Sound Field Reconstruction Using Prolate Spheroidal Wave Functions and Sparse Regularization.

Near-field acoustic holography (NAH) based on compressing sensing (CS) theory enables accurate reconstruction of sound fields using a limited number of sampling points. However, the successful implementation of this technique depends on two crucial factors: (1) the appropriate selection or construction of the spatial basis and (2) an effective sparse regularization process. To enhance reconstruction performance for elongated sound sources, this paper proposes a novel sound field reconstruction method that combines prolate spheroidal wave functions (PSWFs) with the orthogonal matching pursuit (OMP) algorithm. In this method, PSWFs serve as a sparse spatial basis for representing the radiated sound field. The sparse coefficients are determined by the OMP algorithm in a linear subspace composed of basic functions that best match the residual error. The OMP algorithm effectively identifies significant components before potentially selecting incorrect ones by setting an appropriate stopping rule. Numerical simulations are conducted using a line-array source model. The results show that the proposed method can accurately reconstruct the sound pressures of the elongated source model using a relatively small number of samplings. In addition, the proposed method exhibits robustness across a wide frequency range, diverse array configurations and various sampling numbers. The experimental results further validate the feasibility and reliability of the proposed method.

Serum versican as a potential biomarker in patients with uterine fibroids: A study from Eastern India.

Objective: Versican is a chondroitin sulphate proteoglycan with raised expression at site of inflammation, and uterine fibroids are associated with local inflammation. Hence, this study aimed to estimate serum Versican levels in pre-menopausal women with uterine fibroids to evaluate its diagnostic efficiency. Materials and Methods: This case-control study included forty uterine fibroid cases and 40 healthy controls. Cases clinically evaluated with USG findings, that is number, location of fibroid and volume calculated by prolate ellipse formula a × b × c × 0.523 (a - height, b - width, c - depth). Biochemical investigations, that is serum Versican levels, were estimated by ELISA with total cholesterol, HDLc and LDLc. Triglycerides by fully automated chemistry analysers. Serum biochemical parameters were compared and correlated with volume of fibroid. Area under receiver operating characteristic curve was calculated along with cut-off value to determine diagnostic potential of Versican, differentiating women with fibroids. Results: In the present study, patients with fibroids had decreased levels of serum Versican (79.43 ± 18.60) as compared to healthy controls (101.81 ± 28.24, P < 0.001). There was a statistically significant negative correlation (r = - 0. 307, P = 0.04) between serum Versican level and volume of fibroid. Area under ROC was 0.726 (95% CI: 0.616-0.836; P = 0.001). The best cut-off value for serum Versican level was 96.90 ng/ml with 90% sensitivity and 48% specificity. Conclusion: Serum Versican levels were found significantly lower in women with fibroid with a negative correlation with volume of fibroid uterus. Furthermore, extensive study would help in substantiating diagnostic potential of serum Versican in fibroid uterus patients.

Pheno- and Genotyping of Three Novel Bacteriophage Genera That Target a Wheat Phyllosphere Sphingomonas Genus.

Bacteriophages are viral agents that infect and replicate within bacterial cells. Despite the increasing importance of phage ecology, environmental phages-particularly those targeting phyllosphere-associated bacteria-remain underexplored, and current genomic databases lack high-quality phage genome sequences linked to specific environmentally important bacteria, such as the ubiquitous sphingomonads. Here, we isolated three novel phages from a Danish wastewater treatment facility. Notably, these phages are among the first discovered to target and regulate a Sphingomonas genus within the wheat phyllosphere microbiome. Two of the phages displayed a non-prolate Siphovirus morphotype and demonstrated a narrow host range when tested against additional Sphingomonas strains. Intergenomic studies revealed limited nucleotide sequence similarity within the isolated phage genomes and to publicly available metagenome data of their closest relatives. Particularly intriguing was the limited homology observed between the DNA polymerase encoding genes of the isolated phages and their closest relatives. Based on these findings, we propose three newly identified genera of viruses: Longusvirus carli, Vexovirus birtae, and Molestusvirus kimi, following the latest ICTV binomial nomenclature for virus species. These results contribute to our current understanding of phage genetic diversity in natural environments and hold promising implications for phage applications in phyllosphere microbiome manipulation strategies.

Mathematical Study of the Perturbation of Magnetic Fields Caused by Erythrocytes.

