A review and implementation of swarm pattern formation and transformation models

Purpose: The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need for mathematical foundations in swarm systems. Design/methodology/approach: The work is separated out as inspirations, applications, definitions, challenges and classifications of pattern formation in swarm systems based on recent literature. Further, the work proposes a mathematical model for swarm pattern formation and transformation. Findings: A swarm pattern formation model based on mathematical foundations and macroscopic primitives is proposed. A formal definition for swarm pattern transformation and four special cases of transformation are introduced. Two general methods for transforming patterns are investigated and a comparison of the two methods is presented. The validity of the proposed models, and the feasibility of the methods investigated are confirmed on the Traer Physics and Processing environment. Originality/value: This paper helps in understanding the limitations of existing research in pattern formation and the lack of mathematical foundations for swarm systems. The mathematical model and transformation methods introduce two key concepts, namely macroscopic primitives and a mathematical model. The exercise of implementing the proposed models on physics simulator is novel.

Representing the acquisition and use of energy by individuals in agent-based models of animal populations

Summary 1. Agent-based models (ABMs) are widely used to predict how populations respond to changing environments. As the availability of food varies in space and time, individuals should have their own energy budgets, but there is no consensus as to how these should be modelled. Here, we use knowledge of physiological ecology to identify major issues confronting the modeller and to make recommendations about how energy budgets for use in ABMs should be constructed. 2. Our proposal is that modelled animals forage as necessary to supply their energy needs for maintenance, growth and reproduction. If there is sufficient energy intake, an animal allocates the energy obtained in the order: maintenance, growth, reproduction, energy storage, until its energy stores reach an optimal level. If there is a shortfall, the priorities for maintenance and growth/reproduction remain the same until reserves fall to a critical threshold below which all are allocated to maintenance. Rates of ingestion and allocation depend on body mass and temperature. We make suggestions for how each of these processes should be modelled mathematically. 3. Mortality rates vary with body mass and temperature according to known relationships, and these can be used to obtain estimates of background mortality rate. 4. If parameter values cannot be obtained directly, then values may provisionally be obtained by parameter borrowing, pattern-oriented modelling, artificial evolution or from allometric equations. 5. The development of ABMs incorporating individual energy budgets is essential for realistic modelling of populations affected by food availability. Such ABMs are already being used to guide conservation planning of nature reserves and shell fisheries, to assess environmental impacts of building proposals including wind farms and highways and to assess the effects on nontarget organisms of chemicals for the control of agricultural pests. Keywords: bioenergetics; energy budget; individual-based models; population dynamics.

Study of the interaction between cardiolipin bilayers and methylene blue in polymer-based Layer-by-Layer and Langmuir films applied as membrane mimetic systems

An increase of the reports involving mimetic systems has been observed. Briefly, these systems use biological phospholipids to exploit specific interactions between membrane-models and drugs. Here, the Layer-by-Layer (LbL) and Langmuir techniques were used to investigate the interaction between cardiolipin (CLP-negative phospholipid) and a cationic-like drug methylene blue (MB). Supported by a cationic polyelectrolyte (PAH), LbL films containing PAH/(CLP + MB) and PAH/(CLP + MB + AgNP) were grown up to 14 bilayers. The optical microscopy analysis revealed a decrease of the CLP vesicle sizes in the presence of MB as a possible consequence of the MB action onto the mechanical properties of the CLP membrane. From FTIR spectra, changes mainly related to peak position and band intensity and shape were observed in the spectra from PAH/CLP when in the presence of MB. The latter supports that the interactions between the phosphate and amine charged groups from CLP and PAH, respectively, established during the LbL film fabrication, besides the CLP hydrocarbon environment, are influenced by the presence of MB. Using the micro-Raman technique, a chemical mapping was build based on MB spectrum by resonance Raman scattering (RRS) and surface-enhanced resonance Raman scattering (SERRS). The later phenomenon was activated by Ag nanoparticles (AgNPs) trapped within the LbL film allowing collecting spectra for a single bilayer of PAH/(CLP + MB + AgNP). A rough estimation showed a SERRS amplification of 10(3) in comparison to RRS spectra. As a complementary approach, Langmuir films of CLP in the presence of co-spread MB were investigated through surface pressure vs mean molecular area (pi-A) isotherms. The results showed that for concentrations of MB below 100 mol%, the drug is expelled to water subphase for high values of surface pressure (condensed phase). For concentration at 100% and higher, the MB keeps bound to CLP floating monolayer. (C) 2010 Elsevier B.V. All rights reserved.

