Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

Semiclassical back reaction in the formation of a straight cosmic string

We derive the back reaction on the gravitational field of a straight cosmic string during its formation due to the gravitational coupling of the string to quantum matter fields. A very simple model of string formation is considered. The gravitational field of the string is computed in the linear approximation. The vacuum expectation value of the stress tensor of a massless scalar quantum field coupled to the string gravitational field is computed to one loop order. Finally, the back-reaction effect is obtained by solving perturbatively the semiclassical Einsteins equations.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

Front propagation in the A+B->2A reaction under subdiffusion

We consider an irreversible autocatalytic conversion reaction A+B->2A under subdiffusion described by continuous-time random walks. The reactants transformations take place independently of their motion and are described by constant rates. The analog of this reaction in the case of normal diffusion is described by the Fisher-Kolmogorov-Petrovskii-Piskunov equation leading to the existence of a nonzero minimal front propagation velocity, which is really attained by the front in its stable motion. We show that for subdiffusion, this minimal propagation velocity is zero, which suggests propagation failure.

The prediction of chemical reactivity from first principles: Collision and reaction dynamics

Aquest treball fa una revisió de mesures experimentals i càlculs teòrics sobre la dinàmica de col·lisions i reaccions moleculars. Els experiments se centren en col·lisions, a energies intermèdies, que involucren sistemes del tipus ió-àtom i iómolècula, per les quals es mesuren seccions eficaces totals, estat a estat, així com aquelles que discerneixen les diferents contribucions del moment angular d'espín. Els resultats obtinguts s'interpreten satisfactòriament en termes d'acoblaments no adiabàtics entre els diferents estats electrònics dels sistemes col·lisionants. Els càlculs teòrics utilitzen la metodologia quasiclàssica, així com metodologies mecanoquàntiques recentment desenvolupades, tant aproximades com exactes. S'han obtingut resultats totalment convergits per sistemes tipus, mentre que s'han analitzat, de manera detallada i extensiva, les característiques dinàmiques de sistemes triatòmic, tetraatòmic i pentaatòmic.

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H2(ν, j) → HD(ν′, j′) + H reaction for J = 0.

Experimental evidence of localized oscillations in the photosensitive chlorine dioxide-iodine-malonic acid reaction

The interaction between Hopf and Turing modes has been the subject of active research in recent years. We present here experimental evidence of the existence of mixed Turing-Hopf modes in a two-dimensional system. Using the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) and external constant background illumination as a control parameter, standing spots oscillating in amplitude and with hexagonal ordering were observed. Numerical simulations in the Lengyel-Epstein model for the CDIMA reaction confirmed the results.

Iowa Sex Offender Treatment and Supervision Task Force Report to the Iowa General Assembly, January 15, 2007