The purpose of this chapter is the mathematical study of the perturbation of a homogeneous static magnetic field caused by the embedding of a red blood cell. Analytical expressions for the magnetic potential and the magnetic strength vector are derived. From the obtained results, it emerges that the magnetic field inside the red blood cell is not uniform and the magnitude depends on the orientation of the erythrocyte. The expressions for the magnetic field quantities are significant in applications such as the magnetic resonance imaging and in the magnetic resonance spectroscopy.

Local and Global Order in Dense Packings of Semi-Flexible Polymers of Hard Spheres.

The local and global order in dense packings of linear, semi-flexible polymers of tangent hard spheres are studied by employing extensive Monte Carlo simulations at increasing volume fractions. The chain stiffness is controlled by a tunable harmonic potential for the bending angle, whose intensity dictates the rigidity of the polymer backbone as a function of the bending constant and equilibrium angle. The studied angles range between acute and obtuse ones, reaching the limit of rod-like polymers. We analyze how the packing density and chain stiffness affect the chains' ability to self-organize at the local and global levels. The former corresponds to crystallinity, as quantified by the Characteristic Crystallographic Element (CCE) norm descriptor, while the latter is computed through the scalar orientational order parameter. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies, developing a complete phase diagram as a function of packing density and equilibrium bending angle. A plethora of structures are obtained, ranging between random hexagonal closed packed morphologies of mixed character and almost perfect face centered cubic (FCC) and hexagonal close-packed (HCP) crystals at the level of monomers, and nematic mesophases, with prolate and oblate mesogens at the level of chains. For rod-like chains, a delay is observed between the establishment of the long-range nematic order and crystallization as a function of the packing density, while for right-angle chains, both transitions are synchronized. A comparison is also provided against the analogous packings of monomeric and fully flexible chains of hard spheres.

New Class of Polymer Materials-Quasi-Nematic Colloidal Particle Self-Assemblies: The Case of Assemblies of Prolate Spheroidal Poly(Styrene/Polyglycidol) Particles.

Assemblies of colloidal polymer particles find various applications in many advanced technologies. However, for every type of application, assemblies with properly tailored properties are needed. Until now, attention has been concentrated on the assemblies composed of spherical particles arranged into so-called perfect colloidal crystals and on complex materials containing mixtures of crystal and disordered phases. However, new opportunities are opened by using assemblies of spheroidal particles. In such assemblies, the particles, in addition to the three positional have three angular degrees of freedom. Here, the preparation of 3D assemblies of reference microspheres and prolate spheroidal poly(styrene/polyglycidol) microparticles by deposition from water and water/ethanol media on silicon substrates is reported. The particles have the same polystyrene/polyglycidol composition and the same volumes but differ with respect to their aspect ratio (AR) ranged from 1 to 8.5. SEM microphotographs reveal that particles in the assembly top layers are arranged into the quasi-nematic structures and that the quality of their orientation in the same direction increase with increasing AR. Nano- and microindentation studies demonstrate that interactions of sharp and flat tips with arrays of spheroidal particles lead to different types of particle deformations.

3-D reconstruction of rice leaf tissue for proper estimation of surface area of mesophyll cells and chloroplasts facing intercellular airspaces from 2-D section images.

BACKGROUND AND AIMS: The surface area of mesophyll cells (Smes) and chloroplasts (Sc) facing the intercellular airspace (IAS) are important parameters for estimating photosynthetic activity from leaf anatomy. Although Smes and Sc are estimated based on the shape assumption of mesophyll cells (MCs), it is questionable if the assumption is correct for rice MCs with concave-convex surfaces. Therefore, in this study, we establish a reconstruction method for the 3-D representation of the IAS in rice leaf tissue to calculate the actual Smes and Sc with 3-D images and to determine the correct shape assumption for the estimation of Smes and Sc based on 2-D section images. METHODS: We used serial section light microscopy to reconstruct 3-D representations of the IAS, MCs and chloroplasts in rice leaf tissue. Actual Smes and Sc values obtained from the 3-D representation were compared with those estimated from the 2-D images to find the correct shape-specific assumption (oblate or prolate spheroid) in different orientations (longitudinal and transverse sections) using the same leaf sample. KEY RESULTS: The 3-D representation method revealed that volumes of the IAS and MCs accounted for 30 and 70 % of rice leaf tissue excluding epidermis, respectively, and the volume of chloroplasts accounted for 44 % of MCs. The shape-specific assumption on the sectioning orientation affected the estimation of Smes and Sc using 2-D section images with discrepancies of 10-38 %. CONCLUSIONS: The 3-D representation of rice leaf tissue was successfully reconstructed using serial section light microscopy and suggested that estimation of Smes and Sc of the rice leaf is more accurate using longitudinal sections with MCs assumed as oblate spheroids than using transverse sections with MCs as prolate spheroids.