Exploring community assembly through an individual-based model for trophic interactions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Damage detection in a benchmark structure using AR-ARX models and statistical pattern recognition

Structural health monitoring (SHM) is related to the ability of monitoring the state and deciding the level of damage or deterioration within aerospace, civil and mechanical systems. In this sense, this paper deals with the application of a two-step auto-regressive and auto-regressive with exogenous inputs (AR-ARX) model for linear prediction of damage diagnosis in structural systems. This damage detection algorithm is based on the. monitoring of residual error as damage-sensitive indexes, obtained through vibration response measurements. In complex structures there are. many positions under observation and a large amount of data to be handed, making difficult the visualization of the signals. This paper also investigates data compression by using principal component analysis. In order to establish a threshold value, a fuzzy c-means clustering is taken to quantify the damage-sensitive index in an unsupervised learning mode. Tests are made in a benchmark problem, as proposed by IASC-ASCE with different damage patterns. The diagnosis that was obtained showed high correlation with the actual integrity state of the structure. Copyright © 2007 by ABCM.

Interaction between wave and coastal structure: Validation of two lagrangian numerical models with experimental results marine 2011

Numerical modeling of the interaction among waves and coastal structures is a challenge due to the many nonlinear phenomena involved, such as, wave propagation, wave transformation with water depth, interaction among incident and reflected waves, run-up / run-down and wave overtopping. Numerical models based on Lagrangian formulation, like SPH (Smoothed Particle Hydrodynamics), allow simulating complex free surface flows. The validation of these numerical models is essential, but comparing numerical results with experimental data is not an easy task. In the present paper, two SPH numerical models, SPHysics LNEC and SPH UNESP, are validated comparing the numerical results of waves interacting with a vertical breakwater, with data obtained in physical model tests made in one of the LNEC's flume. To achieve this validation, the experimental set-up is determined to be compatible with the Characteristics of the numerical models. Therefore, the flume dimensions are exactly the same for numerical and physical model and incident wave characteristics are identical, which allows determining the accuracy of the numerical models, particularly regarding two complex phenomena: wave-breaking and impact loads on the breakwater. It is shown that partial renormalization, i.e. renormalization applied only for particles near the structure, seems to be a promising compromise and an original method that allows simultaneously propagating waves, without diffusion, and modeling accurately the pressure field near the structure.

An introductory informatics theoretical framework, based on an integrable lattice model using quantized function algebras, for studying DNA-ionized gas interaction system

Usually we observe that Bio-physical systems or Bio-chemical systems are many a time based on nanoscale phenomenon in different host environments, which involve many particles can often not be solved explicitly. Instead a physicist, biologist or a chemist has to rely either on approximate or numerical methods. For a certain type of systems, called integrable in nature, there exist particular mathematical structures and symmetries which facilitate the exact and explicit description. Most integrable systems, we come across are low-dimensional, for instance, a one-dimensional chain of coupled atoms in DNA molecular system with a particular direction or exist as a vector in the environment. This theoretical research paper aims at bringing one of the pioneering ‘Reaction-Diffusion’ aspects of the DNA-plasma material system based on an integrable lattice model approach utilizing quantized functional algebras, to disseminate the new developments, initiate novel computational and design paradigms.

Specification, execution and verification of interaction protocols: an approach based on computational logic

Interaction protocols establish how different computational entities can interact with each other. The interaction can be finalized to the exchange of data, as in 'communication protocols', or can be oriented to achieve some result, as in 'application protocols'. Moreover, with the increasing complexity of modern distributed systems, protocols are used also to control such a complexity, and to ensure that the system as a whole evolves with certain features. However, the extensive use of protocols has raised some issues, from the language for specifying them to the several verification aspects. Computational Logic provides models, languages and tools that can be effectively adopted to address such issues: its declarative nature can be exploited for a protocol specification language, while its operational counterpart can be used to reason upon such specifications. In this thesis we propose a proof-theoretic framework, called SCIFF, together with its extensions. SCIFF is based on Abductive Logic Programming, and provides a formal specification language with a clear declarative semantics (based on abduction). The operational counterpart is given by a proof procedure, that allows to reason upon the specifications and to test the conformance of given interactions w.r.t. a defined protocol. Moreover, by suitably adapting the SCIFF Framework, we propose solutions for addressing (1) the protocol properties verification (g-SCIFF Framework), and (2) the a-priori conformance verification of peers w.r.t. the given protocol (AlLoWS Framework). We introduce also an agent based architecture, the SCIFF Agent Platform, where the same protocol specification can be used to program and to ease the implementation task of the interacting peers.

