study of the required number of elements and their dimensions is carried out in order to suppress the surface wave propagation modes and consequently to reduce the mutual coupling between radiating elements in low-permittivity substrates. By applying these techniques, the size of the EBG mushroom is reduced by 30%; however, the bandwidth operation maintains its value, and these structures can be integrated between radiating elements in broad bandwidth antennas.

Current collection by an active spherical electrode in an unmagnetized plasma

A theoretical model for the steady-state response of anodic contactors that emit a plasma current Ii and collect electrons from a collisionless, unmagnetized plasma is presented. The use of a (kinetic) monoenergetic population for the attracted species, well known in passive probe theory, gives both accuracy and tractability to the theory. The monoenergetic population is proved to behave like an isentropic fluid with radial plus centripetal motion, allowing direct comparisons with ad hoc fluid models. Also, a modification of the original monoenergetic equations permits analysis of contactors operating in orbit-limited conditions. Besides that, the theory predicts that, only for plasma emissions above certain threshold current a presheath/double layer/core structure for the potential is formed (the core mode), while for emissions below that threshold, a plasma contactor behaves exactly as a positive-ion emitter with a presheath/sheath structure (the no-core mode). Ion emitters are studied as a particular case. Emphasis is placed on obtaining dimensionless charts and approximate asymptotic laws of the current-voltage characteristic.

Bare-tether cathodic contact through thermoionic emission by low work-function materials

A new material, C12A7 : electride, which might present a work function as low as 0.6 eV and moderately high temperature stability, was recently proposed as coating for floating bare tethers. Arising from heating under space operation, current is emitted by thermionic emission along a thus coated cathodic segment. A preliminary study on the space-charge-limited (SCL) double layer in front of the cathodic segment is presented using Langmuir’s SCL electron current between cylindrical electrodes and orbital-motion-limited ion-collection sheath. A detailed calculation of current and bias profiles along the entire tether length is carried out with ohmic effects and the transition from SCL to full Richardson-Dushman emission included. Analysis shows that in the simplest drag mode, under typical orbital and tether conditions, thermionic emission leads to a short cathodic section and may eliminate the need for an active cathodic device and its corresponding gas feed requirements and power subsystem, which results in a truly “propellant-less” tether system for such basic applications as de-orbiting low earth orbit satellites.

Analysis of Magnetic Nozzles For Space Plasma Thrusters = Análisis de Toberas Magnéticas para Motores Espaciales de Plasma