Structures of a large prolate virus capsid in unexpanded and expanded states generate insights into the icosahedral virus assembly.

Many icosahedral viruses assemble proteinaceous precursors called proheads or procapsids. Proheads are metastable structures that undergo a profound structural transition known as expansion that transforms an immature unexpanded head into a mature genome-packaging head. Bacteriophage T4 is a model virus, well studied genetically and biochemically, but its structure determination has been challenging because of its large size and unusually prolate-shaped, ∼1,200-Å-long and ∼860-Å-wide capsid. Here, we report the cryogenic electron microscopy (cryo-EM) structures of T4 capsid in both of its major conformational states: unexpanded at a resolution of 5.1 Å and expanded at a resolution of 3.4 Å. These are among the largest structures deposited in Protein Data Bank to date and provide insights into virus assembly, head length determination, and shell expansion. First, the structures illustrate major domain movements and ∼70% additional gain in inner capsid volume, an essential transformation to contain the entire viral genome. Second, intricate intracapsomer interactions involving a unique insertion domain dramatically change, allowing the capsid subunits to rotate and twist while the capsomers remain fastened at quasi-threefold axes. Third, high-affinity binding sites emerge for a capsid decoration protein that clamps adjacent capsomers, imparting extraordinary structural stability. Fourth, subtle conformational changes at capsomers' periphery modulate intercapsomer angles between capsomer planes that control capsid length. Finally, conformational changes were observed at the symmetry-mismatched portal vertex, which might be involved in triggering head expansion. These analyses illustrate how small changes in local capsid subunit interactions lead to profound shifts in viral capsid morphology, stability, and volume.

Predictive Shapes of Ellipsoid PPDL-PTHF Copolymer Particles Prepared by the Phantom Stretching Technique.

Ellipsoidal polymer particles can be prepared from spheres by unidirectional stretching at elevated temperatures, while the particles' aspect ratios (AR) that result from this phantom stretching methodology are often not precisely predictable. Here, an elastic deformation model was exemplarily evaluated for ~50 µm spherical microparticles from PPDL-PTHF block copolymers. The prolate ellipsoidal particles, obtained by stretching in polyvinyl alcohol phantoms, differed in dimensions at identical relative phantoms elongations up to 150%, depending on the relative polymer composition and their systematically altered mechanical properties. Importantly, the resulting particle shapes within the studied range of AR up to ~4 matched the predictions of the elastic deformation model, which includes information of the elastic moduli of phantom and particle materials. These data suggest that the model may be applicable to predict the conditions needed to precisely prepare ellipsoids of desired AR and may be applicable to various deformable particle materials.

The UV prolate spectrum matches the zeros of zeta.

SignificanceWe show that the eigenvalues of the self-adjoint extension (introduced by A.C. in 1998) of the prolate spheroidal operator reproduce the UV behavior of the squares of zeros of the Riemann zeta function, and we construct an isospectral family of Dirac operators whose spectra have the same UV behavior as those zeros.

Cloud point, auto-coacervation, and nematic ordering of micelles formed by ethylene oxide containing carboxylate surfactants.

HYPOTHESIS: In a recent paper, we determined the phase behavior of an aqueous solution of octyl ether octaethylene oxide carboxylic acid ([H+][C8E8c-], Akypo™ LF2) and with partial replacement of H+ by Na+ and Ca2+. It was found that even the neat surfactants are liquid at room temperature and that they form only direct micelles for any aqueous content and over large temperature ranges. The aim of the present work was to find an explanation for the clouding in these systems as well as for the coacervation observed at very low surfactant content. We expected that very similar phase diagrams would be found for a full replacement of H+ by the mentioned ions. EXPERIMENTS: We established the respective phase diagrams of the above-mentioned salts in water and determined the structures of the occurring phases in detail with small-and wide-angle X-ray scattering, small-angle neutron scattering, dynamic light scattering, heat flux differential scanning calorimetry, as well as surface tension, ESI-MS, and NMR experiments. FINDINGS: To our surprise, we discovered a new type of nematic phase between an isotropic and a hexagonal phase. Based on the complete description of all occurring phases both in the acidic and the charged surfactant systems, we were able to design a coherent and unified picture of all these phases, including the auto-coacervation at low surfactant concentration, the non-conventional clouding at high temperatures, the unusual liquid crystalline phases in a small domain at high surfactant concentrations, and the Lß phase at low temperatures and at very low water content. It turned out that all phenomena are a consequence of the subtle interplay between a) the packing constraint due to the very large head-group, b) the relatively small hydrocarbon chain and c) the tunable electrostatic interactions versus entropy.