Automatic (data-based) learning of expressive indicators for machine failure detection : a proposal

Máster Universitario en Sistemas Inteligentes y Aplicaciones Numéricas en Ingeniería (SIANI)

Development of Clinical Decision Support Systems based on Mathematical Models of Physiological Systems

In the last years of research, I focused my studies on different physiological problems. Together with my supervisors, I developed/improved different mathematical models in order to create valid tools useful for a better understanding of important clinical issues. The aim of all this work is to develop tools for learning and understanding cardiac and cerebrovascular physiology as well as pathology, generating research questions and developing clinical decision support systems useful for intensive care unit patients. I. ICP-model Designed for Medical Education We developed a comprehensive cerebral blood flow and intracranial pressure model to simulate and study the complex interactions in cerebrovascular dynamics caused by multiple simultaneous alterations, including normal and abnormal functional states of auto-regulation of the brain. Individual published equations (derived from prior animal and human studies) were implemented into a comprehensive simulation program. Included in the normal physiological modelling was: intracranial pressure, cerebral blood flow, blood pressure, and carbon dioxide (CO2) partial pressure. We also added external and pathological perturbations, such as head up position and intracranial haemorrhage. The model performed clinically realistically given inputs of published traumatized patients, and cases encountered by clinicians. The pulsatile nature of the output graphics was easy for clinicians to interpret. The manoeuvres simulated include changes of basic physiological inputs (e.g. blood pressure, central venous pressure, CO2 tension, head up position, and respiratory effects on vascular pressures) as well as pathological inputs (e.g. acute intracranial bleeding, and obstruction of cerebrospinal outflow). Based on the results, we believe the model would be useful to teach complex relationships of brain haemodynamics and study clinical research questions such as the optimal head-up position, the effects of intracranial haemorrhage on cerebral haemodynamics, as well as the best CO2 concentration to reach the optimal compromise between intracranial pressure and perfusion. We believe this model would be useful for both beginners and advanced learners. It could be used by practicing clinicians to model individual patients (entering the effects of needed clinical manipulations, and then running the model to test for optimal combinations of therapeutic manoeuvres). II. A Heterogeneous Cerebrovascular Mathematical Model Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral haemodynamics. In this work, the mathematical model of cerebral haemodynamics and intracranial pressure dynamics, described in the point I, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the intracranial pressure-volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular haemodynamics and can not only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions. III. Effect of Cushing Response on Systemic Arterial Pressure. During cerebral hypoxic conditions, the sympathetic system causes an increase in arterial pressure (Cushing response), creating a link between the cerebral and the systemic circulation. This work investigates the complex relationships among cerebrovascular dynamics, intracranial pressure, Cushing response, and short-term systemic regulation, during plateau waves, by means of an original mathematical model. The model incorporates the pulsating heart, the pulmonary circulation and the systemic circulation, with an accurate description of the cerebral circulation and the intracranial pressure dynamics (same model as in the first paragraph). Various regulatory mechanisms are included: cerebral autoregulation, local blood flow control by oxygen (O2) and/or CO2 changes, sympathetic and vagal regulation of cardiovascular parameters by several reflex mechanisms (chemoreceptors, lung-stretch receptors, baroreceptors). The Cushing response has been described assuming a dramatic increase in sympathetic activity to vessels during a fall in brain O2 delivery. With this assumption, the model is able to simulate the cardiovascular effects experimentally observed when intracranial pressure is artificially elevated and maintained at constant level (arterial pressure increase and bradicardia). According to the model, these effects arise from the interaction between the Cushing response and the baroreflex response (secondary to arterial pressure increase). Then, patients with severe head injury have been simulated by reducing intracranial compliance and cerebrospinal fluid reabsorption. With these changes, oscillations with plateau waves developed. In these conditions, model results indicate that the Cushing response may have both positive effects, reducing the duration of the plateau phase via an increase in cerebral perfusion pressure, and negative effects, increasing the intracranial pressure plateau level, with a risk of greater compression of the cerebral vessels. This model may be of value to assist clinicians in finding the balance between clinical benefits of the Cushing response and its shortcomings. IV. Comprehensive Cardiopulmonary Simulation Model for the Analysis of Hypercapnic Respiratory Failure We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions. In conclusion, models are not only capable of summarizing current knowledge, but also identifying missing knowledge. In the former case they can serve as training aids for teaching the operation of complex systems, especially if the model can be used to demonstrate the outcome of experiments. In the latter case they generate experiments to be performed to gather the missing data.