Esta tesis presenta un análisis teórico del funcionamiento de toberas magnéticas para la propulsión espacial por plasmas. El estudio está basado en un modelo tridimensional y bi-fluido de la expansión supersónica de un plasma caliente en un campo magnético divergente. El modelo básico es ampliado progresivamente con la inclusión de términos convectivos dominantes de electrones, el campo magnético inducido por el plasma, poblaciones electrónicas múltiples a distintas temperaturas, y la capacidad de integrar el flujo en la región de expansión lejana. La respuesta hiperbólica del plasma es integrada con alta precisión y eficiencia haciendo uso del método de las líneas características. Se realiza una caracterización paramétrica de la expansión 2D del plasma en términos del grado de magnetización de iones, la geometría del campo magnético, y el perfil inicial del plasma. Se investigan los mecanismos de aceleración, mostrando que el campo ambipolar convierte la energía interna de electrones en energía dirigida de iones. Las corrientes diamagnéticas de Hall, que pueden hallarse distribuidas en el volumen del plasma o localizadas en una delgada capa de corriente en el borde del chorro, son esenciales para la operación de la tobera, ya que la fuerza magnética repulsiva sobre ellas es la encargada de confinar radialmente y acelerar axialmente el plasma. El empuje magnético es la reacción a esta fuerza sobre el motor. La respuesta del plasma muestra la separación gradual hacia adentro de los tubos de iones respecto de los magnéticos, lo cual produce la formación de corrientes eléctricas longitudinales y pone el plasma en rotación. La ganancia de empuje obtenida y las pérdidas radiales de la pluma de plasma se evalúan en función de los parámetros de diseño. Se analiza en detalle la separación magnética del plasma aguas abajo respecto a las líneas magnéticas (cerradas sobre sí mismas), necesaria para la aplicación de la tobera magnética a fines propulsivos. Se demuestra que tres teorías existentes sobre separación, que se fundamentan en la resistividad del plasma, la inercia de electrones, y el campo magnético que induce el plasma, son inadecuadas para la tobera magnética propulsiva, ya que producen separación hacia afuera en lugar de hacia adentro, aumentando la divergencia de la pluma. En su lugar, se muestra que la separación del plasma tiene lugar gracias a la inercia de iones y la desmagnetización gradual del plasma que tiene lugar aguas abajo, que permiten la separación ilimitada del flujo de iones respecto a las líneas de campo en condiciones muy generales. Se evalúa la cantidad de plasma que permanece unida al campo magnético y retorna hacia el motor a lo largo de las líneas cerradas de campo, mostrando que es marginal. Se muestra cómo el campo magnético inducido por el plasma incrementa la divergencia de la tobera magnética y por ende de la pluma de plasma en el caso propulsivo, contrariamente a las predicciones existentes. Se muestra también cómo el inducido favorece la desmagnetización del núcleo del chorro, acelerando la separación magnética. La hipótesis de ambipolaridad de corriente local, común a varios modelos de tobera magnética existentes, es discutida críticamente, mostrando que es inadecuada para el estudio de la separación de plasma. Una inconsistencia grave en la derivación matemática de uno de los modelos más aceptados es señalada y comentada. Incluyendo una especie adicional de electrones supratérmicos en el modelo, se estudia la formación y geometría de dobles capas eléctricas en el interior del plasma. Cuando dicha capa se forma, su curvatura aumenta cuanto más periféricamente se inyecten los electrones supratérmicos, cuanto menor sea el campo magnético, y cuanto más divergente sea la tobera magnética. El plasma con dos temperaturas electrónicas posee un mayor ratio de empuje magnético frente a total. A pesar de ello, no se encuentra ninguna ventaja propulsiva de las dobles capas, reforzando las críticas existentes frente a las propuestas de estas formaciones como un mecanismo de empuje. Por último, se presenta una formulación general de modelos autosemejantes de la expansión 2D de una pluma no magnetizada en el vacío. El error asociado a la hipótesis de autosemejanza es calculado, mostrando que es pequeño para plumas hipersónicas. Tres modelos de la literatura son particularizados a partir de la formulación general y comparados. Abstract This Thesis presents a theoretical analysis of the operation of magnetic nozzles for plasma space propulsion. The study is based on a two-dimensional, two-fluid model of the supersonic expansion of a hot plasma in a divergent magnetic field. The basic model is extended progressively to include the dominant electron convective terms, the plasma-induced magnetic field, multi-temperature electron populations, and the capability to integrate the plasma flow in the far expansion region. The hyperbolic plasma response is integrated accurately and efficiently with the method of the characteristic lines. The 2D plasma expansion is characterized parametrically in terms of the ion magnetization strength, the magnetic field geometry, and the initial plasma profile. Acceleration mechanisms are investigated, showing that the ambipolar electric field converts the internal electron energy into directed ion energy. The diamagnetic electron Hall current, which can be distributed in the plasma volume or localized in a thin current sheet at the jet edge, is shown to be central for the operation of the magnetic nozzle. The repelling magnetic force on this current is responsible for the radial confinement and axial acceleration of the plasma, and magnetic thrust is the reaction to this force on the magnetic coils of the thruster. The plasma response exhibits a gradual inward separation of the ion streamtubes from the magnetic streamtubes, which focuses the jet about the nozzle axis, gives rise to the formation of longitudinal currents and sets the plasma into rotation. The obtained thrust gain in the magnetic nozzle and radial plasma losses are evaluated as a function of the design parameters. The downstream plasma detachment from the closed magnetic field lines, required for the propulsive application of the magnetic nozzle, is investigated in detail. Three prevailing detachment theories for magnetic nozzles, relying on plasma resistivity, electron inertia, and the plasma-induced magnetic field, are shown to be inadequate for the propulsive magnetic nozzle, as these mechanisms detach the plume outward, increasing its divergence, rather than focusing it as desired. Instead, plasma detachment is shown to occur essentially due to ion inertia and the gradual demagnetization that takes place downstream, which enable the unbounded inward ion separation from the magnetic lines beyond the turning point of the outermost plasma streamline under rather general conditions. The plasma fraction that remains attached to the field and turns around along the magnetic field back to the thruster is evaluated and shown to be marginal. The plasmainduced magnetic field is shown to increase the divergence of the nozzle and the resulting plasma plume in the propulsive case, and to enhance the demagnetization of the central part of the plasma jet, contrary to existing predictions. The increased demagnetization favors the earlier ion inward separation from the magnetic field. The local current ambipolarity assumption, common to many existing magnetic nozzle models, is critically discussed, showing that it is unsuitable for the study of plasma detachment. A grave mathematical inconsistency in a well-accepted model, related to the acceptance of this assumption, is found out and commented on. The formation and 2D shape of electric double layers in the plasma expansion is studied with the inclusion of an additional suprathermal electron population in the model. When a double layer forms, its curvature is shown to increase the more peripherally suprathermal electrons are injected, the lower the magnetic field strength, and the more divergent the magnetic nozzle is. The twoelectron- temperature plasma is seen to have a greater magnetic-to-total thrust ratio. Notwithstanding, no propulsive advantage of the double layer is found, supporting and reinforcing previous critiques to their proposal as a thrust mechanism. Finally, a general framework of self-similar models of a 2D unmagnetized plasma plume expansion into vacuum is presented and discussed. The error associated with the self-similarity assumption is calculated and shown to be small for hypersonic plasma plumes. Three models of the literature are recovered as particularizations from the general framework and compared.