The shape of fluvial bedload gravels: A large, high-quality dataset of active-channel deposits.

Isotropic bedload gravels from an active fluvial system were collected from seven stations along the length of the Sabeto River of western Viti Levu, Fiji. Sampling was confined to clasts of Navilawa Monzonite, an intrusive rock that crops out only along the upper reaches of the river. The sampled gravels consisted of stream-bed surface material obtained from transects normal to the active channel. An additional sample was collected from an outcrop of fresh Navilawa Monzonite undergoing active physical breakdown on the side of the bedrock channel immediately adjacent to the river. A total of 883 clasts, ranging in diameter (b-axis) from 12 to 337 mm, was collected. The long (a), intermediate (b) and short (c) axis of each clast was measured, along with the diameter of the sharpest corner of the maximum projection outline (Di ) and the diameter of the maximum inscribed circle (Dk ). At six of the stations, the mass of each clast was recorded. Measurements were also made of the density of fresh Navilawa Monzonite. The dataset includes measurements of Navilawa Monzonite density and determinations of the Modified Wentworth Roundness, Maximum Projection Sphericity and Oblate-Prolate Index of each clast. At six of the stations the volume of each particle was estimated using measurements of particle mass and rock density. The repository, in Mendeley Data [1], provides a large, high-quality dataset of the shape of isotropic bedload gravels from an active fluvial system, affording information on the downstream evolution of particle shape. The dataset will be useful for sedimentologists, fluvial geomorphologists, hydraulic engineers and those concerned with fluvial bedload transport.

Routes for Metallization of Perovskite Solar Cells.

The application of metallic nanoparticles leads to an increase in the efficiency of solar cells due to the plasmonic effect. We explore various scenarios of the related mechanism in the case of metallized perovskite solar cells, which operate as hybrid chemical cells without p-n junctions, in contrast to conventional cells such as Si, CIGS or thin-layer semiconductor cells. The role of metallic nano-components in perovskite cells is different than in the case of p-n junction solar cells and, in addition, the large forbidden gap and a large effective masses of carriers in the perovskite require different parameters for the metallic nanoparticles than those used in p-n junction cells in order to obtain the increase in efficiency. We discuss the possibility of activating the very poor optical plasmonic photovoltaic effect in perovskite cells via a change in the chemical composition of the perovskite and through special tailoring of metallic admixtures. Here we show that it is possible to increase the absorption of photons (optical plasmonic effect) and simultaneously to decrease the binding energy of excitons (related to the inner electrical plasmonic effect, which is dominant in perovskite cells) in appropriately designed perovskite structures with multishell elongated metallic nanoparticles to achieve an increase in efficiency by means of metallization, which is not accessible in conventional p-n junction cells. We discuss different methods for the metallization of perovskite cells against the background of a review of various attempts to surpass the Shockley-Queisser limit for solar cell efficiency, especially in the case of the perovskite cell family.

Inverted lens provides reverse geometry solution for post laser vision correction (LVC) corneas.

Many patients require optical correction post-laser vision correction (LVC). While mildly irregular corneal topographic patterns or asymmetry can sometimes be treated with conventional soft lenses, often this proves inadequate. This article introduces a novel technique to provide visual improvement and comfort for these patients. An inverted senofilcon A (Acuvue Oasys®, Johnson & Johnson Vision Care) lens (off-label)was inserted on a patient's eyes that reported discomfort with his current soft contact lenses, which provided improved centration as was seen with a slit lamp and high molecular fluorescein through a yellow filter. The patient achieved a visual acuity of 6/6+ in each eye and reported that the vision did not fluctuate. The post-lens tear film decreased to 35micron versus 43micron in the conventional position, as shown in OCT. The patient reported that he wore the lenses 9 hours a day. His Dry Eye Questionnaire-8 (CLDEQ-8) score decreased from 22 to 15 when wearing the lenses in the inverted position. This case demonstrates that post-laser vision correction patients with minimal asymmetric topography within the treated zone requiring refractive correction may be helped using an inverted conventional soft frequent replacement lens.