Fiber beam-columns models with flexure-shear interaction for nonlinear analysis of reinforced concrete structures

The aim of this study was to develop a model capable to capture the different contributions which characterize the nonlinear behaviour of reinforced concrete structures. In particular, especially for non slender structures, the contribution to the nonlinear deformation due to bending may be not sufficient to determine the structural response. Two different models characterized by a fibre beam-column element are here proposed. These models can reproduce the flexure-shear interaction in the nonlinear range, with the purpose to improve the analysis in shear-critical structures. The first element discussed is based on flexibility formulation which is associated with the Modified Compression Field Theory as material constitutive law. The other model described in this thesis is based on a three-field variational formulation which is associated with a 3D generalized plastic-damage model as constitutive relationship. The first model proposed in this thesis was developed trying to combine a fibre beamcolumn element based on the flexibility formulation with the MCFT theory as constitutive relationship. The flexibility formulation, in fact, seems to be particularly effective for analysis in the nonlinear field. Just the coupling between the fibre element to model the structure and the shear panel to model the individual fibres allows to describe the nonlinear response associated to flexure and shear, and especially their interaction in the nonlinear field. The model was implemented in an original matlab® computer code, for describing the response of generic structures. The simulations carried out allowed to verify the field of working of the model. Comparisons with available experimental results related to reinforced concrete shears wall were performed in order to validate the model. These results are characterized by the peculiarity of distinguishing the different contributions due to flexure and shear separately. The presented simulations were carried out, in particular, for monotonic loading. The model was tested also through numerical comparisons with other computer programs. Finally it was applied for performing a numerical study on the influence of the nonlinear shear response for non slender reinforced concrete (RC) members. Another approach to the problem has been studied during a period of research at the University of California Berkeley. The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. A generalized plasticity model is implemented for structural steel and a 3D plastic-damage model is used for the simulation of concrete. The transverse normal stress is used to satisfy the transverse equilibrium equations of at each control section, this criterion is also used for the condensation of degrees of freedom from the 3D constitutive material to a beam element. In this thesis is presented the beam formulation and the constitutive relationships, different analysis and comparisons are still carrying out between the two model presented.

Development of control-oriented models of Dual Clutch Transmission systems

A control-oriented model of a Dual Clutch Transmission was developed for real-time Hardware In the Loop (HIL) applications, to support model-based development of the DCT controller. The model is an innovative attempt to reproduce the fast dynamics of the actuation system while maintaining a step size large enough for real-time applications. The model comprehends a detailed physical description of hydraulic circuit, clutches, synchronizers and gears, and simplified vehicle and internal combustion engine sub-models. As the oil circulating in the system has a large bulk modulus, the pressure dynamics are very fast, possibly causing instability in a real-time simulation; the same challenge involves the servo valves dynamics, due to the very small masses of the moving elements. Therefore, the hydraulic circuit model has been modified and simplified without losing physical validity, in order to adapt it to the real-time simulation requirements. The results of offline simulations have been compared to on-board measurements to verify the validity of the developed model, that was then implemented in a HIL system and connected to the TCU (Transmission Control Unit). Several tests have been performed: electrical failure tests on sensors and actuators, hydraulic and mechanical failure tests on hydraulic valves, clutches and synchronizers, and application tests comprehending all the main features of the control performed by the TCU. Being based on physical laws, in every condition the model simulates a plausible reaction of the system. The first intensive use of the HIL application led to the validation of the new safety strategies implemented inside the TCU software. A test automation procedure has been developed to permit the execution of a pattern of tests without the interaction of the user; fully repeatable tests can be performed for non-regression verification, allowing the testing of new software releases in fully automatic mode.