In situ control of the GE(100)surface domain structure for III-V multijunction solar cells

Vicinal Ge(100) is the common substrate for state of the art multi-junction solar cells grown by metal-organic vapor phase epitaxy (MOVPE). While triple junction solar cells based on Ge(100) present efficiencies mayor que 40%, little is known about the microscopic III-V/Ge(100) nucleation and its interface formation. A suitable Ge(100) surface preparation prior to heteroepitaxy is crucial to achieve low defect densities in the III-V epilayers. Formation of single domain surfaces with double layer steps is required to avoid anti-phase domains in the III-V films. The step formation processes in MOVPE environment strongly depends on the major process parameters such as substrate temperature, H2 partial pressure, group V precursors [1], and reactor conditions. Detailed investigation of these processes on the Ge(100) surface by ultrahigh vacuum (UHV) based standard surface science tools are complicated due to the presence of H2 process gas. However, in situ surface characterization by reflection anisotropy spectroscopy (RAS) allowed us to study the MOVPE preparation of Ge(100) surfaces directly in dependence on the relevant process parameters [2, 3, 4]. A contamination free MOVPE to UHV transfer system [5] enabled correlation of the RA spectra to results from UHV-based surface science tools. In this paper, we established the characteristic RA spectra of vicinal Ge(100) surfaces terminated with monohydrides, arsenic and phosphorous. RAS enabled in situ control of oxide removal, H2 interaction and domain formation during MOVPE preparation.