Over the last several years, lawmakers have been responding to several highly publicized child abduction, assault and murder cases. While such cases remain rare in Iowa, the public debates they have generated are having far-reaching effects. Policy makers are responsible for controlling the nature of such effects. Challenges they face stem from the need to avoid primarily politically-motivated responses and the desire to make informed decisions that recognize both the strengths and the limitations of the criminal justice system as a vehicle for promoting safe and healthy families and communities. Consensus was reached by the Task Force at its first meeting that one of its standing goals is to provide nonpartisan guidance to help avoid or fix problematic sex offense policies and practices. Setting this goal was a response to the concern over what can result from elected officials’ efforts to respond to the types of sex offender-related concerns that can easily become emotionally laden and politically charged due to the universally held abhorrence of sex crimes against children. The meetings of the Task Force and the various work groups it has formed have included some spirited and perhaps emotionally charged discussions, despite the above-stated ground rule. However, as is described in the report, the Task Force’s first set of recommendations and plans for further study were approved through consensus. It is hoped that in upcoming legislative deliberations, it will be remembered that the non-legislative members of the Task Force all agreed on the recommendations contained in this report. The topics discussed in this first report from the Task Force are limited to the study issues specifically named in H.F. 619, the Task Force’s enabling legislation. However, other topics of concern were discussed by the Task Force because of their immediacy or because of their possible relationships with one or more of the Task Force’s mandated study issues. For example, it has been reported by some probation/parole officers and others that the 2000 feet rule has had a negative influence on treatment participation and supervision compliance. While such concerns were noted, the Task Force did not take it upon itself to investigate them at this time and thus broaden the agenda it was given by the General Assembly last session. As a result, the recently reinstated 2000 feet rule, the new cohabitation/child endangerment law and other issues of interest to Task Force members but not within the scope of their charge are not discussed in the body of this report. An issue of perhaps the greatest interest to most Task Force members that was not a part of their charge was a belief in the benefit of viewing Iowa’s efforts to protect children from sex crimes with as comprehensive a platform as possible. It has been suggested that much more can be done to prevent child-victim sex crimes than would be accomplished by only concentrating on what to do with offenders after a crime has occurred. To prevent child victimization, H.F. 619 policy provisions rely largely on incapacitation and future deterrent effects of increased penalties, more restrictive supervision practices and greater public awareness of the risk presented by a segment of Iowa’s known sex offenders. For some offenders, these policies will no doubt prevent future sex crimes against children, and the Task Force has begun long-term studies to look for the desired results and for ways to improve such results through better supervision tools and more effective offender treatment. Unfortunately, much of the effects from the new policies may primarily influence persons who have already committed sex offenses against minors and who have already been caught doing so. Task Force members discussed the need for a range of preventive efforts and a need to think about sex crimes against children from other than just a “reaction- to-the-offender” perspective. While this topic is not addressed in the report that follows, it was suggested that some of the Task Force’s discussions could be briefly shared through these opening comments. Along with incapacitation and deterrence, comprehensive approaches to the prevention of child-victim sex crimes would also involve making sure parents have the tools they need to detect signs of adults with sex behavior problems, to help teach their children about warning signs and to find the support they need for healthy parenting. School, faithbased and other community organizations might benefit from stronger supports and better tools they can use to more effectively promote positive youth development and the learning of respect for others, respect for boundaries and healthy relationships. All of us who have children, or who live in communities where there are children, need to understand the limitations of our justice system and the importance of our own ability to play a role in preventing sexual abuse and protecting children from sex offenders, which are often the child’s own family members. Over 1,000 incidences of child sexual abuse are confirmed or founded each year in Iowa, and most such acts take place in the child’s home or the residence of the caretaker of the child. Efforts to prevent child sexual abuse and to provide for early interventions with children and families at risk could be strategically examined and strengthened. The Sex Offender Treatment and Supervision Task Force was established to provide assistance to the General Assembly. It will respond to legislative direction for adjusting its future plans as laid out in this report. Its plans could be adjusted to broaden or narrow its scope or to assign different priority levels of effort to its current areas of study. Also, further Task Force considerations of the recommendations it has already submitted could be called for. In the meantime, it is hoped that the information and recommendations submitted through this report prove helpful.

Iowa Sex Offender Treatment and Supervision Task Force Report to the Iowa General Assembly, January 15, 2008