Molecular interaction of the human metalloprotease meprin beta with the amyloid precursor protein, ADAM10, and ADAM17 based on proteomics

Die Zinkendopeptidasen Meprin α und β sind Schlüsselkomponenten in patho(physiologischen) Prozessen wie Entzündung, Kollagenassemblierung und Angiogenese. Nach ihrer Entdeckung in murinen Bürstensaummembranen und humanen Darmepithelien, wurden weitere Expressionsorte identifiziert, z.B. Leukozyten, Krebszellen und die humane Haut. Tiermodelle, Zellkulturen und biochemische Analysen weisen auf Funktionen der Meprine in der Epithelialdifferenzierung, Zellmigration, Matrixmodellierung, Angiogenese, Bindegewebsausbildung und immunologische Prozesse hin. Dennoch sind ihre physiologischen Substrate weitgehend noch unbekannt. Massenspektrometrisch basierte Proteomics-Analysen enthüllten eine einzigartige Spaltspezifität für saure Aminosäurereste in der P1´ Position und identifizierten neue biologische Substratkandidaten. Unter den 269 extrazellulären Proteinen, die in einem Substratscreen identifiziert wurden, stellten sich das amyloid precursor protein (APP) and ADAM10 (a disintegrin and metalloprotease 10) als sehr vielversprechende Kandidaten heraus. Mehrere Schnittstellen innerhalb des APP Proteins, hervorgerufen durch verschiedenen Proteasen, haben unterschiedlichen Auswirkungen zur Folge. Die β-Sekretase BACE (β-site APP cleaving enzyme) prozessiert APP an einer Schnittstelle, welche als initialer Schritt in der Entwicklung der Alzheimer Erkrankung gilt. Toxische Aβ (Amyloid β)-Peptide werden in den extrazellulären Raum freigesetzt und aggregieren dort zu senilen Plaques. Membran verankertes Meprin β hat eine β-Sekretase Aktivität, die in einem Zellkultur-basierten System bestätigt werden konnte. Die proteolytische Effizienz von Meprin β wurde in FRET (Fluorescence Resonance Energy Transfer)-Analysen bestimmt und war um den Faktor 104 höher als die von BACE1. Weiterhin konnte gezeigt werden, dass Meprin β die ersten zwei Aminosäuren prozessiert und somit aminoterminal einen Glutamatrest freisetzt, welcher nachfolgend durch die Glutaminylzyklase in ein Pyroglutamat zykliert werden kann. Trunkierte Aβ-Peptide werden nur in Alzheimer Patienten generiert. Aufgrund einer erhöhten Hydrophobie weisen diese Peptide eine höhere Tendenz zur Aggregation auf und somit eine erhöhte Toxizität. Bis heute wurde keine Protease identifiziert, welche diese Schnittstelle prozessiert. Die Bildung der Meprin vermittelten N-terminalen APP Fragmenten wurde in vitro und in vivo detektiert. Diese N-APP Peptide hatten keine cytotoxischen Auswirkungen auf murine und humane Gehirnzellen, obwohl zuvor N-APP als Ligand für den death receptor (DR) 6 identifiziert wurde, der für axonale Degenerationsprozesse verantwortlich ist. rnIm nicht-amyloidogenen Weg prozessiert ADAM10 APP und entlässt die Ektodomäne von der Zellmembran. Wir konnten das ADAM10 Propeptid als Substrat von Meprin β identifizieren und in FRET Analysen, in vitro und in vivo zeigen, dass die Meprin vermittelte Prozessierung zu einer erhöhten ADAM10 Aktivität führt. Darüber hinaus wurde ADAM10 als Sheddase für Meprin β identifiziert. Shedding konnte durch Phorbol 12-myristate 13-acetate (PMA) oder durch das Ionophor A23187 hervorgerufen werden, sowie durch ADAM10 Inhibitoren blockiert werden. rnDiese Arbeit konnte somit ein komplexes proteolytisches Netwerk innerhalb der Neurophysiologie aufdecken, welches für die Entwicklung der Alzheimer Demenz wichtig sein kann.rn

Shear band evolution in Zr/Hf-based bulk metallic glasses under static and dynamic indentations