Validation of 2d ultrasound and volume estimation formulae for volume assessment of kidneys and spleens: an in-vitro study / alidación de la fórmula de estimación de volumen y ultrasonido 2D para la evaluación del volumen de los riñones y el bazo: un estudio in vitro

The accuracy of internal organ volume estimation done with ultrasound (US) was found to be multifactorial. Hence, we aimed to describe and validate the volume assessment of ultrasound and standard volume estimation formulae for different shaped intra-abdominal organs using spleens and kidneys.Dissected cadaveric kidneys (n=25) and spleens (n=29) were scanned to obtain linear measurements and ultrasound auto-generated volumes (USV). Linear measurements were used to calculate the volumes manually with ellipsoid, prolate, and Lambert volume estimating formulae. The actual volumes (AV) of organs were obtained by the water displacement method. Volume assessment accuracy of USV and different formulae were compared by comparing bias, precision and Bland-Altman plot analysis. The US linear and volume measurement procedure was reliable with high inter and intra-observer agreements (linear: Chronbach's α=0.983 to 0.934; volumes: Chronbach's α=0.989). USV estimates were accurate with a high correlation to AV and low estimation bias (-5.9%). Also, prolate (bias=-0.75%) and ellipsoid formulae (bias=-3.75%) were reliable with a negligible bias in estimated volumes. Contrary, the Lambert formula was unreliable due to a high bias (41.6%). For all evaluated methods, the estimation error found to be related to the organ size (T=3.483; p=0.001), mainly when the assessed organ is larger than 50 ml. Also, the shape related estimation error found to be related to the volume estimation formula used.This study has validated the USV for kidney and splenic volume assessments while describing volume-calculating formula employed, organ size and shape as significant contributors for volume estimation accuracy.

Se encontró que la precisión de la estimación del volumen de órganos internos realizada con ultrasonido (US) es multifactorial. El objetivo fue describir y validar la evaluación de volumen mediante ecografía y las fórmulas estándar de estimación de volumen para órganos intraabdominales de diferentes formas utilizando bazos y riñones.Se evaluaron riñones cadavéricos disecados (n = 25) y bazos (n = 29) para obtener medidas lineales y volúmenes autogenerados por ultrasonido (USV). Se utilizaron medidas lineales para calcular los volúmenes manualmente con fórmulas de estimación de volumen elipsoide, prolate y Lambert. Los volúmenes reales (AV) de los órganos se obtuvieron mediante el método de desplazamiento de agua. Se comparó la precisión de la evaluación del volumen de USV y diferentes fórmulas comparando el sesgo, la precisión y el análisis de la gráfica de Bland-Altman. El procedimiento de medición lineal y de volumen mediante US fue confiable con alta concordancia inter e intraobservadores (lineal: α de Chronbach = 0,983 a 0,934; volúmenes: α de Chronbach = 0,989). Las estimaciones de USV fueron precisas con una alta correlación con AV y un bajo sesgo de estimación (-5,9%). Además, las fórmulas prolate (sesgo= -0,75%) y elipsoide (sesgo = -3,75%) fueron confiables con un sesgo insignificante en los volúmenes estimados. Por el contrario, la fórmula de Lambert no fue confiable debido a un alto sesgo (41,6%). Para todos los métodos evaluados, se encontró que el error de estimación estaba relacionado con el tamaño del órgano (T = 3.483; p = 0.001), principalmente cuando el órgano evaluado es mayor de 50 ml. Además, se encontró que el error de estimación de forma está relacionado con la fórmula de estimación de volumen utilizada.Este estudio ha validado el USV para evaluaciones de volumen renal y esplénico al mismo tiempo que describe la fórmula de cálculo de volumen empleada, el tamaño y la forma de los órganos como contribuyentes significativos de la precisión de la estimación de volumen.

Quantum Confined Stark Effect on the Linear and Nonlinear Optical Properties of SiGe/Si Semi Oblate and Prolate Quantum Dots Grown in Si Wetting Layer.

We have studied the parallel and perpendicular electric field effects on the system of SiGe prolate and oblate quantum dots numerically, taking into account the wetting layer and quantum dot size effects. Using the effective-mass approximation in the two bands model, we computationally calculated the extensive variation of dipole matrix (DM) elements, bandgap and non-linear optical properties, including absorption coefficients, refractive index changes, second harmonic generation and third harmonic generation as a function of the electric field, wetting layer size and the size of the quantum dot. The redshift is observed for the non-linear optical properties with the increasing electric field and an increase in wetting layer thickness. The sensitivity to the electric field toward the shape of the quantum dot is also observed. This study is resourceful for all the researchers as it provides a pragmatic model by considering oblate and prolate shaped quantum dots by explaining the optical and electronic properties precisely, as a consequence of the confined stark shift and wetting layer.