Over the last several years, lawmakers have been responding to several highly publicized child abduction, assault and murder cases. While such cases remain rare in Iowa, the public debates they have generated are having far-reaching effects. Policy makers are responsible for controlling the nature of such effects. Challenges they face stem from the need to avoid primarily politically-motivated responses and the desire to make informed decisions that recognize both the strengths and the limitations of the criminal justice system as a vehicle for promoting safe and healthy families and communities. Consensus was reached by the Task Force at its first meeting that one of its standing goals is to provide nonpartisan guidance to help avoid or fix problematic sex offense policies and practices. Setting this goal was a response to the concern over what can result from elected officials’ efforts to respond to the types of sex offender-related concerns that can easily become emotionally laden and politically charged due to the universally held abhorrence of sex crimes against children. The meetings of the Task Force and the various work groups it has formed have included some spirited and perhaps emotionally charged discussions, despite the above-stated ground rule. However, as is described in the report, the Task Force’s first set of recommendations and plans for further study were approved through consensus. It is hoped that in upcoming legislative deliberations, it will be remembered that the non-legislative members of the Task Force all agreed on the recommendations contained in this report. The topics discussed in this first report from the Task Force are limited to the study issues specifically named in H.F. 619, the Task Force’s enabling legislation. However, other topics of concern were discussed by the Task Force because of their immediacy or because of their possible relationships with one or more of the Task Force’s mandated study issues. For example, it has been reported by some probation/parole officers and others that the 2000 feet rule has had a negative influence on treatment participation and supervision compliance. While such concerns were noted, the Task Force did not take it upon itself to investigate them at this time and thus broaden the agenda it was given by the General Assembly last session. As a result, the recently reinstated 2000 feet rule, the new cohabitation/child endangerment law and other issues of interest to Task Force members but not within the scope of their charge are not discussed in the body of this report. An issue of perhaps the greatest interest to most Task Force members that was not a part of their charge was a belief in the benefit of viewing Iowa’s efforts to protect children from sex crimes with as comprehensive a platform as possible. It has been suggested that much more can be done to prevent child-victim sex crimes than would be accomplished by only concentrating on what to do with offenders after a crime has occurred. To prevent child victimization, H.F. 619 policy provisions rely largely on incapacitation and future deterrent effects of increased penalties, more restrictive supervision practices and greater public awareness of the risk presented by a segment of Iowa’s known sex offenders. For some offenders, these policies will no doubt prevent future sex crimes against children, and the Task Force has begun long-term studies to look for the desired results and for ways to improve such results through better supervision tools and more effective offender treatment. Unfortunately, much of the effects from the new policies may primarily influence persons who have already committed sex offenses against minors and who have already been caught doing so. Task Force members discussed the need for a range of preventive efforts and a need to think about sex crimes against children from other than just a “reaction- to-the-offender” perspective. While this topic is not addressed in the report that follows, it was suggested that some of the Task Force’s discussions could be briefly shared through these opening comments. Along with incapacitation and deterrence, comprehensive approaches to the prevention of child-victim sex crimes would also involve making sure parents have the tools they need to detect signs of adults with sex behavior problems, to help teach their children about warning signs and to find the support they need for healthy parenting. School, faithbased and other community organizations might benefit from stronger supports and better tools they can use to more effectively promote positive youth development and the learning of respect for others, respect for boundaries and healthy relationships. All of us who have children, or who live in communities where there are children, need to understand the limitations of our justice system and the importance of our own ability to play a role in preventing sexual abuse and protecting children from sex offenders, which are often the child’s own family members. Over 1,000 incidences of child sexual abuse are confirmed or founded each year in Iowa, and most such acts take place in the child’s home or the residence of the caretaker of the child. Efforts to prevent child sexual abuse and to provide for early interventions with children and families at risk could be strategically examined and strengthened. The Sex Offender Treatment and Supervision Task Force was established to provide assistance to the General Assembly. It will respond to legislative direction for adjusting its future plans as laid out in this report. Its plans could be adjusted to broaden or narrow its scope or to assign different priority levels of effort to its current areas of study. Also, further Task Force considerations of the recommendations it has already submitted could be called for. In the meantime, it is hoped that the information and recommendations submitted through this report prove helpful.

Iowa Sex Offender Research Council Report to the Iowa General Assembly January 22, 2009