Double ion implantation and pulsed laser melting processes for third generation solar cells

In the framework of the third generation of photovoltaic devices, the intermediate band solar cell is one of the possible candidates to reach higher efficiencies with a lower processing cost. In this work, we introduce a novel processing method based on a double ion implantation and, subsequently, a pulsed laser melting (PLM) process to obtain thicker layers of Ti supersaturated Si. We perform ab initio theoretical calculations of Si impurified with Ti showing that Ti in Si is a good candidate to theoretically form an intermediate band material in the Ti supersaturated Si. From time-of-flight secondary ion mass spectroscopy measurements, we confirm that we have obtained a Ti implanted and PLM thicker layer of 135 nm. Transmission electron microscopy reveals a single crystalline structure whilst the electrical characterization confirms the transport properties of an intermediate band material/Si substrate junction. High subbandgap absorption has been measured, obtaining an approximate value of 104 cm−1 in the photons energy range from 1.1 to 0.6 eV.

InN/GaN heterojunction electrical behavior

Indium nitride (InN) has been the subject of intense research in recent years. Some of its most attractive features are its excellent transport properties such as its small band edge electron effective mass, high electron mobilities and peak drift velocities, and high frequency transient drift velocity oscillations [1]. These suggest enormous potential applications for InN in high frequency electronic devices. But to date the high unintentional bulk electron concentration (n~1018 cm-3) of undoped InN samples and the surface electron accumulation layer make it a hard task to create a reliable metalsemiconductor Schottky barrier. Some attempts have been made to overcome this problem by means of material oxidation [2] or deposition of insulators [3]. In this work we present a way to obtain an electrical rectification behaviour by means of heterojunction growth. Due to the big band gap differences among nitride semiconductors, it’s possible to create a structure with high band offsets. In InN/GaN heterojunctions, depending on the GaN doping, the magnitude of conduction and valence band offset are critical parameters which allow distinguishing among different electrical behaviours. The earliest estimate of the valence band offset at an InN–GaN heterojunction in a wurtzite structure was measured to be ~0.85 eV [4], while the Schottky barrier heights were determined to be ~ 1,4 eV [5].We grew In-face InN layer with varying thickness (between 150 nm and 1 mm) by plasma assisted molecular beam epitaxy (PA-MBE) on GaNntemplates (GaN/Al2O3), with temperatures ranging between 300°C and 450°C. The different doping in GaN template (Si doping, Fe doping and Mg doping) results in differences in band alignments of the two semiconductors changing electrical barriers for carriers and consequently electrical conduction behaviour. The processing of the devices includes metallization of the ohmic contacts on InN and GaN, for which we used Ti/Al/Ni/Au. Whereas an ohmic contact on InN is straightforward, the main issue was the fabrication of the contact on GaN due to the very low decomposition temperature of InN. A standard ohmic contact on GaN is generally obtained by high temperature rapid thermal annealing (RTA), typically done between 500ºC and 900ºC[6]. In this case, the limitation due to the presence of In-face InN imposes an upper limit on the temperature for the thermal annealing process and ohmic contact formation of about 450°C. We will present results on the morphology of the InN layers by X-Ray diffraction and SEM, and electrical measurements, in particular current-voltage and capacitance-voltage characteristics.

Study of the Electrical Behavior in Intermediate Band-Si Junctions

In this study we analyze the electrical behavior of a junction formed by an ultraheavily Ti implanted Si layer processed by a Pulsed Laser Melting (PLM) and the non implanted Si substrate. This electrical behavior exhibits an electrical decoupling effect in this bilayer that we have associated to an Intermediate Band (IB) formation in the Ti supersaturated Si layer. Time-of-flight secondary ion mass spectrometry (ToFSIMS) measurements show a Ti depth profile with concentrations well above the theoretical limit required to the IB formation. Sheet resistance and Hall mobility measurements in the van der Pauw configuration of these bilayers exhibit a clear dependence with the different measurement currents introduced (1menor queA-1mA). We find that the electrical transport properties measured present an electrical decoupling effect in the bilayer as function of the temperature. The dependence of this effect with the injected current could be explained in terms of an additional current flow in the junction from the substrate to the IB layer and in terms of the voltage dependence in the junction with the measurement current.