Characterization and complete genome sequence of Privateer, a highly prolate Proteus mirabilis podophage.

The Gram-negative bacterium Proteus mirabilis causes a large proportion of catheter-associated urinary tract infections, which are among the world's most common nosocomial infections. Here, we characterize P. mirabilis bacteriophage Privateer, a prolate podophage of the C3 morphotype isolated from Texas wastewater treatment plant activated sludge. Basic characterization assays demonstrated Privateer has a latent period of ~40 min and average burst size around 140. In the 90.7 kb Privateer genome, 43 functions were assigned for the 144 predicted protein-coding genes. Genes encoding DNA replication proteins, DNA modification proteins, four tRNAs, lysis proteins, and structural proteins were identified. Cesium-gradient purified Privateer particles analyzed via LC-MS/MS verified the presence of several predicted structural proteins, including a longer, minor capsid protein apparently produced by translational frameshift. Comparative analysis demonstrated Privateer shares 83% nucleotide similarity with Cronobacter phage vB_CsaP_009, but low nucleotide similarity with other known phages. Predicted structural proteins in Privateer appear to have evolutionary relationships with other prolate podophages, in particular the Kuraviruses.

A bacteriophage infecting Mesorhizobium species has a prolate capsid and shows similarities to a family of Caulobacter crescentus phages.

Mesorhizobium phage vB_MloS_Cp1R7A-A1 was isolated from soil planted with chickpea in Saskatchewan. It is dissimilar in sequence and morphology to previously described rhizobiophages. It is a B3 morphotype virus with a distinct prolate capsid and belongs to the tailed phage family Siphoviridae. Its genome has a GC content of 60.3% and 238 predicted genes. Putative functions were predicted for 57 genes, which include 27 tRNA genes with anticodons corresponding to 18 amino acids. This represents the highest number of tRNA genes reported yet in a rhizobiophage. The gene arrangement shows a partially modular organization. Most of the structural genes are found in one module, whereas tRNA genes are in another. Genes for replication, recombination, and nucleotide metabolism form the third module. The arrangement of the replication module resembles the replication module of Enterobacteria phage T5, raising the possibility that it uses a recombination-based replication mechanism, but there is also a suggestion that a T7-like replication mechanism could be used. Phage termini appear to be long direct repeats of just over 12 kb in length. Phylogenetic analysis revealed that Cp1R7A-A1 is more closely related to PhiCbK-like Caulobacter phages and other B3 morphotype phages than to other rhizobiophages sequenced thus far.

Approximate analytic expressions for the electrophoretic mobility of spheroidal particles.

Approximate analytic expressions are derived for the electrophoretic mobility of spheroidal particles (prolate and oblate) carrying low zeta potential in an electrolyte solution under an applied tangential or transverse electric field. The present approximation method, which is based on the observation that the electrophoretic mobility of a particle is determined mainly by the distortion of the applied electric field by the presence of the particle. The exact expression for the equilibrium electric potential distribution around the particle, which can be expressed as an infinite sum of spheroidal wave functions, is not needed in the present approximation. The electrophoretic mobility values calculated with these approximate expressions for spheroidal particles with constant surface potential or constant surface charge density are in excellent agreement with the exact numerical results of previous reports with the relative errors less than about 4%.

Time-Limited Codewords over Band-Limited Channels: Data Rates and the Dimension of the W-T Space.

We consider a communication system whereby T-seconds time-limited codewords are transmitted over a W-Hz band-limited additive white Gaussian noise channel. In the asymptotic regime as WT→∞, it is known that the maximal achievable rates with such a scheme converge to Shannon's capacity with the presence of 2WT degrees of freedom. In this work we study the degrees of freedom and the achievable information rates for finite values of WT. We use prolate spheroidal wave functions to obtain an information lossless equivalent discrete formulation and then we apply Polyanskiy's results on coding in the finite block-length regime. We derive upper and lower bounds on the achievable rates and the corresponding degrees of freedom and we numerically evaluate them for sample values of 2WT. The bounds are asymptotically tight and numerical computations show the gap between them decreases as 2WT increases. Additionally, the possible decrease from 2WT in the available degrees of freedom is upper-bounded by a logarithmic function of 2WT.