Over the last several years, lawmakers have been responding to several highly publicized child abduction, assault and murder cases. While such cases remain rare in Iowa, the public debates they have generated are having far-reaching effects. Policy makers are responsible for controlling the nature of such effects. Challenges they face stem from the need to avoid primarily politically-motivated responses and the desire to make informed decisions that recognize both the strengths and the limitations of the criminal justice system as a vehicle for promoting safe and healthy families and communities. Consensus was reached by the Task Force at its first meeting that one of its standing goals is to provide nonpartisan guidance to help avoid or fix problematic sex offense policies and practices. Setting this goal was a response to the concern over what can result from elected officials’ efforts to respond to the types of sex offender-related concerns that can easily become emotionally laden and politically charged due to the universally held abhorrence of sex crimes against children. The meetings of the Task Force and the various work groups it has formed have included some spirited and perhaps emotionally charged discussions, despite the above-stated ground rule. However, as is described in the report, the Task Force’s first set of recommendations and plans for further study were approved through consensus. It is hoped that in upcoming legislative deliberations, it will be remembered that the non-legislative members of the Task Force all agreed on the recommendations contained in this report. The topics discussed in this first report from the Task Force are limited to the study issues specifically named in H.F. 619, the Task Force’s enabling legislation. However, other topics of concern were discussed by the Task Force because of their immediacy or because of their possible relationships with one or more of the Task Force’s mandated study issues. For example, it has been reported by some probation/parole officers and others that the 2000 feet rule has had a negative influence on treatment participation and supervision compliance. While such concerns were noted, the Task Force did not take it upon itself to investigate them at this time and thus broaden the agenda it was given by the General Assembly last session. As a result, the recently reinstated 2000 feet rule, the new cohabitation/child endangerment law and other issues of interest to Task Force members but not within the scope of their charge are not discussed in the body of this report. An issue of perhaps the greatest interest to most Task Force members that was not a part of their charge was a belief in the benefit of viewing Iowa’s efforts to protect children from sex crimes with as comprehensive a platform as possible. It has been suggested that much more can be done to prevent child-victim sex crimes than would be accomplished by only concentrating on what to do with offenders after a crime has occurred. To prevent child victimization, H.F. 619 policy provisions rely largely on incapacitation and future deterrent effects of increased penalties, more restrictive supervision practices and greater public awareness of the risk presented by a segment of Iowa’s known sex offenders. For some offenders, these policies will no doubt prevent future sex crimes against children, and the Task Force has begun long-term studies to look for the desired results and for ways to improve such results through better supervision tools and more effective offender treatment. Unfortunately, much of the effects from the new policies may primarily influence persons who have already committed sex offenses against minors and who have already been caught doing so. Task Force members discussed the need for a range of preventive efforts and a need to think about sex crimes against children from other than just a “reaction- to-the-offender” perspective. While this topic is not addressed in the report that follows, it was suggested that some of the Task Force’s discussions could be briefly shared through these opening comments. Along with incapacitation and deterrence, comprehensive approaches to the prevention of child-victim sex crimes would also involve making sure parents have the tools they need to detect signs of adults with sex behavior problems, to help teach their children about warning signs and to find the support they need for healthy parenting. School, faithbased and other community organizations might benefit from stronger supports and better tools they can use to more effectively promote positive youth development and the learning of respect for others, respect for boundaries and healthy relationships. All of us who have children, or who live in communities where there are children, need to understand the limitations of our justice system and the importance of our own ability to play a role in preventing sexual abuse and protecting children from sex offenders, which are often the child’s own family members. Over 1,000 incidences of child sexual abuse are confirmed or founded each year in Iowa, and most such acts take place in the child’s home or the residence of the caretaker of the child. Efforts to prevent child sexual abuse and to provide for early interventions with children and families at risk could be strategically examined and strengthened. The Sex Offender Treatment and Supervision Task Force was established to provide assistance to the General Assembly. It will respond to legislative direction for adjusting its future plans as laid out in this report. Its plans could be adjusted to broaden or narrow its scope or to assign different priority levels of effort to its current areas of study. Also, further Task Force considerations of the recommendations it has already submitted could be called for. In the meantime, it is hoped that the information and recommendations submitted through this report prove helpful.