Self-consistent resonance absorption with two layer profile steepening

Resonance absorption of p-polarized light, incident at angle 6 on a flowing, stratified plasma, is analyzed; profile steepening within (i) a layer around the turning point, and (ii) a thinner,embedded sublayer at the critical surface is taken into account self-consistently. The entire steepened region is taken as collisionless and isothermal. The structure of the main layer shows a variety of regimes, depending on how the flow crosses a sonic point. The structure of the sublayer is also determined; it is entirely subsonic (with no wave breaking) for a well-defined,broad parameter range. Density changes across both layer and sublayer, and fractional absorption, are given in terms of [(wavelength)2 Xintensity/temperature], and (temperature/mec2). The flow outside the double structure is also analyzed for particular conditions.

Electrical properties of silicon supersaturated with titanium or vanadium for intermediate band material

We have fabricated titanium and vanadium supersaturated silicon layers on top of a silicon substrate by means of ion implantation and pulsed laser melting processes. This procedure has proven to be suitable to fabricate an intermediate band (IB) material, i.e. a semiconductor material with a band of allowed states within the bandgap. Sheet resistance and Hall mobility measurements as a function of the temperature show an unusual behavior that has been well explained in the framework of the IB material theory, supposing that we are dealing with a junction formed by the IB material top layer and the n-Si substrate. Using an analytical model that fits with accuracy the experimental sheet resistance and mobility curves, we have obtained the values of the exponential factor for the thermically activated junction resistance of the bilayer, showing important differences as a function of the implanted element. These results could allow us to engineer the IB properties selecting the implanted element depending on the required properties for a specific application.

Electrical decoupling effect on intermediate band Ti-implanted silicon layers

We investigated the electrical transport properties of ultraheavily Ti-implanted silicon layers subsequently pulsed laser melted (PLM). After PLM, the samples exhibit anomalous electrical behaviour in sheet resistance and Hall mobility measurements, which is associated with the formation of an intermediate band (IB) in the implanted layer. An analytical model that assumes IB formation and a current limitation effect between the implanted layer and the substrate was developed to analyse this anomalous behaviour. This model also describes the behaviour of the function V/Delta V and the electrical function F that can be extracted from the electrical measurements in the bilayer. After chemical etching of the implanted layer, the anomalous electrical behaviour observed in sheet resistance and Hall mobility measurements vanishes, recovering the unimplanted Si behaviour, in agreement with the analytical model. The behaviour of V/Delta V and the electrical function F can also be successfully described in terms of the analytical model in the bilayer structure with the implanted layer entirely stripped.

Development of One Meter Long Double-Sided CeO2 Buffered Ni-5at.W Templates by Reel-to-Reel Chemical Solution Deposition Route

High performance long-length coated conductors fabricated using various techniques have attracted a lot of interest recently. In this work, a reel-to-reel design for depositing double-sided coatings on long-length flexible metallic tapes via a chemical solution method is proposed and realized. The major achievement of the design is to combine the dip coating and drying processes in order to overcome the technical difficulties of dealing with the wet films on both sides of the tape. We report the successful application of the design to fabricate a one-meter-long double side coated CeO2/Ni-5at%W template. The CeO2 films on both sides exhibit a dense, crack-free morphology, and a high fraction of cube texture on the surface. Homogeneity studies on global texture over the length also reveal that the average full width at half maximum values of the in-plane and out-of-plane orientation on the CeO2 layer are 7.2 ° and 5.8° with standard deviation of 0.26° and 0.34°, respectively, being indicative of the high quality epitaxial growth of the films prepared in the continuous manner. An all chemical solution derived YBCOLow-TFA/Ce0.9La0.1O2 /Gd2Zr2O7/CeO2 structure is obtained on a short sample, demonstrating the possibility of producing long-length texture templates for coated conductors by this low cost deposition route.