Bulk metallic glasses (BMGs) exhibit superior mechanical properties as compared with other conventional materials and have been proposed for numerous engineering and technological applications. Zr/Hf-based BMGs or tungsten reinforced BMG composites are considered as a potential replacement for depleted uranium armor-piercing projectiles because of their ability to form localized shear bands during impact, which has been known to be the dominant plastic deformation mechanism in BMGs. However, in conventional tensile, compressive and bending tests, limited ductility has been observed because of fracture initiation immediately following the shear band formation. To fully investigate shear band characteristics, indentation tests that can confine the deformation in a limited region have been pursued. In this thesis, a detailed investigation of thermal stability and mechanical deformation behavior of Zr/Hf-based BMGs is conducted. First, systematic studies had been implemented to understand the influence of relative compositions of Zr and Hf on thermal stability and mechanical property evolution. Second, shear band evolution under indentations were investigated experimentally and theoretically. Three kinds of indentation studies were conducted on BMGs in the current study. (a) Nano-indentation to determine the mechanical properties as a function of Hf/Zr content. (b) Static Vickers indentation on bonded split specimens to investigate the shear band evolution characteristics beneath the indention. (c) Dynamic Vickers indentation on bonded split specimens to investigate the influence of strain rate. It was found in the present work that gradually replacing Zr by Hf remarkably increases the density and improves the mechanical properties. However, a slight decrease in glass forming ability with increasing Hf content has also been identified through thermodynamic analysis although all the materials in the current study were still found to be amorphous. Many indentation studies have revealed only a few shear bands surrounding the indent on the top surface of the specimen. This small number of shear bands cannot account for the large plastic deformation beneath the indentations. Therefore, a bonded interface technique has been used to observe the slip-steps due to shear band evolution. Vickers indentations were performed along the interface of the bonded split specimen at increasing loads. At small indentation loads, the plastic deformation was primarily accommodated by semi-circular primary shear bands surrounding the indentation. At higher loads, secondary and tertiary shear bands were formed inside this plastic zone. A modified expanding cavity model was then used to predict the plastic zone size characterized by the shear bands and to identify the stress components responsible for the evolution of the various types of shear bands. The applicability of various hardness—yield-strength ( H −σγ ) relationships currently available in the literature for bulk metallic glasses (BMGs) is also investigated. Experimental data generated on ZrHf-based BMGs in the current study and those available elsewhere on other BMG compositions were used to validate the models. A modified expanding-cavity model, employed in earlier work, was extended to propose a new H −σγ relationship. Unlike previous models, the proposed model takes into account not only the indenter geometry and the material properties, but also the pressure sensitivity index of the BMGs. The influence of various model parameters is systematically analyzed. It is shown that there is a good correlation between the model predictions and the experimental data for a wide range of BMG compositions. Under dynamic Vickers indentation, a decrease in indentation hardness at high loading rate was observed compared to static indentation hardness. It was observed that at equivalent loads, dynamic indentations produced more severe deformation features on the loading surface than static indentations. Different from static indentation, two sets of widely spaced semi-circular shear bands with two different curvatures were observed. The observed shear band pattern and the strain rate softening in indentation hardness were rationalized based on the variations in the normal stress on the slip plane, the strain rate of shear and the temperature rise associated with the indentation deformation. Finally, a coupled thermo-mechanical model is proposed that utilizes a momentum diffusion mechanism for the growth and evolution of the final spacing of shear bands. The influence of strain rate, confinement pressure and critical shear displacement on the shear band spacing, temperature rise within the shear band, and the associated variation in flow stress have been captured and analyzed. Consistent with the known pressure sensitive behavior of BMGs, the current model clearly captures the influence of the normal stress in the formation of shear bands. The normal stress not only reduces the time to reach critical shear displacement but also causes a significant temperature rise during the shear band formation. Based on this observation, the variation of shear band spacing in a typical dynamic indentation test has been rationalized. The temperature rise within a shear band can be in excess of 2000K at high strain rate and high confinement pressure conditions. The associated drop in viscosity and flow stress may explain the observed decrease in fracture strength and indentation hardness. The above investigations provide valuable insight into the deformation behavior of BMGs under static and dynamic loading conditions. The shear band patterns observed in the above indentation studies can be helpful to understand and model the deformation features under complex loading scenarios such as the interaction of a penetrator with armor. Future work encompasses (1) extending and modifying the coupled thermo-mechanical model to account for the temperature rise in quasistatic deformation; and (2) expanding this model to account for the microstructural variation-crystallization and free volume migration associated with the deformation.