Iowa Sex Offender Research Council Report to the Iowa General Assembly, January 15, 2010

Over the last several years, lawmakers have been responding to several highly publicized child abduction, assault and murder cases. While such cases remain rare in Iowa, the public debates they have generated are having far-reaching effects. Policy makers are responsible for controlling the nature of such effects. Challenges they face stem from the need to avoid primarily politically-motivated responses and the desire to make informed decisions that recognize both the strengths and the limitations of the criminal justice system as a vehicle for promoting safe and healthy families and communities. Consensus was reached by the Task Force at its first meeting that one of its standing goals is to provide nonpartisan guidance to help avoid or fix problematic sex offense policies and practices. Setting this goal was a response to the concern over what can result from elected officials’ efforts to respond to the types of sex offender-related concerns that can easily become emotionally laden and politically charged due to the universally held abhorrence of sex crimes against children. The meetings of the Task Force and the various work groups it has formed have included some spirited and perhaps emotionally charged discussions, despite the above-stated ground rule. However, as is described in the report, the Task Force’s first set of recommendations and plans for further study were approved through consensus. It is hoped that in upcoming legislative deliberations, it will be remembered that the non-legislative members of the Task Force all agreed on the recommendations contained in this report. The topics discussed in this first report from the Task Force are limited to the study issues specifically named in H.F. 619, the Task Force’s enabling legislation. However, other topics of concern were discussed by the Task Force because of their immediacy or because of their possible relationships with one or more of the Task Force’s mandated study issues. For example, it has been reported by some probation/parole officers and others that the 2000 feet rule has had a negative influence on treatment participation and supervision compliance. While such concerns were noted, the Task Force did not take it upon itself to investigate them at this time and thus broaden the agenda it was given by the General Assembly last session. As a result, the recently reinstated 2000 feet rule, the new cohabitation/child endangerment law and other issues of interest to Task Force members but not within the scope of their charge are not discussed in the body of this report. An issue of perhaps the greatest interest to most Task Force members that was not a part of their charge was a belief in the benefit of viewing Iowa’s efforts to protect children from sex crimes with as comprehensive a platform as possible. It has been suggested that much more can be done to prevent child-victim sex crimes than would be accomplished by only concentrating on what to do with offenders after a crime has occurred. To prevent child victimization, H.F. 619 policy provisions rely largely on incapacitation and future deterrent effects of increased penalties, more restrictive supervision practices and greater public awareness of the risk presented by a segment of Iowa’s known sex offenders. For some offenders, these policies will no doubt prevent future sex crimes against children, and the Task Force has begun long-term studies to look for the desired results and for ways to improve such results through better supervision tools and more effective offender treatment. Unfortunately, much of the effects from the new policies may primarily influence persons who have already committed sex offenses against minors and who have already been caught doing so. Task Force members discussed the need for a range of preventive efforts and a need to think about sex crimes against children from other than just a “reaction- to-the-offender” perspective. While this topic is not addressed in the report that follows, it was suggested that some of the Task Force’s discussions could be briefly shared through these opening comments. Along with incapacitation and deterrence, comprehensive approaches to the prevention of child-victim sex crimes would also involve making sure parents have the tools they need to detect signs of adults with sex behavior problems, to help teach their children about warning signs and to find the support they need for healthy parenting. School, faithbased and other community organizations might benefit from stronger supports and better tools they can use to more effectively promote positive youth development and the learning of respect for others, respect for boundaries and healthy relationships. All of us who have children, or who live in communities where there are children, need to understand the limitations of our justice system and the importance of our own ability to play a role in preventing sexual abuse and protecting children from sex offenders, which are often the child’s own family members. Over 1,000 incidences of child sexual abuse are confirmed or founded each year in Iowa, and most such acts take place in the child’s home or the residence of the caretaker of the child. Efforts to prevent child sexual abuse and to provide for early interventions with children and families at risk could be strategically examined and strengthened. The Sex Offender Treatment and Supervision Task Force was established to provide assistance to the General Assembly. It will respond to legislative direction for adjusting its future plans as laid out in this report. Its plans could be adjusted to broaden or narrow its scope or to assign different priority levels of effort to its current areas of study. Also, further Task Force considerations of the recommendations it has already submitted could be called for. In the meantime, it is hoped that the information and recommendations submitted through this report prove helpful.